PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

AN EXPERIMENTAL STUDY ON AEROACOUSTICS AND SHOCKDYNAMICS ASSOCIATED WITH HARTMANN WHISTLE
Sonu THOMAS1; K SRINIVASAN2
1

Indian Institute of Technology Madras, India

2

Indian Institute of Technology Madras, India

ABSTRACT
Experiments are conducted to study the mechanisms involved in the workings of a cylindrical Hartmann
whistle at two different NPRs. The focus is more on the shock dynamics associated with the Hartmann
whistle phenomenon. The sound field of the order of 130 dB is produced. Distinct peaks are observed at thefundamental frequency as well as the higher harmonics. The relationship between the flow pattern seen form
Schlieren data with the acoustic measurements is highlighted. The cavity gas oscillation and the high speed
Schlieren data showed the non-sinusoidal movement pattern of the stand-off shock. The static pressure
variation in an under-expanded jet is found to be responsible for non-sinusoidal shock movement.
Keywords: Hartmann whistle, Shock-dynamics, resonance

1INTRODUCTION

Hartmann whistles have been a subject of investigation for almost a century now. Hartmann whistle
consists of a sonic under-expanded jet impinging on the open end of a cavity, placed in line with theaxis of the jet. When the open end of the cavity is kept at certain regions of the under-expanded jet,strong flow oscillations occur. The regions where these strong oscillations occur are termed as regionsof instability, which was explained by Smith and Powell (1,2). These devices are used to produce
strong unsteady flow fields and high temperature at closed end. Since these devices employ
no-moving-part, it is more reliable and safe to operate. These devices are also capable of producing
resonance induced heating attending around 1000 K, which can be used for heating related
applications. In few literatures, this device is also referred to as the Powered Resonance Tube(PRT) (3–5), as the power source is the constant high pressure air supply. Sarohia and Back (6)identified the different operational modes of Hartmann whistle; namely, jet instability mode, jetregurgitant mode, and jet screech mode. In the case of an under-expanded jet, the ‘jet regurgitant mode’is usually in operation. The strong oscillations thus caused produces high intensity acoustic radiationof discrete nature. These devices can be tuned to any desired frequency. The resonance frequencies arestrong function of the geometry of the Hartmann whistle, especially the length of the tube. Raman andco-workers (3,5,7) have used resonant acoustics produced by Hartmann whistle in Active Flow
Control (AFC) applications. Raman and Srinivasan (4) gave a comprehensive review that includes
plethora of work done over a period of 90 years. Sreejith et al. (8) studied the aero-acoustic aspects ofa conical Hartmann resonator and compared the results with a conventional cylindrical Hartmann
whistle. Recently, Narayanan et al. (9–13) conducted comprehensive studies to understand theinfluence of geometrical aspects affecting the aero-acoustic behavior (such as spectra and directivity)of the resonator. Narayanan et al. (14) also used the intense acoustic field produced by Hartmann
whistle to enhance the fuel droplet atomization. More recently, Lu and Liu (15) used forward facing
cavity (shaped like a Hartmann resonator) as part of the thermal protection mechanism in a hyper-sonicvehicle, to reduce heating. Huang et al. (16) showed that by using a forward facing cavity embedded in
the fore-body of a hypersonic vehicle, drag and stagnation point heat flux can be reduced. XinDong etal. (17) showed that the forward facing nose cavity can act as a thermal protection for a hypersonicvehicle.
1
2

sonuthomas9100@gmail.com
ksri@iitm.ac.in5391

Form the literature it is clear that, given that these find its use in many practical applications. Hence,
it is important to understand the underlying mechanisms involved Hartmann whistle operation. Thisunderstanding can used to tailor this device for a specific application. The intended work primarily
focuses on the study of the mechanisms involved in the Hartmann whistle working. In the present
study aspects like, acoustic data (spectrum and directivity), cavity gas oscillation and high speed
Schlieren flow visualization for a cylindrical Hartmann whistle are compared at two different Nozzle
Pressure Ratios (NPRs). The main intend of the present work is to understand the underlying physicsof such flows interacting with open-closed end cavity in detail. A detailed study of these aspects cangive a better physical understanding of the device Hartmann cavity performance.

