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Shock-cell structures and corresponding sound pressure levels emitted from closely spaced supersonic jet arrays
Applied Acoustics 74 (2013) 1519–1526
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Shock-cell structures and corresponding sound pressure levels emitted from closely spaced supersonic jet arrays Ian S. Coltrin a, Jonathan D. Blotter a,⇑, R. Daniel Maynes a, Kent L. Gee b a b
Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, United States Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, United States
a r t i c l e
i n f o
Article history: Received 12 December 2012 Received in revised form 7 June 2013 Accepted 24 June 2013 Available online 20 July 2013 Keywords: Supersonic jet arrays Acoustic emissions Jet noise
a b s t r a c t Shockwave structures and overall sound pressure levels from 8 8 arrays of axisymmetric supersonic jets were experimentally characterized for 14 different arrays. The results were also compared to behavior for single jets of similar dimensions. The jet diameters ranged from 3.2 to 6.4 mm and the jet spacing to diameter ratio ranged from 1.44 to 3. The arrays were tested at nominal net pressure ratios ranging from 2 to 24. It was found that above a certain net pressure ratio level, the array of jets coalesced into an interacting lattice of oblique shock interactions. These shock structures consisted of oscillatory shocks at lower pressure ratios and then developed into stable shock structures as the pressure ratio increased. The formation of the interacting shock lattices is strongly correlated with the measured sound pressure levels. Initially the arrays emitted low sound pressure levels, similar to that of a single jet within the array. As the shock structure transitioned from weak to strong the sound pressure levels transitioned to a level similar to that of a single nozzle with an exit area equivalent of the entire array. Shadow graph images of the flow in the arrays are used to correlate to the sound pressure levels measured. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Acoustic emissions from supersonic jet arrays represent an area of significant research need. Practical applications not only exist in the area of aero-acoustics, where high pressure sound waves from engine exhausts can induce structural fatigue as well as significant human discomfort, they also exist in the energy industry, among others which involve high pressure let down processes. In these types of industries high pressure acoustical loadings have caused severe fatigue in piping networks, and other mechanical systems, sometimes causing them to fail within hours [1]. Thus, this paper focuses on better understanding the relationships between parallel supersonic jet flows which create severe acoustic emissions. Theoretical and experimental advances in jet flow noise were performed during the 1980s and 1990s. A comprehensive presentation of these advances is provided by Hubbard [2]. Tam [3,4] and others continued during the 1990s with significant contributions. During the early 2000s until present, significant research has been performed in developing microphone array systems to characterize the noise from single jets [5–9]. Beam forming measurement methods have also been investigated [10]. A significant amount of work has been done in relation to twin supersonic jets. Raman et al. [11] gives a summary of this work. Although some ⇑ Corresponding author. Tel.: +1 801 422 7820; fax: +1 801 422 0516. E-mail address: [email protected] (J.D. Blotter). 0003-682X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2013.06.010
work has been done on linear supersonic jet arrays [12,13], compared to single or twin supersonic jets very little research on multiple jet arrays has been done. Therefore, the focus of this paper is to investigate the shock-cell structure and corresponding sound pressure levels in multiple jet arrays. From the point of view of industry, high acoustical loadings have been examined from the aspect of sound transmission and noise generation in the surroundings of piping systems. Work that combined structural fatigue and the acoustic loading within a pipe was done by Carucci and Mueller [1]; and which was later refined by Eisinger [14]. As a method to reduce the acoustic emissions, Carucci and Mueller suggested dividing a single jet into multiple smaller jets. Their suggestion was to implement Venturi slots into valves which would create several smaller parallel plane jets out of a single, larger jet. There are three main mechanisms which describe the total acoustic emissions from supersonic jets. Tam [15] reported that the three supersonic jets mechanisms consisted of turbulent mixing noise, broadband shock associated noise, and narrowband shock associated noise, or screech. Although these mechanisms all contribute to the same acoustic loads they are generated in different ways. The source of noise from turbulent mixing is generated from the shear layer between the jet and the quiescent medium. The instability wave created from this shear layer is much like a supersonic fluid moving past a wavy wall. The unstable shear layer causes
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Mach waves to build up and radiate downstream and away from the jet. The pressure decrease across the continually radiating Mach waves can be viewed as an acoustic pressure wave. Broadband shock-cell noise generated by the interaction of the turbulent eddies of the jet with the structure of the shock cell [16]. Tam [15] states that this component of noise is a result of the constructive scattering of the turbulence by the stationary quasi-periodic shock cells in the jet plume. The shock cells mentioned here are formed as a result of the expanding fluid of a jet which creates a shock against the quiescent medium. Due to the high pressure rise of the shock, the jet flow is reflected back into the jet where it then expands again as it moves downstream. These processes can be repeated several times for a supersonic jet. As viewed from the jet flow perspective these shock cells are a superposition of the waveguide modes at different wavelength and are a disturbance which is one way to create turbulent energy within the flow [15]. This turbulent energy is then translated into acoustic energy which radiates outward and downstream. The first to investigate this noise source were Yu [17] and Harper-Bourne and Fisher [18]. Several others followed up on this research including Seiner and Norum [19], and Tam [15]. The last mechanism is narrowband shock associated noise, or screech. Screech tones were first investigated by Powell [20] when discrete tones produced from under expanded supersonic jets were observed. In Raman’s [21] review on screech he described screech generation from a feedback loop created from a distinct formation of shocks. These distinct shocks may have a vortical structure, either toroidal or helical, which are convected downstream in the near field of the jet. The vortical nature of the shocks causes the jet flow to become unstable and wavy. The unstable flow would in turn cause the shock cells of the jet to interact with the vortical shock waves which then would generate a discrete acoustic tone. Dual jet streams and other multiple jet flow techniques have been used to restrict these mechanisms, particularly screech [21– 23]. As mentioned, the feedback loop which generates screech is dependent upon the existence of vortical shock formations. Such shock formations can be manipulated with the existence of several jets. As reported by Raman [21] in the case of rectangular jets the effects of screech can be minimized with the addition of a second, parallel jet stream. Here the vortical shock formation of the second jet reduces the effects of the first due to a phase mismatch of the two vortical shock formations. An extension into several axisymmetric jets was performed by Umeda and Ishii [22,23]. Here they investigated the oscillation modes of two and four axisymmetric jet arrays, as well as a single nozzle jet. Since phase mismatching does not work in the same fashion with axisymmetric jets as it does with rectangular jets, they focused their research on the oscillation modes and screech frequencies produced from multiple jets. In this present investigation, instead of concentrating on the narrowband shock associated noise which has been thoroughly investigated, this paper concentrates on the broadband shock associated noise and turbulent mixing noise that radiates from a larger jet array. This paper presents the acoustic emission and shock structure characteristics of several different arrays of parallel axisymmetric supersonic jets. The results include a shadowgraph investigation of the formation of shock cells from single jets and interacting shock cells from multiple jets as a function of the net pressure ratio (NPR). Also, the resulting overall sound pressure levels the arrays emit as a function of the NPR are provided.
