The effect of corrugation on the crackle noise in underexpanded

impinging jets

Debivarati Sarangi 1 TDCE Lab Department of Mechanical Engineering IIT Madras R Karthik 2 TDCE Lab Department of Mechanical Engineering IIT Madras K Srinivasan 3 Professor TDCE Lab Department of Mechanical Engineering IIT Madras

ABSTRACT

The present study investigates crackle noise of the impinging jet over the flat and corrugated plate. The experiments are conducted using a 10 mm diameter (d) orifice for jet production. The standoff distance is varied from 1.5d to 6d, incrementing 0.5d. The nozzle pressure ratio (NPR) is varied from 4 to 5.6 with a step size of 0.2. Results are discussed by plotting the probability density function of normalized pressure data and its derivative and the measured skewness values. For the flat plate, the positive skewed pressure data associated with strong compression and expansion is observed for all NPRs, and the skewness value fluctuates with the change in NPR. The crackle noise is absent in the corrugated plate for most NPRs and standoff distances, although it is observed within a short duration at some NPRs. In contrast, the crackle noise is persistent for the flat plate throughout the time range and is observed even the skewness of the normalized acoustic pressure exceeds the skewness of the derivative of acoustic pressure data.

1 debi.sarangi53@gmail.com 2 ME19D026@smail.iitm.ac.in 3 ksri@iitm.ac.in

1. INTRODUCTION

Crackle is present in the form of a wave of intermittent sharp compression followed by gradual expansion. The presence of crackle can be measured from the skewness value. The skewness value less than 0.3 is crackle-free for the jet [1]. In heated supersonic jets, the coalesce of Mach waves causes steepening of wavefronts in the near field, which exceeds a certain level produces crackle noise [2]. The design and underexpanded rectangular supersonic jet produces crackle noise when skewness value exceeds 0.4 and the propagation direction of peak skewness corresponds to the peak jet noise direction [3]. Waveforms with positive pressure skewness radiate in the upstream direction and the skewness of the time derivative of the pressure waveforms increases significantly with range, which indicates the formation of shocks during propagation [4]. Crackle is observed in the form of strong positive pressure impulses associated with N-shaped waveforms involving a shock like compression. Unlike broadband shock-associated noise which dominates at upstream angles, crackle noise dominates at downstream direction. There has been some debate about the mechanism by which N-shaped waves are generated. These waves are generated either directly by the supersonic jet itself, or they may be a result of nonlinear acoustic propagation. High-amplitude acoustic waves are subject to nonlinear propagation effects leading to wave steepening or wave-coalescence, which might at first seem to explain shock- like compressions associated with crackle [5]. According to Joseph et. al. the N-shaped waves are directly generated by the supersonic jet itself [6]. 2. EXPERIMENTAL SETUP Experiments are conducted for the flat plate and corrugated plate with pitch 63 mm by varying the standoff distance from 1.5d to 6d and nozzle pressure ratio from 4 to 6. The experiments are conducted in an anechoic chamber of size 2.5 m x 2 m x 2 m, as shown in Figure 1 (a). The chamber walls, roof, and door are made of plywood. The inner surfaces of the anechoic chamber are fixed with square pyramidal polyurethane foam wedges to create an acoustic free field. An orifice of 10 mm diameter is used to supply high-speed air for impingement. The impinging plates are made up of Aluminum and have a dimension of 315 x 315 mm as shown in Figure 1 (b). The acoustic data are measured using ¼- in. microphone (PCB 378C01), which is placed at a distance 50 d above the orifice center. The microphone is calibrated using a B&K piston phone type 4228 calibrator at 250 Hz and 124 dB. The sensitivity of the microphone used is 1.55 mV/Pa. The Nyquist criterion is satisfied by passing the signal through a low pass filter by maintaining the cut-off frequency as 70 kHz. The acoustic signals are acquired using the National Instruments data acquisition board (NI-PCI-6143). The settling chamber pressure is continuously monitored using a piezo-resistive pressure transducer (Endevco Model 8510C-100). The settling chamber pressure is monitored using a piezo-resistive transducer with an uncertainty of ±0.2% of full scale. The anechoic chamber environment temperature and relative humidity is almost constant during all the experiments. The reference sound pressure is 20 µPa. 3. RESULTS & DISCUSSIONS