2EXPERIMENTAL SETUP

2.1 Anechoic test facility and other arrangement
All the experiments are conducted in an anechoic test facility (see Figure 1). The anechoic
chamber has dimensions of 2.5 m x 2 m x 2 m (wedge tip-to-tip). The cut-off frequency of chamberis 700 Hz. High compressed air is delivered to the settling chamber at a pressure of 9 bar. The
upstream of the settling chamber is fitted with a moisture remover, an air filter, and a pressure
regulator. The air filter removes particles above 5-microns in size. The stagnation pressure inside thesettling chamber is controlled using pressure regulator valve. Flow conditioning meshes ofprogressive fineness are provided in the settling chamber to reduce the initial turbulence level.

Directivity
Measurement
Plane

Microphone

Jet
Orifice

120 deg
SettlingChamberHigh Pressure
SupplyR = 400mm

40 degHartmann
CavitySPressureRegulatingValve

D

EntrainedAirPressure
Gauge

ExhaustAirLZY
Three Axis
X Traverse

Figure 1 – Schematic of the anechoic test facility and experimental setup
The experimental setup (see Figure 1) also consists of an under-expanded jet issuing from a
10 mm orifice diameter, impinging on Hartmann cavity. Provision is made to connect a dynamic
pressure sensor at the closed end of Hartmann cavity. The entire Hartmann test setup is bracketed on acompound rest, which had movement control in all three axes direction. Angular traverse mountedwith a microphone is used to measure the directivity of the sound field at different emission angles.
The angle is varied from 40° to 120° in steps of 5°. The 0° coincides with jet axis direction. Figure 2
shows the picture of the setup kept in the anechoic facility.

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Jet Orifice

Hartmann Cavity

Dynamic Pressure
SensorFigure 2 – Photograph of the Hartmann whistle set-up kept in an anechoic chamber
2.2

Hartmann whistle geometry
Table 1 – The Hartmann cavity geometry and other dimensions
NPR

Separation (S), mm

Length (L), mm

Diameter (D), mm

3.01645

115.03245

11Table 1 gives the details of Hartmann cavity geometry. It also gives the separation (S) between thejet orifice and the mouth of the cavity. The mouth of the cavity is kept at the end of the second sho ck
cell of the under-expanded jet. As the NPR increases the shock cell length increases, which in turnresults in increased separation. It is important to place the mouth of the Hartmann cavity at these
specified locations in order for it to operate. These locations are often termed as regions of instability
in literature (1)2.3 Instrumentation
Far-field acoustic pressure is measured using a 1/4-inch pre-polarized microphone (PCB Model378C01). The sensitivity of the microphone is 2 mV/Pa at 250 Hz. A piezoelectric sensor (PCBModel 113B27) is used to measure the gas oscillation pressure at the closed end of the cavity. The
far-field acoustic and gas oscillation signals are acquired at a sampling rate of 250 kS/sec. Themicrophone has a flat response in the frequency range of 4 Hz to 70 kHz, within 1 dB variation. Apistonphone (B&K Type 4228) is used to calibrate the microphone, at 250 Hz and 124 dB. The dataacquired is low-pass filtered at 70 kHz using an analog filter (Krohn-Hite Model 3364) to avoidaliasing. A 16-bit resolution, 8-channel data acquisition board (National Instruments PCI-6143) isused to acquire the data. Measurements of pressure inside the settling chamber is monitored by aBourdon gauge. The reference pressure used to calculate SPL and OASPL is 20 μPa. The uncertainty
in SPL calculations is within ±1 dB. The microphone angle measured, has an uncertainty of ±1° inthe directivity experiments. The error in axial static pressure measurement probe location is ±0.1 mm.
Schlieren flow visualization technique was used to study the shock dynamics. High speed Schlieren
images were captured using Phantom v1212 high speed camera at the frame rate of 40,000 Hz.