axisymmetric jets. A schematic view of an array is provided in Fig. 1. The nozzle diameters investigated ranged from 3.2 mm (1/ 8 in.) to 6.4 mm (1/4 in.). The center-to-center spacing over the nozzle diameter (S/d) ratios investigated ranged from 1.44 to 3. The nozzles were machined in a flat surface which was then fixed onto the exit of a large pressure let down facility. The nozzles are straight cylinders and the nozzle entrances and exits were sharp but with all burrs removed. The NPR values investigated ranged between 2 and 24. This ratio is defined as the static pressure of the flow, acquired upstream of the jet arrays, over the pressure of the quiescent medium, in this case the atmosphere. Static pressure measurements were acquired with an Omega PX309–500G5 V pressure transducer and differential pressure measurements were acquired with a pitot tube and an Omega PX409–015WU5 V. Temperature measurements were acquired with a type K thermocouple. Table 1 shows the full range of nominal NPR values investigated. Measurements of single hole plates were also acquired for comparison and are listed in Table 2. The 3.2 mm and 6.4 mm diameter single jets from Table 2 represent a single nozzle with the same diameter as found in the 3.2 mm and 6.4 mm arrays from Table 1. The 25.4 mm (1 in.) and 50.8 mm (2 in.) diameter single jets represent the total exit area of 3.2 mm and 6.4 mm diameter arrays from Table 1, respectively. In summary, 14, 8 8 arrays and 4 single jets were investigated for a total of eighteen plates. For each plate, measurements were acquired at approximately 10 NPR values. The facility used to produce the range of NPR values was the high pressure blowdown facility owned by Brigham Young University’s Mechanical Engineering Department. This facility has a maximum capacity of 11.0 MPa and a total volume of 24.1 m3. Flow was released through a control valve which controls the air flow passing through the array. Just downstream of the control valve is 15.2 cm (6 in.) schedule 80 piping that expands to 20.3 cm (8 in.) schedule 80 piping. The plates are mounted at the exit of the 20.3 cm pipe section where shadowgraph images and acoustic measurements were acquired. The acoustic emissions were measured with a 6.4 mm (1/4 in.) GRAS 40BE free field microphone. The frequency range for this microphone is 10 Hz to 100 kHz and has a dynamic range of 40– 170 dB; consistent with the range necessary to measure supersonic jet noise. The microphone was placed on a 1 m radius, 30° off the centerline axis of the flow, as seen in Fig. 2. This is consistent with the research of Yu [17], and Norum and Seiner [19]. Past research has confirmed that at 30° offset from the centerline axis of the flow
2. Experiment The goal of this research is to investigate and characterize the flow regime with the acoustic field from 8 8 arrays of supersonic
Fig. 1. Schematic view of a typical jet array.
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1.44 2 2.5 3
Nozzle diameters (mm) 3.2 (1/8 in.)
3.7 (18/125 in.)
4.0 (5/32 in.)
6.4 (1/4 in.)
2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,18,20,24
2,3,4,6,8,10,12,15,20,24 None 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24 None 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
Table 2 Nominal net pressure ratios investigated for single jets. Nozzle diameters (mm)
3.2 (1/8 in.)
6.4 (1/4 in.)
25.4 (1 in.)
50.8 (2 in.)
Net Pressure Ratios
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
Fig. 2. Microphone experimental setup.
is the highest acoustic pressure output from a single axisymmetric supersonic jet. Thus, at this position the acoustic emissions from the main noise mechanism being acquired will be turbulent mixing noise [15,17]. A single microphone was used instead of an array as this point captures the turbulent mixing noise and is typically where numerical models calculate results [20]. Furthermore, it is desired to develop correlations between the flow field and the acoustical field with a single acoustical measurement. Shadowgraph was chosen as the technique to visualize shock cell formations. The images presented in this paper view the arrays from the side such that eight shock cell structures are evident with the flow from left to right. Shadowgraph images for all the test configurations given in Table 1 were acquired. The trends observed in all the cases were similar, therefore only the shadowgraph images for the 4.0 mm (5/32 in.) diameter jet arrays will be shown in this paper. 3. Shock formations Figs. 3–5 display shadowgraph images for 4.0 mm diameter jet arrays with S/d ratios of 1.44, 2.5, and 3, respectively. The jets display three stages of shock formations. These shock formations consist of standard shock cells as well as shock lattices which form when the shock cells expand large enough to interact with their neighbors. The shock lattices can be observed in Figs. 3b–f, 4c–d, and 5d.
In order to best explain the stages of shock formation, Fig. 3 will be used as an example. Fig. 3a displays standard supersonic jet shock formations. Here, the jets are forming individual shock cells which do not interact with neighboring jets. As the NPR is increased the sizes of the shock cells expand, however the shock cells do not interact with neighboring shock cells below an NPR of approximately 6. As the NPR is increased further the shock cells of the individual jets expand enough to interact with each other. This interaction is defined as shock interaction, where several jets are involved in creating a single shock. When this event occurs in several places it creates a lattice of shockwaves as observed in Fig. 3b–f. The shock lattices go through two stages of formation; oscillatory and stable. The characteristic of oscillatory shock formation is the unstable nature of the flow; this can be seen in Fig. 3b and c. This unstable nature involves the transient movement of shocks within the shock lattice as well as a flapping motion of the jet just outside of the lattice. The oscillatory shock lattice also randomly generates screech tones. This is also confirmed by examining the acoustic pressure as the NPR is increased in the frequency domain. Fig. 6 illustrates the sound pressure levels in the frequency domain as the NPR is increased. The discrete tone in the spectra can be observed at an NPR of 8.1 where the highest amplitude sound pressure level can be observed. The high amplitude spike represents a screech tone which can be correlated to Fig. 3c. Other spectra containing screech tones can also be correlated to weak shock
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Fig. 3. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 1.44 and at NPR values ranging from 3.0 to 24.2.
Fig. 4. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 2.5 and at NPR values ranging from 5.5 to 23.5.
lattices produced from jet arrays. Though screech tones only randomly occur during an oscillatory shock formation the reason the screech tones are being generated are yet unknown.
Stable shock formations are those occurring in Fig. 3d–f. They are characterized by their symmetrical formation of oblique shocks about the jet centerline and flow conditions that are
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Fig. 5. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 3 and at NPR values ranging from 6.3 to 23.2.
non-oscillatory. Fig. 3d illustrates that the lattice structure is much longer than those occurring at lower NPR values. As the NPR is increased further, the outer oblique shocks shown in Fig. 3d are pushed outward, resulting in the pyramidal shock lattice evident in Fig. 3e and f. It should be noted that once the shock lattice forms these pyramidal type structures, there is little change in the structure with increasing NPR. Comparison of the shadowgraph images from Figs. 3–5 reveal that when the jet spacing is increased the NPR level where interaction between jets occurs also increases. In Fig. 3 (S/d = 1.44) the initial shock interaction occurs at an NPR of approximately 6. In Fig. 4 (S/d = 2.5) shock interaction first occurs at an NPR of approximately 13–14, and in Fig. 5 (S/d = 3) shock interaction first occurs at an NPR of approximately 20. The images of Figs. 4 and 5 reveal that weak lattice formations occur at NPR values of ranging approximately from 20 to 24 for S/d = 2.5, and at an NPR of approximately 24 for S/d = 3.
and translated onto a logarithmic scale as defined by Eq. (1). Here it is used as a measure of the overall noise emitted from the arrays. The OASPL for the single jet scenarios will first be presented and discussed; then the OASPL for the jet arrays will be presented.
