Fundamental Screech Tone Analysis of Elliptic Pipe Jet ^†

Abstract

The elliptic pipe jet screech is explored at a pressure ratio from 2 to 6. The pipe length to diameter ratio is 5. The fundamental screech frequency and magnitude are obtained from the sound pressure level spectrum. The screech frequency decreases as the pressure ratio increases. The minor plane has more tones than the major plane at an emission angle of 75 degrees from the jet axis. The amplitude of the screech differs among the planes. The amplitude is higher at lower emission angles from 45 to 75 degrees and lower at a sideline angle of 90 degrees.

1. Introduction

Circular and non-circular shapes, such as rectangles and ellipses, are used in aircraft nozzles. A pipe jet can be used as a fuel injector inside the combustion chamber of a jet engine. Non-circular forms of cross-sections, such as clovers [1], rectangles [2,3], and ellipses [4,5,6,7], are used to provide better mixing. The exit of an aircraft nozzle has a small pipe with a small length-to-diameter (L/D) ratio.

Elliptic jets [8,9] have differential spread along the major and minor axes, whereas the spread is the same for circular jets. This differential spread promotes axis switching in elliptical jets. Off-center peaks can be found in pressure profiles, with asymmetric exits at high nozzle pressure ratios (NPR) for elliptic jets. Thus, elliptic jets promote better mixing than circular jets. K.K. Ahuja et al. [10] studied various nozzle exit modifications, such as rectangular and elliptic shapes, notches, tabs at the exit, and co-flow rectangles used to reduce jet noise [11]. The notches with square and triangle shapes are cut at the elliptic slot exit. Square notches exhibit better noise reduction regarding shock-associated noise. In their experimental work on circular, rectangular, and elliptic jets, J. Panda et al. [4] presented a discussion of different modes of screech and used the standing wavelength (L_sw) to predict the screech frequency, in addition to the conventional technique of using the shock cell spacing (L). S.B. Verma and E. Rathakrishnan [5] investigated the effects of elliptic slot jets with three different moderate aspect ratios on the acoustics of underexpanded jets. The aspect ratio seemed to affect the screech feedback loop, thus reducing the magnitude of the screech tone. Kevin W. Kinzie and D.K. McLaughlin [6] investigated the correctly expanded elliptic M = 1.5 jet under heated and unheated jet flow conditions. The velocity of a large-scale turbulent structure was increased by a helium mixed-air jet, thereby leading to noise due to the Mach wave radiation phenomenon. A clover-shaped pipe jet [1], a circular slot jet for transonic tones [12], an annular jet [13], and a hexagonal pipe jet [14] have been investigated for their acoustic characteristics.

The high-pressure-ratio jet flow from a non-circular cross-section will have mixing- and shock-associated noise. The screech tone appears at one particular frequency with a high amplitude. Screech noise is said to appear with harmonics. The first harmonic is the fundamental screech tone (f_s or f₁). The fundamental tone moves in the upstream direction (180° from the jet axis) towards the nozzle exit. The screech frequency of the fundamental tone [15] is f_s = U_c/(L × (1 + M_c)), where L is the shock cell spacing, and U_c and M_c are the convective speed and Mach number of a turbulent structure. Aoki [16] found that an increase in lip thickness reactivates the screech loop. A detailed review was given by G. Raman [15] on the various features of the screech for a nozzle jet flow. Screech is produced as a result of a feedback mechanism that exists due to the interaction between the large-scale (LS) turbulence and shock cells, thus producing acoustic feedback waves, which in turn trigger instability when they hit the nozzle lip. Sometimes, there may be two feedback mechanisms [17], creating two screech tones at a given Mach number (M).

Noise reduction in circular pipe jets can be achieved by modifying the internal surface roughness [18], exit castellation [19], or co-flow swirler [20], as described in published research works. Jet noise reduction using a non-circular pipe, such as an ellipse, has not yet been investigated by researchers. Pipe jets are operated in underexpanded conditions. An underexpanded jet is one where the nozzle exit pressure (P_e) is greater than the ambient pressure (P_a). Underexpanded operation occurs above the pipe choking pressure ratio (settling chamber pressure/ambient pressure) R = 1.89 [21]. Hence, the operating pressure is chosen from R = 2 to 6, covering low to high underexpansion levels. An underexpanded jet will have a shock cell structure. Shock-associated noise is produced as a result of the interaction between the turbulence structure and shock cells. Screech is a type of shock-associated noise. The aim of this work is to analyze the screech behavior of an elliptic pipe jet in underexpanded conditions.