The skewness of pressure data is plotted in Figure 2. The negative skewness value is observed for most of the NPRs and standoff distances for the corrugated plate. For the flat plate, positive skewness is observed for all cases. For the flat plate at standoff distance 1.5 the skewness value exceeds 0.4 for NPR 4.8, 5, 5.4 and 5.6. At standoff distance 2 the skewness value lies below 0.4. At standoff distance 2.5 the skewness value exceeds 0.4 for NPR 4, 4.2, 4.4, 4.8, 5, 5.4. At standoff distance 3 the skewness value exceeds 0.4 at NPR 4, 4.2, 5. At standoff distance 3.5 the skewness value rises above 0.4 for NPR 4.8 and 5. At standoff distance 4 the skewness value exceeds 0.4 for NPR 4.8, 5, 5.6. At standoff distance 4.5 the skewness value exceeds 0.4 for NPR 4.8, 5.6. At standoff distance 5, 5.5 and 6 the skewness

value falls below 0.4 for all NPRs. The skewness of derivative of pressure data is calculated further to analyze the presence of crackle noise as shown in Figure 3. The skewness of derivative of pressure data reduces significantly for the flat plate. The derivative of pressure data shows negative skewness for both the flat plate as well as the corrugated plate for most of the NPRs. (a) (b) (c)

1-Compressed air inlet, 2-Moisture remover, 3-Air Purifier/Filter, 4-Pressure regulating valve, 5-Bourdon Tube Pressure Gauge, 6-Settling Chamber, 7-Orifice, 8-Microphone, 9-Corrugated Plate, 10- Anechoic chamber

Figure 1: (a) Schematic representation of the experimental setup (b) Flat plate (c) Corrugated plate

Figure 2: Skewness of normalized acoustic pressure data

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Leer evsocron Corrugated plate (NPR 4) Flat Plate (NPR 4) Corugated plate (NPR 4.2) Flat Plate (NPR 4.2) Corrugated plate(NPR 4.4) Flat Plate(NPR 4.4) Corrugated plate (NPR 4.6) Flat Plate(NPR 4.6) Corugated plate(NPR 4.8) Flat Plate (NPR 4.8) Corrugated plate(NPR 5) Flat Plate (NPR 5) Corugated plate (NPR 5.2) Flat Plate(NPR 5.2) Corrugated plate (NPR 5.4) Flat Plate (NPR 5.4) Corrugated plate (NPR 5.6) Flat Plate (NPR 5.6)