OASPL ¼ 20 log
rmsðPacoustic Þ Pref
ð1Þ
The overall sound pressure level (OASPL) is the root mean square of the acoustic signal which is detected by the microphone
Fig. 7 presents the OASPL as a function of the NPR for four single jets with diameters of 3.2, 6.4, 25.4, and 50.8 mm. As shown, between NPR values of approximately 2–5 there is a sharp rise in the OASPL for all single jet diameters. After the initial rise, the slopes of the OASPL vs. NPR data decrease and exhibit only modest increase as the NPR increases. The data also show that the OASPL increases with nozzle diameter. Although the scope of this research investigates significantly higher NPR values, the overall behavior of the OASPL for low NPR values seen here for single jets is similar to the results presented by Powell et al. [24] and Umeda, and Ishii [21]. Measurements for the OASPL of the 8 8 jet arrays are shown in Figs. 8–11 for S/d = 1.44, 2, 2.5, and 3 respectively. Note that
Fig. 6. Frequency spectra for a 4.0 mm diameter jet array and S/d ratio of 1.44.
Fig. 7. Overall sound pressure levels as a function of the NPR for single jets of diameters 3.2 mm, 6.4 mm, 25.4 mm, and 50.8 mm.
4. Overall sound pressure levels
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Figs. 8–10 are divided into three regions labeled A, B, and C. Fig. 11 is also divided, but only into two regions instead of three, labeled A and B. These regions will be used to identify the noise characteristics of the jet arrays as well as correlate the visualizations of shock formations with the measured OASPL. The OASPL data in region A show characteristics similar to a single jet. In this region the data exhibit a sharp initial rise followed by a general leveling off in the OASPL. This behavior is best illustrated in Figs. 8–11. The data from Figs. 9–11 reveal that region A extends over a smaller range of NPR values as the S/d ratio is reduced. Thus, for S/d = 1.44 (Fig. 8), the OASPL data never level off because region A is so short that region B occurs right after the steep initial rise in the OASPL. At NPR values above region A, the OASPL for the jet arrays are no longer similar to the single jet noise characteristics. Rather the data begin to display characteristics unique to that of interacting jet arrays. Fig. 10 will be used as an example in order to better explain these unique characteristics. Fig. 10 presents the OASPL for a 4.0 mm diameter jet array with S/d = 2.5. The data in region B in Fig. 10 exhibit an upward trend in the OASPL with increasing NPR. This occurs until the OASPL for the jet arrays level off at a higher OASPL level (region C) as compared to region A. In summary, the OASPL in region A is similar to that of a single jet of the same diameter as one of the array jets. Also, region C can be viewed as a region where the radiated noise has leveled off to much higher nominal levels as compared to region A. Region B can be viewed as the transition region between these two regimes. Comparison of region B in Figs. 8–11 shows that the transition regime shifts to higher NPR values as S/d increases. The larger the S/d ratio, the higher the NPR where region B begins. The total NPR range over which region B extends also increases as S/d increases. The variation in the OASPL with varying jet diameter also varies with the S/d. As observed in Fig. 11 (S/d = 3), the OASPL data for the four jet diameters (3.2–6.4 mm) show marked variation. Conversely, when the nozzles are spaced closer together, as seen in Fig. 8 where the S/d = 1.44, the OASPL data for each of the four nozzle diameters are clustered much tighter. In general, the data of Figs. 8–11 reveal that for increasing S/d the OASPL values for the four different nozzle sizes show greater variation. For all S/d, the largest OASPL values correspond to the 6.4 mm diameter jet arrays and the lowest OASPL values correspond to the 3.2 mm diameter arrays. Figs. 12 and 13 present the OASPL data for the 3.2 and 6.4 mm jet arrays with corresponding single jet data. Fig. 12 displays the OASPL for the 3.2 mm diameter jet arrays, a 3.2 mm diameter single jet, and a 25.4 mm diameter single jet. Recall that the 25.4 mm
Fig. 9. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 2.
Fig. 10. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 2.5.
Fig. 11. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 3.
Fig. 8. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 1.44.
diameter single jet represents a jet with an equivalent exit area to the entire 3.2 mm diameter jet array. Likewise, Fig. 13 presents the OASPL for 6.4 mm diameter jet arrays, a 6.4 mm diameter single jet, and a 50.8 mm diameter single jet. Again, the 50.8 mm jet represents the same flow area as the 6.4 mm diameter jet array.
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Fig. 12. Overall sound pressure levels as a function of the NPR for 3.2 mm diameter jet arrays, a 3.2 mm diameter single jet, and a 25.4 mm diameter single jet.
graph images and the OASPL in order to more fully understand the acoustic emissions of jet arrays. The acoustic response was divided above into three regions, A– C. These regions also correlate to shock formations. Comparing region A from Figs. 8–11 to the shadowgraph images from Figs. 3.3a, 3.4a, and 3.5a reveal that when the array jets are unmerged the acoustic response is similar to the acoustic response of a single smaller jet. Comparing region B from Figs. 8–11 to Figs. 3b and c, 4b and c, and 5b and c reveal that when the jets begun to share shocks and have formed a lattice of weak shocks the OASPL is transitioning from a lower level to a higher level. Comparing region C to Figs. 3d–f, and 4d reveal that when the jets have formed a lattice of strong shocks the jets have transitioned to a higher decibel, equivalent to a single larger jet of the same total flow area. Thus, it is evident that the acoustic emissions from jet arrays are similar to the turbulent mixing noise of a single jet within an array initially at lower NPR values. When the jets interact the turbulence increases, increasing the acoustic levels similar to that of a single jet of equivalent exit area to an entire jet array. The transition of the OASPL from that of a single small jet to a single larger jet is initiated by the sharing of shocks between the multiple small jets of the array. For example, Fig. 3b, which displays a shadowgraph image a 4.0 mm diameter jet array, with S/ d = 1.44 at an NPR of 6.0, where there is initial shock interaction, can be correlated to Fig. 8, which displays the OASPL for that array. At this NPR the OASPL from the array has transitioned from regions A to B. Figs. 4b and 10, and 5c and 11 also confirm this behavior. Considering the data of Figs. 12 and 13, jet array data that lie on the lower bound display unmerged shock formations. The array measurements which lie on the upper boundary display strong shock lattice formations. And all the jet array data which lie within the envelope display weak shock lattice formations. 6. NPR, Mach number, and mass flow rate
Fig. 13. Overall sound pressure levels as a function of the NPR for 6.4 mm diameter jet arrays, a 6.4 mm diameter single jet, and a 50.8 mm diameter single jet.