3RESULTS AND DISCUSSION

3.1 Schlieren Flow Visualization Data
Figure 3 shows a Schlieren image encapsulating all the flow features of the Hartmann whistle
phenomenon. It shows the under-expanded jet emanating from the orifice impinging the mouth of theHartmann cavity axially. The complicated flow interaction of jet with the mouth of the cavity can alsobe seen. Also, since the mouth is place in the expansion region of the under-expanded jet we can see astand-off shock upstream of the Hartmann cavity mouth. The oscillation of this stand -off shock is5393

responsible for the intense sound produced by this device. High speed images capture this shock
dynamics more clearly.
Hartmann Cavity
Mouth
Jet Orifice

Under-expanded
Under-expanded
Jet JetFigure 3 – The Schlieren image showing the complicated flow aspects involved in the operation of Hartmanncavity
3.1.1 NPR 3.0
Figure 4 (a) and (b) shows the high speed image sequences for the compression and expansion
cycle, respectively. Compression cycle here is indicated by the movement of the stand -off shock
towards the mouth of the Hartmann cavity (downstream direction). On the other hand, the expansion
cycle is indicated by the movement of the stand-off shock away from the mouth of the Hartmann cavity(upstream direction). The inset number on each image refers to the frame number in the image
sequence. Frames 244 and 258 represent the starting and ending of the compression cycle. E ach
successive frame is separated by 25 µsec, hence the time taken for compression cycle is 350 µsec.
Frames 259 and 269 represent the starting and ending of the expansion cycle. These frames areseparated by 250 µsec. It can be clearly seen that the compression cycle takes more time than theexpansion cycle. This is due to the non-sinusoidal static pressure variation in an under-expanded jet.
One full cycle takes around 600 µsec to complete which corresponds to a frequency value of 1.666 Hz.
An interesting thing to note here is, the stand-off shock merges with the 1 st shock cell when it moves inthe upstream direction.

244

253

247

250

259

261

263

256

258

265

267

269

(a)

(b)

Figure 4 – High speed Schlieren sequence images for NPR = 3.0 (a) compression and (b) expansion cycles
3.1.2 NPR 5.0
Figure 5 (a) and (b) shows the high speed image sequences for the compression and expansion
cycle, respectively. The inset number on each image refers to the frame number in the image sequence.
Frames 87 and 104 represent the starting and ending of the compression cycle. Each frame is separated
by 25 µsec, hence the time taken for compression cycle is 425 µsec. Frames 105 and 115 represent thestarting and ending of the expansion cycle. These frames are separated by 250 µsec. It can be clearlyseen that the compression cycle takes more time than the expansion cycle. This again is due to thenon-sinusoidal static pressure variation in an under-expanded jet. One full cycle takes around 600 µsec
to complete which corresponds to a frequency value of 1.481 kHz. Unlike NPR 3.0 case, here thestand-off shock does not merge with the 1 st shock cell when it moves in the upstream direction.

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Another, interesting observation is that the expansion cycle takes the same amount of time, whereas
the compression cycle in NPR 5.0 case takes longer time than NPR 3.0 case.

87

91

95

99

102104(a)

105

107

109

111

113115(b)Figure 5 – High speed Schlieren sequence images for NPR = 5.0 (a) compression and (b) expansion cycles
3.2

Sound Pressure Level (SPL)140
NPR 3.0130

SPL (dB/Hz)

SPL (dB/Hz)

130

140
1.526 kHz

12011010090

NPR 5.01.404 kHz120
110
100

0.5

11.522.5
Frequency (Hz)(a)33.5

44x 10

900.5

11.5
22.5
Frequency (Hz)33.5

44x 10(b)Figure 6 – Sound Pressure Level (a) NPR = 3.0 and (b) NPR = 5.0
SPL is measured at distance 40 times the jet orifice diameter (R=400 mm). These measurements
can be safely assumed to be in the far-field where plane wave assumption is valid. Figure 6 (a) and (b)shows the SPL measured at 90 deg and 400 mm from the orifice center, at two different NPRs 3.0 and5.0, respectively. The Hartmann whistle clearly shows distinct peaks in the spectrum. The fundamental
mode frequency corresponds to 1.526 Hz and 1.404 kHz respectively. The frequency obtained is closer
to the quarter-wave-tube frequency. When compared to NPR 3.0 case, the frequency of oscillation islesser for NPR 5.0, which is also corroborated by the frequency data obtained from high speed
Schlieren images.