2. Experimental Methodology

The anechoic chamber and high-speed jet facility at the Department of Aeronautical Engineering, Rajalakshmi Engineering College, Chennai was used for the experiments, and its details can be found in [2,3]. The facility consists of two reciprocating compressors (15 hp), an air dryer, a storage tank (5 m³), and a settling chamber. The elliptic pipe is connected to the settling chamber via proper fitting to produce a compressible jet flow inside the anechoic chamber. The anechoic chamber’s dimensions are 2.8 m $\times$ 2.5 m $\times$ 2.15 m; it provides a free field environment for acoustic measurements. The inner walls of the chamber are lined with polyurethane (PU) foam. The jet flow structure arises from a pipe in the underexpanded condition (P_e > P_a), with features such as shock cells, vortices, and acoustic waves (fundamental screech tone), as shown in Figure 1.

The 3D-printed elliptic pipe is made up of acrylonitrile butadiene styrene (ABS). The dimensions of the elliptic pipe can be found in

Table 1. Operating conditions of the jet.

Operating and Geometric Parameters	Value
Pipe pressure ratio $={\displaystyle \frac{\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{c}\mathrm{h}\mathrm{a}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} {(P}_o)}{\mathrm{a}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e} {(P}_a)}}$	R = 2 to 6 (in steps of 1)
Semi-major axis	a = 3.05 mm
Semi-minor axis	b = 2.05 mm
Area of ellipse	A = 19.64 mm2
Aspect ratio	AR = 1.5
Equivalent diameter	De = 5 mm
Length of pipe	L = 25 mm
Radial distance	r = 100 × De

. For a circular jet, acoustic measurement in one plane is sufficient. However, for elliptic jets with two planes, the major plane (X-Y) and minor plane (X-Z) are considered for acoustic measurements. The jet spread is different along the two planes. The jet noise produced along the two planes also differs. The microphone locations or emission angles (ϕ) are varied from 45° to 90° at an interval of 15° each in both planes, as seen in Figure 2. The minimum angle ϕ = 45° is chosen, such that the microphone is at a safe distance from the jet. Large-scale turbulence noise is dominant from ϕ = 45° to 60° and fine-scale turbulence noise is dominant from ϕ = 60° to 90° [22]. The screech propagates in the upstream direction and can be captured at ϕ = 90°.

The jet noise is acquired through a pre-polarized condenser microphone (PCB 378C01, PCB Piezotronics, Inc., Depew, NY, USA), which is kept inside the anechoic room. The 6.35 mm free field microphone with sensitivity S = 2 mV/Pa, with a range of 3 Hz to 100 kHz (+2/−3 dB), measures the maximum sound pressure level (SPL) up to 165 dB. A 4-channel signal conditioner (PCB 482C54, PCB Piezotronics, Inc., Depew, NY, USA) powers the microphone and receives the signal from the microphone; it conditions and sends it to a data card (PicoLog 1012, St Neots, Cambridgeshire, UK). The data card is a 12-channel DAQ connected to a computer via a USB cable. The data card is controlled using Picoscope 6.0, a PC-based software program. The sound signals are acquired at an FFT length equal to 4096, with a bandwidth of 24.41 Hz. The sound spectrum ranges from 630 Hz to 100 kHz, where 630 Hz is the cut-off frequency of the anechoic room. The speed of sound is assumed constant at $a_{\infty }=346.03 \mathrm{m}/\mathrm{s}$ at a standard reference temperature of 25 °C. The density of air is 1.225 kg/m³, and the atmospheric pressure at reference conditions is P_a = 101.325 kPa. The temperature ratio (settling chamber temperature/ambient temperature) is taken as $T_R$ = 1, indicating that it is a cold jet.

3. Results

SPL Spectrum

Figure 3 gives the typical sound pressure level (SPL) spectrum of the pipe jet noise for R = 4 at ϕ = 45° in the minor plane. This spectrum is characterized by a screech tone and broadband shock-associated noise (BSAN), as shown in Figure 3. Both of the above noise types are due to shock formation in the compressible jet flow. Noise at the frequency range of up to 20 kHz is low-frequency noise (detectable by the human ear), that from 20 kHz to 50 kHz is mid-frequency noise, and that above 50 kHz is high-frequency noise. The reference sound pressure level is 20 μPa. Large-scale turbulent noise occurs at low frequencies, whereas fine-scale turbulent noise occurs at high frequencies. The screech is high-amplitude tonal noise in the spectrum. Screech tones can be harmonic in nature, consisting of multiple tones. The first one is the fundamental tone (f_s or f₁) and is analyzed in this paper, while harmonics are not considered. The shock-associated noise is broadband in nature, and, at its unique frequency, it propagates in the upstream direction towards the nozzle exit, as described in [17]; this is called the fundamental screech tone. The harmonics may propagate in other directions depending on the harmonic number (f₂, f₃ and so on). In the spectrum shown, the BSAN occurs in the mid-frequency range, and screech occurs at around 30 kHz. The SPL is more in the low- and mid-frequency regions than in the high-frequency range.