The single jet data from Figs. 12 and 13 yield approximately an upper (25.4 and 50.8 mm) and lower bound (3.2 and 6.4 mm) about the OASPL data from the jet arrays. Within the bounds formed by the single jet data, the 8 8 jet arrays transition from the lower bound (OASPL levels equivalent to a single jet within the array) to the upper bound (OASPL levels equivalent to a nozzle with an equal exit area to that of an entire array) as the NPR increases. This transition occurs at different NPR values depending on the S/d ratio for the array. As evident by Figs. 12 and 13, as the S/d increases the transition from the lower bound to the upper bound occurs at higher NPR values. The bounding behavior of the single jets shown in Figs. 12 and 13 can also be described in terms of regions A–C. The jet array data which reside near the lower bound, before they transition, correspond to region A. The jet array data which lie near the upper boundary, after they transition, correspond to region C. All the jet array data that lie within the bounds from the single jets are within region B.
5. Shock formations and OASPL The shock formation structures and OASPL from a supersonic jet array have been shown to be functions of both NPR and S/d. This section correlates the observed shock formations from the shadow-
_ The fully expanded Mach numbers (Mj) and mass flow rates ðmÞ also displayed consistent increase with increasing NPR. The values for the d = 3.97 mm (5/32 in.) jet arrays will be used as an example in this section. Table 3 presents the NPR, fully expanded Mach numbers, and mass flow rates for the d = 3.97 mm (5/32 in.) jet arrays. By examination of Table 3 it can be concluded that by plotting the shadowgraph images or OASPL against either fully expanded Mach number or mass flow rate would reveal the same trends in shock formations and OASPL. In the field of supersonic jet noise it is common to relate acoustic parameters to the fully expanded Mach number which takes into account the NPR as well as the density of the supersonic fluid, theoretically, based upon measured parameters. But, since the fully expanded point cannot be determined when the shocks from a jet Table 3 Net pressure ratios, fully expanded mach numbers, and mass flow rates for d = 5/ 32 in. jet arrays. S/d = 1.44
S/d = 2.5
S/d = 3
NPR
Mj
_ (kg/s) m
NPR
Mj
_ (kg/s) m
NPR
Mj
_ (kg/s) m
2.1 3.0 4.1 6.0 8.1 10.2 12.1 15.2 20.2 24.2
1.1 1.4 1.6 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.3 1.8 2.7 3.6 4.5 6.2 7.6 9.5 10.9 15.3
2.2 2.9 3.9 5.5 8.4 10.3 13.1 14.9 20.1 23.5
1.1 1.3 1.5 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.4 1.7 2.4 3.3 4.8 5.7 6.2 8.4 11.6 13.2
2.3 3.2 3.9 6.3 8.0 9.9 13.2 14.5 19.7 23.2
1.0 1.4 1.6 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.5 1.9 2.5 3.6 4.2 6.0 8.0 7.4 12.4 13.8
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array interact to form shock lattices it would not be appropriate to present a theoretical calculation which does not have a physical representation. Thus, this paper presents acoustic parameters which are based upon the NPR.
The authors would like to acknowledge Control Components Inc. for their support of this research.
7. Conclusion
References
This paper has reported on an experimental investigation of the acoustic emissions of arrays of parallel supersonic jets. The supersonic jet arrays were observed to produce three types of shock structures, depending upon the NPR. The first shock structure consisted of standard shock cells produced from the individual jets. These shock cells behave similar to a single jet up until they expand sufficiently enough to interact with their neighbors. The second shock structure occurs when the shock cells interact with their neighbors and multiple jets are involved in the formation of a single shock; when this occurs in several places a lattice of shocks is produced. The lattice goes through two stages of shock formation; oscillatory and stable. The oscillatory lattice formation is the initial formation and consists of a flapping motion of the overall jet stream and transient motion of shocks within the shock lattice. As the NPR is increased the oscillatory formation stabilizes and there is no longer any transient activity. As the jets within the arrays are spaced farther apart the stages of shock formations occur at higher NPR values. The radiated OASPL, generated from turbulent energy and narrowband screech tones, also transition between three stages. The first region is similar to that of a single jet; where there is a sharp initial increase below an NPR of approximately 5, and then the OASPL levels off at a nominal value. The second stage revealed an upward trend in the OASPL which then began to level off. The last stage is a region where the OASPL flattens out at a much higher decibel level as compared to the first region. The transition between the first and final regions occurs at higher NPR values as the jet spacing increases. The OASPL measurements for single jets were shown to nearly envelope those of the arrays. The lower boundaries of the envelope consisted of data for a single jet with a nozzle diameter equivalent to one of the jets within the array, while the upper boundary consisted of data for a jet with an equivalent exit area to the entire array. The three stages of shock structures correlate well with the three OASPL regions. The first region consists of unmerged shock cells. In the second region an oscillatory shock lattice exists. And in the third region a stable shock lattice forms. Thus, the existence of a shock lattice alters the turbulence of a jet array to a turbulent acoustic response of a larger jet with an exit area equivalent to an entire jet array.
[1] Carucci VA, Mueller RT. Acoustically induced piping vibration in high capacity pressure reducing systems. ASME Paper No. 82-WA/PVP-8; 1982. [2] Hubbard HH. Aeroacoustics of flight vehicles, theory and practice, vol. 1. Noise Sources, Acoustical Society of America; 1995. p. 258. [3] Tam CKW. Jet noise generated by large scale coherent motion. In: Hubbard H, editor. Aeroacoustics of flight vehicles, theory and practice, vol. 1. ASA/AIP; 1991. p. 311–90. [4] Tam CKW, Chen P. Turbulent mixing noise from supersonic jets. AIAA J 1994;32(9):17744–80. [5] Veggeberg K, James M. Development of a large-scale microphone array for aircraft jet plume noise source characterization. SAE technical papers, 2011, SAE 2011 noise and vibration conference and exhibition, NVC; 2011. [6] James M, Gee K. Aircraft jet plume source noise measurement system. Sound Vib 2010;44(8):14–7. [7] Viswanathan K. Instrumentation considerations for accurate jet noise measurements. AIAA J 2006;44(6):1137–49. [8] Dougherty RP, Panda J, Lee SS. Non-intrusive jet noise study combining Rayleigh scattering and phased array measurement techniques. In: Collection of technical papers – 11th AIAA/CEAS aeroacoustics conference, vol. 1; 2005. p. 574–91. [9] Brusniak L, Shur ML, Spalart PR. Phased array imaging of jet noise sources in a Large-Eddy simulation. In: Collection of technical papers – 12th AIAA/CEAS aeroacoustics conference, vol. 1; 2006. p. 609–27. [10] Papamoschou D, Morris PJ, McLaughlin DK. Beamformed flow-acoustic correlations in a supersonic jet. AIAA J 2010;48(10):2445–53. [11] Raman G, Panickar P, Praveen K. Aeroacoustics of twin supersonic jets: a review. Int J Aeroacoust 2012;11(7–8):957–84. [12] Miles JH. Collective interaction in a linear array of supersonic rectangular jets: a linear spatial instability study, Lewis research center, Report: NAS 1.15:208818; NASA/TM-1999-208818, E-11421; 1999. 18p. [13] Raman G, Taghavi R. Resonant interaction of a linear array of supersonic rectangular jets: an experimental study. J Fluid Mech 1996;309:93–111. [14] Eisinger FL. Designing piping systems against acoustically induced structural fatigue. J Press Vess Technol 1997;119:379–83. [15] Tam CKW. Supersonic jet noise. Ann Rev Fluid Mech 1995;27:17–43. [16] Hubbard HH. Aeroacoustics of flight vehicles, theory and practice, vol. 2. Noise Control, Acoustical Society of, America; 1995. p. 258. [17] Yu JC. Investigations of the noise fields of supersonic axisymmetric jet flow. Ph.D. thesis, Syracuse University; 1971. [18] Harper-Bourne M, Fisher MJ. The noise from shock waves in supersonic jets, AGARD-CP-131; 1974. [19] Norum TD, Seiner JM. Measurements of static pressure and far field acoustics of shock-containing supersonic jets, NASA TM 84521; 1982a. [20] Powell A. On the mechanism of chocked jet noise. Proc Phys Soc Lond 1953;66:1039–56. [21] Raman G. Advances in understanding supersonic jet screech: review and perspective. Prog Aerospace Sci 1998;34:45–106. [22] Umeda Y, Ishii R. Oscillation modes of supersonic multijets. J Acoust Soc Am 1997;101:3353–60. [23] Umeda Y, Ishii R. Oscillation modes of supersonic multijets exhausting from very adjacent multiple nozzles. J Acoust Soc Am 2001;110:1873–7. [24] Powell A, Umeda Y, Ishii R. Observations of the oscillation modes of chocked circular jets. J Acoust Soc Am 1992;92:2823–36.