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3.3 Overall Sound Pressure Level (OASPL): Directivity
Figure 7 (a) and (b) shows the directivity (OASPL) at different emission angles at NPR = 3 and 5,
respectively. We can see that there is very little change in directivity at different emission angles. TheOASPL data is not available for angles below 40° and above 120° at a radius of 400 mm. Below 40° thejet will impinge on the microphone which can damage the sensor, whereas beyond 120° the sensor is in
the shadow of orifice, hence measurements were limited between 40 deg-120 deg. It can be clearlyseen that the maximum directivity occurs around 40 deg, which is in the downstream direction. Thisobservation is consistent with early findings (11).

(a)(b)Figure 7 – Directivity (a) NPR = 3.0 and (b) NPR = 5.0
3.4 Cavity Gas Oscillations
The pressure at the closed end of the Hartmann cavity was measured. The closed end pressure
would mimic the gas oscillation inside the cavity. Figure 8 shows the gas oscillation pressure at theclosed end of the cavity at NPRs 3.0 and 5.0, respectively. For NPR 3.0, expansion cycle takes around
380 µsec and compression cycle takes around 240 µsec. For NPR 5.0, expansion cycle takes around
432 µsec and compression cycle takes around 288 µsec. For both the NPRs the expansion cycle takes
more time than compression cycle. This is due to the non-symmetry in the static pressure variation inunder-expanded jets. The time taken for compression and expansion cycle matches well with thatfound using high speed Schlieren data, for both the NPRs.

40

40

20

2000(a)Amplitude (kPa)60

100 100
NPR NPR
3.0 3.0-20 -20(b)
80

60

60

40

40

202000(b)NPR NPR
5.0 5.0-20 -20-40 -40-40 -40-60 -60

80

Amplitude (kPa)

80
(a)
60

Amplitude (kPa)

Amplitude (kPa)

80Compression
Cycle-60 -60

ExpansionCycle-80 -800.50050.50150.50250.5 0.50.50050.5010.501
0.50150.5020.502
0.50250.5030.503
TimeTime(s) (s)-80-80 Compression

Cycle

Expansion
Cycle-100 -1000.50050.50150.50250.5 0.50.50050.5010.501
0.50150.5020.502
0.50250.5030.503
Time(s)Time(s)Figure 8 – Gas oscillations inside the cavity (closed end) (a) NPR = 3.0 and (b) NPR = 5.05396

4CONCLUSIONS

Experimental study was conducted on a cylindrical Hartmann whistle to understand the shock
dynamics associated with it. The aero-acoustic performance is measured in terms of SPL and OASPL,
at two different NPRs. Intense sound field of the order of 130 dB is produced at both NPRs. Maximum
directivity occurs at 40 deg. It was found that, the resonance frequency at NPR 5.0 is less than that atNPR 3.0. All the data from high speed Schlieren, the microphone and the piezoelectric sensor at theclosed end, matched very well.
The aero-acoustic data presented n this study is mixed with the jet noise data. Hence, it is difficult
to comment on the resonance quality based on the aero-acoustic data alone. In the present study, theflow imping on the cavity is just little above sonic. Since, some of the applications of this cavity can befound in hypersonic vehicle fore-body, it would be interesting to do similar studies at high supersonic
Mach numbers. Also, it would be interesting to study Hartmann cavities with different internal
profiles.

ACKNOWLEDGEMENTS
We are grateful to Prof. Baburaj A. P, for lending us the high speed camera used in this study, whichwas funded by the grant Sr/FST/ ETII-064/2015 from DST, Government of India.

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