Figure 4 and Figure 5 give the SPL spectra in both planes at ϕ = 90° (sideline to nozzle exit). The spectra for R = 2 and 3 are similar for both axes. For R = 4, a screech tone is present in the spectra of the major and minor axes at around 63 kHz and has a higher amplitude of 1.5 dB more in the minor axis. A screech tone is also present at R = 6 at around 26 kHz (87.59 dB) only in the minor axis. It can be said that the minor axis has more tones. The spectra for R = 4 to 6 are also very similar for both axes, except for frequencies f < 10 kHz and f > 90 kHz. The peak values of the spectrum are larger in the major plane than the minor plane for higher values of R.

4. Discussion

Fundamental Screech Frequency and Amplitude

The fundamental screech frequency (f_s) as a function of the emission angle (ϕ) is given for various pressure ratios (R). Figure 6 gives the screech tone frequency for the major plane and Figure 7 for the minor plane. Although the sound spectrum is captured for all pressure ratios (R) and all emission angles (ϕ), the screech tone is found to appear from R = 4 onwards. The screech frequency and its amplitudes are obtained from the spectrum and plotted against R for various values of ϕ.

In the major plane in Figure 6, the screech frequency tends to decrease with R, which can be seen for ϕ = 60° and 75°. For ϕ = 90°, the screech tone appears at a high frequency (61.621 kHz) at R = 4, and no other screech is seen after the pressure ratio (R). At ϕ = 45°, a screech tone appears at R = 4 but not for higher R values. In the minor plane in Figure 7, more screech tones are present than in the major plane. Here, again, as R increases, the screech frequency decreases, which can be seen for ϕ = 60° and 75°. At ϕ = 45°, only one screech tone is present at R = 4, which is also present in the major axis. At ϕ = 90°, for R = 4, the second harmonic tone (63.428 kHz) is seen, and, at R = 6, a screech tone (26.465 kHz) is present. In general, the value of the frequency at which the screech occurs tends to decrease with the pressure ratio, as seen in [12,15,17].

• ϕ = 45°—the emission angle at which screech tones are the least produced, occurring only at R = 4;
• ϕ = 60°—f_s occurs for R = 4, 5, and 6 in both planes;
• ϕ = 75°—f_s occurs for R = 4, 5, and 6 in the minor plane and R = 4 and 5 in the major plane;
• ϕ = 90°—screech at the second harmonic occurs at around 63 kHz for R = 4 only.

Figure 8 gives the amplitude of the fundamental screech tone against the pressure ratio (R). At ϕ = 60°, the magnitude slightly decreases, and it then increases from R = 4 to 6. The initial decreasing trend can also be found for ϕ = 75°. Figure 9 corresponds to the amplitude variations in the minor plane. The trend of magnitude variation in the minor plane is different from that in the major plane. The magnitude initially increases and then decreases with respect to R, which can be seen at ϕ = 60° and 75°, respectively. The tone is more dominant at a lower emission angle at ϕ = 45° to 75° and less pronounced at a sideline angle ϕ = 90°.

The screech starts at a pressure ratio R = 4 and is seen up to R = 6. The elliptic pipe jet does not exhibit screech at lower underexpansion levels of R = 2 to 3. The screech is dominant at R = 4. The second harmonic (63.43 kHz) is seen at an emission angle ϕ = 90°, as stated in [17]. The screech of an elliptic jet is similar to that of an underexpanded circular jet, but its directivity is different in both planes. Screech radiation is dominant in the minor axis plane.

5. Conclusions

The acoustic analysis of an elliptic pipe jet shows that screech occurs at R = 4 and can be found up to a maximum of R = 6 in the case under consideration. The screech frequency is found to decrease with the pressure ratio and is evident in both planes. The SPL spectrum shows the screech and BSAN along with mixing noise. The SPL spectrum is different among the planes for R = 4 to 6. A high-frequency second harmonic tone can be found for R = 4 at ϕ = 90° only. The screech amplitudes are dominant at ϕ = 45° and 60° as compared to 75° and 90°. Overall, the screech behavior is found to be similar to that of a circular jet, but the directivity is different among the two planes.