Acknowledgement
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Shock-cell structures and corresponding sound pressure levels emitted from closely spaced supersonic jet arrays Ian S. Coltrin a, Jonathan D. Blotter a,⇑, R. Daniel Maynes a, Kent L. Gee b a b
Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, United States Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, United States
a r t i c l e
i n f o
Article history: Received 12 December 2012 Received in revised form 7 June 2013 Accepted 24 June 2013 Available online 20 July 2013 Keywords: Supersonic jet arrays Acoustic emissions Jet noise
a b s t r a c t Shockwave structures and overall sound pressure levels from 8 8 arrays of axisymmetric supersonic jets were experimentally characterized for 14 different arrays. The results were also compared to behavior for single jets of similar dimensions. The jet diameters ranged from 3.2 to 6.4 mm and the jet spacing to diameter ratio ranged from 1.44 to 3. The arrays were tested at nominal net pressure ratios ranging from 2 to 24. It was found that above a certain net pressure ratio level, the array of jets coalesced into an interacting lattice of oblique shock interactions. These shock structures consisted of oscillatory shocks at lower pressure ratios and then developed into stable shock structures as the pressure ratio increased. The formation of the interacting shock lattices is strongly correlated with the measured sound pressure levels. Initially the arrays emitted low sound pressure levels, similar to that of a single jet within the array. As the shock structure transitioned from weak to strong the sound pressure levels transitioned to a level similar to that of a single nozzle with an exit area equivalent of the entire array. Shadow graph images of the flow in the arrays are used to correlate to the sound pressure levels measured. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Acoustic emissions from supersonic jet arrays represent an area of significant research need. Practical applications not only exist in the area of aero-acoustics, where high pressure sound waves from engine exhausts can induce structural fatigue as well as significant human discomfort, they also exist in the energy industry, among others which involve high pressure let down processes. In these types of industries high pressure acoustical loadings have caused severe fatigue in piping networks, and other mechanical systems, sometimes causing them to fail within hours [1]. Thus, this paper focuses on better understanding the relationships between parallel supersonic jet flows which create severe acoustic emissions. Theoretical and experimental advances in jet flow noise were performed during the 1980s and 1990s. A comprehensive presentation of these advances is provided by Hubbard [2]. Tam [3,4] and others continued during the 1990s with significant contributions. During the early 2000s until present, significant research has been performed in developing microphone array systems to characterize the noise from single jets [5–9]. Beam forming measurement methods have also been investigated [10]. A significant amount of work has been done in relation to twin supersonic jets. Raman et al. [11] gives a summary of this work. Although some ⇑ Corresponding author. Tel.: +1 801 422 7820; fax: +1 801 422 0516. E-mail address: [email protected] (J.D. Blotter). 0003-682X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apacoust.2013.06.010
work has been done on linear supersonic jet arrays [12,13], compared to single or twin supersonic jets very little research on multiple jet arrays has been done. Therefore, the focus of this paper is to investigate the shock-cell structure and corresponding sound pressure levels in multiple jet arrays. From the point of view of industry, high acoustical loadings have been examined from the aspect of sound transmission and noise generation in the surroundings of piping systems. Work that combined structural fatigue and the acoustic loading within a pipe was done by Carucci and Mueller [1]; and which was later refined by Eisinger [14]. As a method to reduce the acoustic emissions, Carucci and Mueller suggested dividing a single jet into multiple smaller jets. Their suggestion was to implement Venturi slots into valves which would create several smaller parallel plane jets out of a single, larger jet. There are three main mechanisms which describe the total acoustic emissions from supersonic jets. Tam [15] reported that the three supersonic jets mechanisms consisted of turbulent mixing noise, broadband shock associated noise, and narrowband shock associated noise, or screech. Although these mechanisms all contribute to the same acoustic loads they are generated in different ways. The source of noise from turbulent mixing is generated from the shear layer between the jet and the quiescent medium. The instability wave created from this shear layer is much like a supersonic fluid moving past a wavy wall. The unstable shear layer causes
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Mach waves to build up and radiate downstream and away from the jet. The pressure decrease across the continually radiating Mach waves can be viewed as an acoustic pressure wave. Broadband shock-cell noise generated by the interaction of the turbulent eddies of the jet with the structure of the shock cell [16]. Tam [15] states that this component of noise is a result of the constructive scattering of the turbulence by the stationary quasi-periodic shock cells in the jet plume. The shock cells mentioned here are formed as a result of the expanding fluid of a jet which creates a shock against the quiescent medium. Due to the high pressure rise of the shock, the jet flow is reflected back into the jet where it then expands again as it moves downstream. These processes can be repeated several times for a supersonic jet. As viewed from the jet flow perspective these shock cells are a superposition of the waveguide modes at different wavelength and are a disturbance which is one way to create turbulent energy within the flow [15]. This turbulent energy is then translated into acoustic energy which radiates outward and downstream. The first to investigate this noise source were Yu [17] and Harper-Bourne and Fisher [18]. Several others followed up on this research including Seiner and Norum [19], and Tam [15]. The last mechanism is narrowband shock associated noise, or screech. Screech tones were first investigated by Powell [20] when discrete tones produced from under expanded supersonic jets were observed. In Raman’s [21] review on screech he described screech generation from a feedback loop created from a distinct formation of shocks. These distinct shocks may have a vortical structure, either toroidal or helical, which are convected downstream in the near field of the jet. The vortical nature of the shocks causes the jet flow to become unstable and wavy. The unstable flow would in turn cause the shock cells of the jet to interact with the vortical shock waves which then would generate a discrete acoustic tone. Dual jet streams and other multiple jet flow techniques have been used to restrict these mechanisms, particularly screech [21– 23]. As mentioned, the feedback loop which generates screech is dependent upon the existence of vortical shock formations. Such shock formations can be manipulated with the existence of several jets. As reported by Raman [21] in the case of rectangular jets the effects of screech can be minimized with the addition of a second, parallel jet stream. Here the vortical shock formation of the second jet reduces the effects of the first due to a phase mismatch of the two vortical shock formations. An extension into several axisymmetric jets was performed by Umeda and Ishii [22,23]. Here they investigated the oscillation modes of two and four axisymmetric jet arrays, as well as a single nozzle jet. Since phase mismatching does not work in the same fashion with axisymmetric jets as it does with rectangular jets, they focused their research on the oscillation modes and screech frequencies produced from multiple jets. In this present investigation, instead of concentrating on the narrowband shock associated noise which has been thoroughly investigated, this paper concentrates on the broadband shock associated noise and turbulent mixing noise that radiates from a larger jet array. This paper presents the acoustic emission and shock structure characteristics of several different arrays of parallel axisymmetric supersonic jets. The results include a shadowgraph investigation of the formation of shock cells from single jets and interacting shock cells from multiple jets as a function of the net pressure ratio (NPR). Also, the resulting overall sound pressure levels the arrays emit as a function of the NPR are provided.