Figure 3: Skewness of derivative of acoustic pressure data

Skewness of the derivative of pressure data increases for the corrugated plate at standoff distance 5, 5.5 and 6 for few NPRs. The observed maximum skewness value for this case is 0.158 at a standoff distance of 5 and NPR 4.8. It was believed that for the crackle to exist the skewness of derivative of acoustic pressure data should be greater than the skewness of acoustic pressure. But in this case crackle is observed even when the skewness of pressure data is more compared to the skewness of derivative of pressure data. The variation of normalized acoustic pressure data skewness values with respect to the NPR is plotted for different standoff distances, as shown in Figure 4. The flat plate shows positive skewness value for all standoff distances and at all NPRs. The corrugated plate shows positive skewness value at NPR 4 for the standoff distances 1.5 to 6 except standoff distances 3.5 and 5. At NPR 4.2 the corrugated plate shows negative skewness for all standoff distances except standoff distance 1.5. At standoff distance 1.5 for the corrugated plate the skewness value decreases up to NPR 4.4. It again increases at NPR 4.6. At NPR 4.8 a trough is observed in the skewness plot. At NPR 5 it again increases beyond which it shows a reducing trend. For the flat plate the skewness value decreases up to NPR 4.4 beyond which it increases up to NPR 4.8. The skewness value decreases up to NPR 5.2. It increases at NPR 5.4 and reduces at NPR 5.6. At standoff distance 2 for the corrugated plate the skewness value reduces up o NPR 4.4 beyond which it increases up to NPR 5.2. It reduces at NPR 5.4 and increases at 5.6. For the flat plate large fluctuation in the skewness value is observed at this standoff distance. At standoff distance 2.5 the skewness value decreases up to NPR 4.4 for the corrugated plate. It again increases at NPR 4.6. At NPR 4.8 a trough is observed in the skewness curve. Beyond NPR 4.8 the skewness value shows increasing trend. The flat plate shows the reducing trend up to NPR 4.6. The skewness value increases at NPR 4.8 and reduces beyond this up to NPR 5.2. It again increases at NPR 5.4 and reduces at NPR 5.6. At standoff distance 3 the trough is observed in the skewness curve at NPR 4.2. It increases at NPR 4.4 and decreases beyond this up to NPR 5.2. It again increases at NPR 5.4 and reduces at NPR 5.8. For the flat plate trough is observed at NPR 4.4 and the skewness value increases beyond this up to NPR 5. At standoff distance 3.5 for the corrugated plate the peak is observed at NPR 4.6 and beyond this the skewness value reduces up to NPR 5.2. For the flat plate the trough is observed at NPR 4.4. The skewness value increases beyond NPR 4.4 upto NPR 5. At standoff distance 4 the trough is observed at NPR 4.2. The skewness value increases at 4.4 and reduces at NPR 4.6 beyond which it starts increasing up to NPR 5.2. For the flat plate at this standoff distance peak is observed at NPR 4.8 and trough is observed at NPR 5.2. At standoff distance 4.5 for the corrugated plate trough is observed at NPR 4.2. A trough is observed again at NPR 5. The skewness value increases at NPR 5.2 beyond which it reduces. For the flat plate at this standoff distance troughs are observed at NPR 4.4 and 5 and

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Leer evsocron Corrugated plate (NPR 4) Flat Plate (NPR 4) Corugated plate (NPR 4.2) Flat Plate (NPR 4.2) Corrugated plate(NPR 4.4) Flat Plate(NPR 4.4) Corrugated plate (NPR 4.6) Flat Plate(NPR 4.6) Corugated plate(NPR 4.8) Flat Plate (NPR 4.8) Corrugated plate(NPR 5) Flat Plate (NPR 5) Corugated plate (NPR 5.2) Flat Plate(NPR 5.2) Corrugated plate (NPR 5.4) Flat Plate (NPR 5.4) Corrugated plate (NPR 5.6) Flat Plate (NPR 5.6)

peak is observed at NPR 4.8. At standoff distance 5 for the corrugated plate the skewness value increases beyond NPR 4.2.

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j)