axisymmetric jets. A schematic view of an array is provided in Fig. 1. The nozzle diameters investigated ranged from 3.2 mm (1/ 8 in.) to 6.4 mm (1/4 in.). The center-to-center spacing over the nozzle diameter (S/d) ratios investigated ranged from 1.44 to 3. The nozzles were machined in a flat surface which was then fixed onto the exit of a large pressure let down facility. The nozzles are straight cylinders and the nozzle entrances and exits were sharp but with all burrs removed. The NPR values investigated ranged between 2 and 24. This ratio is defined as the static pressure of the flow, acquired upstream of the jet arrays, over the pressure of the quiescent medium, in this case the atmosphere. Static pressure measurements were acquired with an Omega PX309–500G5 V pressure transducer and differential pressure measurements were acquired with a pitot tube and an Omega PX409–015WU5 V. Temperature measurements were acquired with a type K thermocouple. Table 1 shows the full range of nominal NPR values investigated. Measurements of single hole plates were also acquired for comparison and are listed in Table 2. The 3.2 mm and 6.4 mm diameter single jets from Table 2 represent a single nozzle with the same diameter as found in the 3.2 mm and 6.4 mm arrays from Table 1. The 25.4 mm (1 in.) and 50.8 mm (2 in.) diameter single jets represent the total exit area of 3.2 mm and 6.4 mm diameter arrays from Table 1, respectively. In summary, 14, 8 8 arrays and 4 single jets were investigated for a total of eighteen plates. For each plate, measurements were acquired at approximately 10 NPR values. The facility used to produce the range of NPR values was the high pressure blowdown facility owned by Brigham Young University’s Mechanical Engineering Department. This facility has a maximum capacity of 11.0 MPa and a total volume of 24.1 m3. Flow was released through a control valve which controls the air flow passing through the array. Just downstream of the control valve is 15.2 cm (6 in.) schedule 80 piping that expands to 20.3 cm (8 in.) schedule 80 piping. The plates are mounted at the exit of the 20.3 cm pipe section where shadowgraph images and acoustic measurements were acquired. The acoustic emissions were measured with a 6.4 mm (1/4 in.) GRAS 40BE free field microphone. The frequency range for this microphone is 10 Hz to 100 kHz and has a dynamic range of 40– 170 dB; consistent with the range necessary to measure supersonic jet noise. The microphone was placed on a 1 m radius, 30° off the centerline axis of the flow, as seen in Fig. 2. This is consistent with the research of Yu [17], and Norum and Seiner [19]. Past research has confirmed that at 30° offset from the centerline axis of the flow
2. Experiment The goal of this research is to investigate and characterize the flow regime with the acoustic field from 8 8 arrays of supersonic
Fig. 1. Schematic view of a typical jet array.
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1.44 2 2.5 3
Nozzle diameters (mm) 3.2 (1/8 in.)
3.7 (18/125 in.)
4.0 (5/32 in.)
6.4 (1/4 in.)
2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,18,20,24
2,3,4,6,8,10,12,15,20,24 None 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24 None 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20 2,3,4,6,8,10,12,15,20,24 2,3,4,6,8,10,12,15,20,24
Table 2 Nominal net pressure ratios investigated for single jets. Nozzle diameters (mm)
3.2 (1/8 in.)
6.4 (1/4 in.)
25.4 (1 in.)
50.8 (2 in.)
Net Pressure Ratios
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
2,3,4,6,8,10,12,15,20,24
Fig. 2. Microphone experimental setup.
is the highest acoustic pressure output from a single axisymmetric supersonic jet. Thus, at this position the acoustic emissions from the main noise mechanism being acquired will be turbulent mixing noise [15,17]. A single microphone was used instead of an array as this point captures the turbulent mixing noise and is typically where numerical models calculate results [20]. Furthermore, it is desired to develop correlations between the flow field and the acoustical field with a single acoustical measurement. Shadowgraph was chosen as the technique to visualize shock cell formations. The images presented in this paper view the arrays from the side such that eight shock cell structures are evident with the flow from left to right. Shadowgraph images for all the test configurations given in Table 1 were acquired. The trends observed in all the cases were similar, therefore only the shadowgraph images for the 4.0 mm (5/32 in.) diameter jet arrays will be shown in this paper. 3. Shock formations Figs. 3–5 display shadowgraph images for 4.0 mm diameter jet arrays with S/d ratios of 1.44, 2.5, and 3, respectively. The jets display three stages of shock formations. These shock formations consist of standard shock cells as well as shock lattices which form when the shock cells expand large enough to interact with their neighbors. The shock lattices can be observed in Figs. 3b–f, 4c–d, and 5d.
In order to best explain the stages of shock formation, Fig. 3 will be used as an example. Fig. 3a displays standard supersonic jet shock formations. Here, the jets are forming individual shock cells which do not interact with neighboring jets. As the NPR is increased the sizes of the shock cells expand, however the shock cells do not interact with neighboring shock cells below an NPR of approximately 6. As the NPR is increased further the shock cells of the individual jets expand enough to interact with each other. This interaction is defined as shock interaction, where several jets are involved in creating a single shock. When this event occurs in several places it creates a lattice of shockwaves as observed in Fig. 3b–f. The shock lattices go through two stages of formation; oscillatory and stable. The characteristic of oscillatory shock formation is the unstable nature of the flow; this can be seen in Fig. 3b and c. This unstable nature involves the transient movement of shocks within the shock lattice as well as a flapping motion of the jet just outside of the lattice. The oscillatory shock lattice also randomly generates screech tones. This is also confirmed by examining the acoustic pressure as the NPR is increased in the frequency domain. Fig. 6 illustrates the sound pressure levels in the frequency domain as the NPR is increased. The discrete tone in the spectra can be observed at an NPR of 8.1 where the highest amplitude sound pressure level can be observed. The high amplitude spike represents a screech tone which can be correlated to Fig. 3c. Other spectra containing screech tones can also be correlated to weak shock
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Fig. 3. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 1.44 and at NPR values ranging from 3.0 to 24.2.
Fig. 4. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 2.5 and at NPR values ranging from 5.5 to 23.5.
lattices produced from jet arrays. Though screech tones only randomly occur during an oscillatory shock formation the reason the screech tones are being generated are yet unknown.
Stable shock formations are those occurring in Fig. 3d–f. They are characterized by their symmetrical formation of oblique shocks about the jet centerline and flow conditions that are
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Fig. 5. Shadowgraph images for a 4.0 mm diameter jet array and S/d ratio of 3 and at NPR values ranging from 6.3 to 23.2.
non-oscillatory. Fig. 3d illustrates that the lattice structure is much longer than those occurring at lower NPR values. As the NPR is increased further, the outer oblique shocks shown in Fig. 3d are pushed outward, resulting in the pyramidal shock lattice evident in Fig. 3e and f. It should be noted that once the shock lattice forms these pyramidal type structures, there is little change in the structure with increasing NPR. Comparison of the shadowgraph images from Figs. 3–5 reveal that when the jet spacing is increased the NPR level where interaction between jets occurs also increases. In Fig. 3 (S/d = 1.44) the initial shock interaction occurs at an NPR of approximately 6. In Fig. 4 (S/d = 2.5) shock interaction first occurs at an NPR of approximately 13–14, and in Fig. 5 (S/d = 3) shock interaction first occurs at an NPR of approximately 20. The images of Figs. 4 and 5 reveal that weak lattice formations occur at NPR values of ranging approximately from 20 to 24 for S/d = 2.5, and at an NPR of approximately 24 for S/d = 3.
and translated onto a logarithmic scale as defined by Eq. (1). Here it is used as a measure of the overall noise emitted from the arrays. The OASPL for the single jet scenarios will first be presented and discussed; then the OASPL for the jet arrays will be presented.
OASPL ¼ 20 log
rmsðPacoustic Þ Pref
ð1Þ
The overall sound pressure level (OASPL) is the root mean square of the acoustic signal which is detected by the microphone
Fig. 7 presents the OASPL as a function of the NPR for four single jets with diameters of 3.2, 6.4, 25.4, and 50.8 mm. As shown, between NPR values of approximately 2–5 there is a sharp rise in the OASPL for all single jet diameters. After the initial rise, the slopes of the OASPL vs. NPR data decrease and exhibit only modest increase as the NPR increases. The data also show that the OASPL increases with nozzle diameter. Although the scope of this research investigates significantly higher NPR values, the overall behavior of the OASPL for low NPR values seen here for single jets is similar to the results presented by Powell et al. [24] and Umeda, and Ishii [21]. Measurements for the OASPL of the 8 8 jet arrays are shown in Figs. 8–11 for S/d = 1.44, 2, 2.5, and 3 respectively. Note that
Fig. 6. Frequency spectra for a 4.0 mm diameter jet array and S/d ratio of 1.44.
Fig. 7. Overall sound pressure levels as a function of the NPR for single jets of diameters 3.2 mm, 6.4 mm, 25.4 mm, and 50.8 mm.
4. Overall sound pressure levels
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Figs. 8–10 are divided into three regions labeled A, B, and C. Fig. 11 is also divided, but only into two regions instead of three, labeled A and B. These regions will be used to identify the noise characteristics of the jet arrays as well as correlate the visualizations of shock formations with the measured OASPL. The OASPL data in region A show characteristics similar to a single jet. In this region the data exhibit a sharp initial rise followed by a general leveling off in the OASPL. This behavior is best illustrated in Figs. 8–11. The data from Figs. 9–11 reveal that region A extends over a smaller range of NPR values as the S/d ratio is reduced. Thus, for S/d = 1.44 (Fig. 8), the OASPL data never level off because region A is so short that region B occurs right after the steep initial rise in the OASPL. At NPR values above region A, the OASPL for the jet arrays are no longer similar to the single jet noise characteristics. Rather the data begin to display characteristics unique to that of interacting jet arrays. Fig. 10 will be used as an example in order to better explain these unique characteristics. Fig. 10 presents the OASPL for a 4.0 mm diameter jet array with S/d = 2.5. The data in region B in Fig. 10 exhibit an upward trend in the OASPL with increasing NPR. This occurs until the OASPL for the jet arrays level off at a higher OASPL level (region C) as compared to region A. In summary, the OASPL in region A is similar to that of a single jet of the same diameter as one of the array jets. Also, region C can be viewed as a region where the radiated noise has leveled off to much higher nominal levels as compared to region A. Region B can be viewed as the transition region between these two regimes. Comparison of region B in Figs. 8–11 shows that the transition regime shifts to higher NPR values as S/d increases. The larger the S/d ratio, the higher the NPR where region B begins. The total NPR range over which region B extends also increases as S/d increases. The variation in the OASPL with varying jet diameter also varies with the S/d. As observed in Fig. 11 (S/d = 3), the OASPL data for the four jet diameters (3.2–6.4 mm) show marked variation. Conversely, when the nozzles are spaced closer together, as seen in Fig. 8 where the S/d = 1.44, the OASPL data for each of the four nozzle diameters are clustered much tighter. In general, the data of Figs. 8–11 reveal that for increasing S/d the OASPL values for the four different nozzle sizes show greater variation. For all S/d, the largest OASPL values correspond to the 6.4 mm diameter jet arrays and the lowest OASPL values correspond to the 3.2 mm diameter arrays. Figs. 12 and 13 present the OASPL data for the 3.2 and 6.4 mm jet arrays with corresponding single jet data. Fig. 12 displays the OASPL for the 3.2 mm diameter jet arrays, a 3.2 mm diameter single jet, and a 25.4 mm diameter single jet. Recall that the 25.4 mm
Fig. 9. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 2.
Fig. 10. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 2.5.
Fig. 11. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 3.
Fig. 8. Overall sound pressure levels as a function of the NPR for jet arrays with S/d ratios of 1.44.
diameter single jet represents a jet with an equivalent exit area to the entire 3.2 mm diameter jet array. Likewise, Fig. 13 presents the OASPL for 6.4 mm diameter jet arrays, a 6.4 mm diameter single jet, and a 50.8 mm diameter single jet. Again, the 50.8 mm jet represents the same flow area as the 6.4 mm diameter jet array.