Figure 4: Skewness comparison at all NPR and standoff distances

It reduces at NPR 5 and again increases beyond this. For the flat plate at this standoff distance trough is observed at NPR 4.8 and peak is observed at NPR 5.2. At standoff distance 5.5 for the corrugated plate the skewness value increases upto NPR 4.4. It increases at NPR 4.6 beyond this it reduces up to NPR 5. It again increases at NPR 5.2 and reduces after this NPR. For the flat plate at this standoff distance peak is observed at NPR 4.6 and two troughs are observed at NPR 5 and 5.4. At standoff distance 6 the trough is observed at NPR 4.4. The skewness value increases upto NPR 4.8 and decreases at NPR 5. It again increases at NPR 5.2 and decreases beyond this. At NPR 4.2 at this standoff distance the skewness value of flat plate coincides with the corrugated plate. For the flat plate two troughs are observed at NPR 4.2 and 4.6 and maximum skewness is observed at NPR 5. For the flat plate the skewness value fluctuates more randomly compared to the corrugated plate at all NPRs and standoff distances. Probability density plot of normalized acoustic pressure data were analyzed further to investigate the presence of crackle noise at different NPR and standoff distances as shown in Figure 5. For the standoff distance 1.5 at NPR 4 and 4.2 the peak of PDF is observed to be more for the flat plate. At NPR 4.4 the peak of PDF reduces for the corrugated plate. At NPR 4.6 and 4.8 the peak increases for the flat plate again. At NPR 5 the peak increases significantly for the flat plate. At NPR 5.2 the peak again reduces for the flat plate. The peak again increases at NPR 5.4. At standoff distance 2 (not shown here) the peak of PDF is observed to be more for the corrugated plate at NPR 4, 4.2, 4.4, 4.6 and 4.8. At NPR 5 the peak increases for the flat plate. At standoff distance 2.5 at NPR 4 the PDF curve is positive skewed for the flat plate whereas it is negative skewed for the corrugated plate. The peak of PDF is observed to be more for the flat plate at NPR 4.2 and 4.4. At NPR 4.6 the peak increases for the corrugated plate. At NPR 4.8 the peak of PDF increases again for the flat plate. At NPR 5 the peak reduces for the flat plate as compared to NPR 4.8 but it is observed to be more in comparison to the corrugated plate. At standoff distance 3 (not shown here) the peak of PDF is observed to be more for the flat plate at NPR 4, 4.2 and 4.4. At NPR 4.6 the peak falls for the flat plate in comparison to the corrugated plate. The peak is observed to be more for the flat plate beyond NPR 4.6. At standoff distance 3.5 the peak of PDF is more for the corrugated plate at NPR 4. At NPR 4.2 the peak increases for the flat plate compared to the corrugated plate. At NPR 4.4 the peak of PDF is highest for the flat plate in comparison to all NPRs. The peak is more for the corrugated plate at NPR 5. The peak is observed to be more for the flat plate in comparison to the corrugated plate beyond NPR 5. At standoff distance 4 (not shown here) the peak of PDF is observed to be more for the flat plate at NPR 4.8, 5 and 5.4 in comparison to all NPRs. The PDF peak is observed to be more for the flat plate than the corrugated plate at all NPR except NPR 4 and 5.4. At NPR 4 and 5.4 the PDF of both the plates approaches to be same. At standoff distance 4.5 (not shown here) the peak is observed to be highest at NPR 5 for the flat plate in comparison to all NPRS. At NPR 4.8 the peak is less for the flat plate in comparison to the corrugated plate. At standoff distance 5 (not shown here) the peak of PDF is observed to be more beyond NPR 5 for the flat plate in comparison to all NPRs. The peak of PDF is more for the flat plate in comparison to the corrugated plate at all NPRs except NPR 4.8. At standoff distance 5.5 (not shown here) the peak is less for the flat plate at NPR 4.2 and 4.4 than the corrugated plate. The peak increases again for the flat plate beyond NPR 4.4 upto NPR 5. At NPR 5.2 and 5.4 the PDF plot merges for both the plates. At NPR 5.6 the peak of PDF is found to be more for the corrugated plate in comparison to the flat plate. At standoff distance 6 the peak of PDF is observed to be more for the flat plate at NPR 4. At NPR 4.2 the peak of PDF for the corrugated plate matches with the flat plate and both approaches Gaussian. At NPR 4.4 the peak reduces for both flat plate and corrugated plate and the peak of PDF for the flat plate reduces compared to the corrugated plate. At NPR 4.6 the peak of PDF for the corrugated plate increases compared to NPR 4.4. But the peak of the PDF for the flat plate is observed to be less compared to the corrugated plate. Beyond NPR 4.6 the peak of PDF for the flat plate is observed to be more compared to the corrugated plate. The derivative of PDF is plotted in Figure 6. This shows that