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Fig. 12. Overall sound pressure levels as a function of the NPR for 3.2 mm diameter jet arrays, a 3.2 mm diameter single jet, and a 25.4 mm diameter single jet.
graph images and the OASPL in order to more fully understand the acoustic emissions of jet arrays. The acoustic response was divided above into three regions, A– C. These regions also correlate to shock formations. Comparing region A from Figs. 8–11 to the shadowgraph images from Figs. 3.3a, 3.4a, and 3.5a reveal that when the array jets are unmerged the acoustic response is similar to the acoustic response of a single smaller jet. Comparing region B from Figs. 8–11 to Figs. 3b and c, 4b and c, and 5b and c reveal that when the jets begun to share shocks and have formed a lattice of weak shocks the OASPL is transitioning from a lower level to a higher level. Comparing region C to Figs. 3d–f, and 4d reveal that when the jets have formed a lattice of strong shocks the jets have transitioned to a higher decibel, equivalent to a single larger jet of the same total flow area. Thus, it is evident that the acoustic emissions from jet arrays are similar to the turbulent mixing noise of a single jet within an array initially at lower NPR values. When the jets interact the turbulence increases, increasing the acoustic levels similar to that of a single jet of equivalent exit area to an entire jet array. The transition of the OASPL from that of a single small jet to a single larger jet is initiated by the sharing of shocks between the multiple small jets of the array. For example, Fig. 3b, which displays a shadowgraph image a 4.0 mm diameter jet array, with S/ d = 1.44 at an NPR of 6.0, where there is initial shock interaction, can be correlated to Fig. 8, which displays the OASPL for that array. At this NPR the OASPL from the array has transitioned from regions A to B. Figs. 4b and 10, and 5c and 11 also confirm this behavior. Considering the data of Figs. 12 and 13, jet array data that lie on the lower bound display unmerged shock formations. The array measurements which lie on the upper boundary display strong shock lattice formations. And all the jet array data which lie within the envelope display weak shock lattice formations. 6. NPR, Mach number, and mass flow rate
Fig. 13. Overall sound pressure levels as a function of the NPR for 6.4 mm diameter jet arrays, a 6.4 mm diameter single jet, and a 50.8 mm diameter single jet.
The single jet data from Figs. 12 and 13 yield approximately an upper (25.4 and 50.8 mm) and lower bound (3.2 and 6.4 mm) about the OASPL data from the jet arrays. Within the bounds formed by the single jet data, the 8 8 jet arrays transition from the lower bound (OASPL levels equivalent to a single jet within the array) to the upper bound (OASPL levels equivalent to a nozzle with an equal exit area to that of an entire array) as the NPR increases. This transition occurs at different NPR values depending on the S/d ratio for the array. As evident by Figs. 12 and 13, as the S/d increases the transition from the lower bound to the upper bound occurs at higher NPR values. The bounding behavior of the single jets shown in Figs. 12 and 13 can also be described in terms of regions A–C. The jet array data which reside near the lower bound, before they transition, correspond to region A. The jet array data which lie near the upper boundary, after they transition, correspond to region C. All the jet array data that lie within the bounds from the single jets are within region B.
5. Shock formations and OASPL The shock formation structures and OASPL from a supersonic jet array have been shown to be functions of both NPR and S/d. This section correlates the observed shock formations from the shadow-
_ The fully expanded Mach numbers (Mj) and mass flow rates ðmÞ also displayed consistent increase with increasing NPR. The values for the d = 3.97 mm (5/32 in.) jet arrays will be used as an example in this section. Table 3 presents the NPR, fully expanded Mach numbers, and mass flow rates for the d = 3.97 mm (5/32 in.) jet arrays. By examination of Table 3 it can be concluded that by plotting the shadowgraph images or OASPL against either fully expanded Mach number or mass flow rate would reveal the same trends in shock formations and OASPL. In the field of supersonic jet noise it is common to relate acoustic parameters to the fully expanded Mach number which takes into account the NPR as well as the density of the supersonic fluid, theoretically, based upon measured parameters. But, since the fully expanded point cannot be determined when the shocks from a jet Table 3 Net pressure ratios, fully expanded mach numbers, and mass flow rates for d = 5/ 32 in. jet arrays. S/d = 1.44
S/d = 2.5
S/d = 3
NPR
Mj
_ (kg/s) m
NPR
Mj
_ (kg/s) m
NPR
Mj
_ (kg/s) m
2.1 3.0 4.1 6.0 8.1 10.2 12.1 15.2 20.2 24.2
1.1 1.4 1.6 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.3 1.8 2.7 3.6 4.5 6.2 7.6 9.5 10.9 15.3
2.2 2.9 3.9 5.5 8.4 10.3 13.1 14.9 20.1 23.5
1.1 1.3 1.5 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.4 1.7 2.4 3.3 4.8 5.7 6.2 8.4 11.6 13.2
2.3 3.2 3.9 6.3 8.0 9.9 13.2 14.5 19.7 23.2
1.0 1.4 1.6 1.8 2.0 2.2 2.3 2.4 2.6 2.7
1.5 1.9 2.5 3.6 4.2 6.0 8.0 7.4 12.4 13.8
1526
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array interact to form shock lattices it would not be appropriate to present a theoretical calculation which does not have a physical representation. Thus, this paper presents acoustic parameters which are based upon the NPR.
The authors would like to acknowledge Control Components Inc. for their support of this research.
7. Conclusion
References
This paper has reported on an experimental investigation of the acoustic emissions of arrays of parallel supersonic jets. The supersonic jet arrays were observed to produce three types of shock structures, depending upon the NPR. The first shock structure consisted of standard shock cells produced from the individual jets. These shock cells behave similar to a single jet up until they expand sufficiently enough to interact with their neighbors. The second shock structure occurs when the shock cells interact with their neighbors and multiple jets are involved in the formation of a single shock; when this occurs in several places a lattice of shocks is produced. The lattice goes through two stages of shock formation; oscillatory and stable. The oscillatory lattice formation is the initial formation and consists of a flapping motion of the overall jet stream and transient motion of shocks within the shock lattice. As the NPR is increased the oscillatory formation stabilizes and there is no longer any transient activity. As the jets within the arrays are spaced farther apart the stages of shock formations occur at higher NPR values. The radiated OASPL, generated from turbulent energy and narrowband screech tones, also transition between three stages. The first region is similar to that of a single jet; where there is a sharp initial increase below an NPR of approximately 5, and then the OASPL levels off at a nominal value. The second stage revealed an upward trend in the OASPL which then began to level off. The last stage is a region where the OASPL flattens out at a much higher decibel level as compared to the first region. The transition between the first and final regions occurs at higher NPR values as the jet spacing increases. The OASPL measurements for single jets were shown to nearly envelope those of the arrays. The lower boundaries of the envelope consisted of data for a single jet with a nozzle diameter equivalent to one of the jets within the array, while the upper boundary consisted of data for a jet with an equivalent exit area to the entire array. The three stages of shock structures correlate well with the three OASPL regions. The first region consists of unmerged shock cells. In the second region an oscillatory shock lattice exists. And in the third region a stable shock lattice forms. Thus, the existence of a shock lattice alters the turbulence of a jet array to a turbulent acoustic response of a larger jet with an exit area equivalent to an entire jet array.
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Acknowledgement