for the flat plate has less energy inside the tails. The PDF for the corrugated plate approaches near to the Gaussian distribution. The presence of less energy inside the tails signifies the presence of crackle when jet impinges on the flat plate [7]. The pressure spectrum is plotted further as shown in the Figure 7 to observe the presence of N-shaped sharp compression and gradual expansion in the waveform. Flat plate shows abrupt increase and decrease in pressure for maximum NPRs and at all standoff distances. The pressure signal for the flat plate shows fluctuation from the lower negative value to the higher positive value in the form of N-shaped compression and gradual expansion.

Figure 5: PDF of normalized acoustic pressure data (a) Sod 1.5 (b) Sod 2.5 (c) Sod 3.5 (d) Sod 6

Figure 6: PDF of derivative of acoustic pressure data (a) Sod 1.5 (b) Sod 2.5 (c) Sod 3.5 (d) Sod 6

(a)

(b)

Figure 7: Pressure spectra at NPR 4.4 and standoff distance 3.5 (a) Flat plate (b) Corrugated plate

4. CONCLUSION The experiments were conducted to investigate the presence of crackle noise for the orifice jet upon impingement over the flat and corrugated geometry. The standoff distance is varied from 1.5d to 6d, incrementing 0.5d. The nozzle pressure ratio (NPR) is varied from 4 to 5.6 with a step size of 0.2. Results were discussed by plotting the probability density function of normalized pressure data and its derivative and the measured skewness values. For the flat plate, the positive skewed pressure data associated with strong compression and expansion is observed for all NPRs, and the skewness value fluctuates randomly with the change in NPR. The crackle noise is absent in the corrugated plate for most NPRs and standoff distances, although it is observed within a short duration at some NPRs. The PDF of normalized acoustic pressure data approaches Gaussian for the corrugated plate for most of the NPRs whereas; it deviates from the Gaussian for the flat plate. N-shaped sharp compression with gradual expansion is observed for the flat plate in the pressure spectra. 5. REFERENCES

[1] Ffowcs Williams, J. E., Simson, J. V., Virchis, J., Crackle : an annoying component of jet noise,

Journal of Fluid Mechanics , 71( 2), 261-271 (1975). [2] Nichols Joseph W., Lele Sanjiva K., Ham Frank E., Martens Steve, Spyropoulo John T.,

Crackle Noise in Heated Supersonic Jets, Journal of Engineering for Gas Turbines and Power , 135, 051202-1-7 (2013). [3] Mora Pablo, Kastner Jeff, Heeb Nick, Munday David, Gutmark Ephraim J., Liu Junhui,

Kailasanath, K., The Impact of Heat on the Near and Far-Field Pressure Skewness in Supersonic Jets, 50th AIAA Aerospace Sciences Meeting , pp. 1-12 (2013). [4] Paul B. Russavage, Tracianne B. Neilsen, Kent L. Gee and S. Hales Swift, 2018, “Rating the

perception of jet noise crackle,” Proceedings of Meetings on Acoustics, 175th Meeting of the Acoustical Society of America, Vol. 33, pp. 1-13 [5] Anderson, A. T., Freund, J. B., Source mechanisms of jet crackle , American Institute of

Aeronautics and Astronautics , 2012-2251 (2012). [6] Nichols Joseph W., Lele Sanjiva K., Spyropoulos John T., The source of crackle noise in heated

supersonic jets, American Institute of Aeronautics and Astronautics , 19th AIAA/CEAS Aeroacoustics Conference, 1-13 (2013). [7] Punekar, J. N., Avital, E., Li, X., Experimental investigation of nonlinear properties of crackle

and screech in supersonic jets, Journal of The Acoustical Society of America , 141 (6), EL567- EL573, (2017).