Background-oriented schlieren of entropy waves advected in straight duct
Markus WEILENMANN(1) , Yuan XIONG(1) , Nicolas NOIRAY(1)(1) CAPS Laboratory, Mechanical and Process Engineering Department, ETH Zürich, Switzerland, noirayn@ethz.ch

Abstract
Entropy waves generate indirect combustion noise when accelerated in the turbine stages of aeroengines. This
indirect combustion noise constitutes a signiﬁcant part of the overall combustion noise. In addition, the indirect combustion noise from entropy waves can constructively interact with ﬂame and induce high amplitude
self-sustained oscillations. A deep understanding of the advection and dispersion of entropy waves is therefore
important for the prediction of noise emissions and thermoacoustic instabilities. This experimental study contributes to that goal: a highly turbulent airﬂow in a rectangular duct at ambient temperature is subject to theforcing of a siren supplied with hot air. This pulsed hot-jet-in-cold-crossﬂow yields coherent entropy waves,which are advected through the channel. The line-of-sight integrated temperature amplitude and phase are measured using high-speed Background-oriented Schlieren (BOS), thermocouples and simultaneous particle image
velocimetry (PIV). This non-invasive method facilitates the observation of low amplitude temperature ﬂuctuations at high frequencies, with a simple and inexpensive setup.
Keywords: Sound, Entropy waves

1

INTRODUCTION

Combustion systems in general, but gas turbines and aero-engines in particular, are prone to combustion noise thatcomprises two components: direct combustion noise and indirect combustion noise. The direct component originatesfrom the unsteady volume expansion caused by ﬂuctuating heat release of non steady ﬂames [1, 11, 2], that are present
in all gas turbine applications. The unsteady heat release also modulates the temperature of the exhaust gas stream
and therefore creates hot pockets which are advected downstream with the ﬂow. These travelling temperature waves
are generally referred to as Entropy Waves [7]. When they are accelerated in a nozzle, or for example a turbine inlet,
indirect noise is generated [6]. To correctly predict indirect noise, it is of great importance to understand and quantify
the dispersion of entropy waves during their advection in the combustion chamber. Recently, signiﬁcant effort was
put into the modeling of such decay processes [5, 8]. The goal of this work is to measure such entropy waves during
the advection process.

2

EXPERIMENTAL SETUP

2.1 Test rig speciﬁcations
The ETH high-speed test rig is a non-reactive air wind tunnel with rectangular cross-section depicted in ﬁgure 1. A
compressor is supplying dry air at a maximal mass ﬂow of 240 g/s at 5.5 bar. For this study, the test rig was operated
at a static pressure of around 1.3 bar. The channel has an inner height of H = 57mm and a width of W = 25mm.
Optical access is available in the test section from the top and the side using borosilicate windows.
Entropy waves are generated by a siren upstream of the test section. The siren consist of a rotating perforated disk andan electric heater, as schematically drawn in ﬁgure 2. The modulation frequency of this pulsed hot jet-in-crossﬂow
is controlled by adjusting the rotational velocity of the disk. The temperature is controlled by thermostat, monitoring
the temperature downstream of the heating element. The generated entropy waves are then advected to the test section
where the optical measurements are performed. The walls of the siren are isolated while the main channel is exposed
to natural convection of the surrounding air at room temperature.

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a) Top view

Heaterb) Side view

Light source
BOS pattern

Siren

Thermocouple

Thermocouple

Piezo sensor

Scheimpflug

BOS
CameraTelecentric lenssystemLaser light

Figure 1. Experimental setup 


 




Figure 2. Siren operating principle
2.2 Instrumentation
To obtain the desired high-speed temperature measurements, a background oriented schlieren (BOS) system with
telecentric optics was mounted perpendicular to the ﬂow direction, as shown in ﬁgure 1 a). To avoid the strong
mechanical vibrations induced by the siren, the BOS camera (Photron HSSX) plus optics (2 simple plano-convex
lenses, Thorlabs LA1979 and Eksma 110-0730E), background pattern and light source (HARDsoft IL-106) wereattached to one single optical rail that was isolated using passive pneumatic vibration dampers (Thorlabs PWA074).
A second high-speed camera to do PIV was placed on a tripod in the same hoizontal plane as the BOS system. The
ﬁeld of vew (FOV) was adjusted to match the BOS one and the tilted focal plane was corrected using a Scheimpﬂug.
The PIV camera was equipped with a Nikon AF 200mm micro Nikkor lens and a 532nm bandpass ﬁlter from Edmund
Optics. A Photonics DM60 Nd:YAG was used to generate a pulsed 532 nm laser light sheet that was introduced in
the center of the channel from the top using a laser arm and sheet optics from Lavision.
To capture the mean temperatures of the main ﬂow, the heated siren ﬂow and the vitiated ﬂow, thermocouples wereplaced at the three locations speciﬁed in ﬁgure 1 b). Additionally, a differential static pressure probe was placeddownstream of the test section and the current ambient air pressure was noted during the experiments.

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3

EXPERIMENTAL METHODOLOGY

3.1 Telecentric BOS
Telecentric BOS relies on the same principles as conventional BOS [10], which is the bending of light rays in nonhomogeneous media due to spatial gradients in refractive index, but brings the advantage of increased depth of ﬁeld
and parallel projection of the background through the observation area and therefore also higher accuracy [9]. The
setup consist of a high-speed camera, 2 convex lenses with focal lengths f 1 and f 2, an aperture, a luminous lightsource and pattern of randomly placed dots. Such a setup is schematically drawn in ﬁgure 3, where Zd is the distance
between the background plane and the center of the observation area, Za the distance between the center of the observation area and Lens 1. The aperture is placed in between Lens 1 and Lens 2 where the distances between the lenses
and the aperture are determined by the lenses focal lengths f 1 and f 2. This allows to block most of the non-parallel
light [9] and therefore increases the depth of ﬁeld and ensures parallel projection of the background pattern throughthe observation area. With smaller aperture, depth of ﬁeld increases, but the light intensity on the camera sensor
decreases. Only a small fraction of the light is parallel or close to parallel, therefore a strong light source is neededalong with a compromise on depth of ﬁeld. This is quantiﬁed in more detail below.
Without being deﬂected by an inhomogeneous media in the observation area, a light ray may travel from the background pattern to the camera sensor via the path depicted by a dashed line in ﬁgure 3. If gradients in refractive index
are present, the light ray is deﬂected by an angle ε. BOS is a line-of-sight integrated method, which means that ε canonly be related to line-of-sight integrated gradients in refractive index n as shown in equation 1 [12], where s and q are
the local coordinates tangential and perpendicular to the light ray and n0 is the refractive index at room temperature.
ε=

1
n0



dn
ds
dq

(1)

Assuming a two-dimensional ﬂow and small deﬂection angles, the deﬂection angle in y direction εy can be expressedas shown below with W being the thickness of the ﬂow.
εy =

W ∂n
n0 ∂ y(2)

Since we are assuming small deﬂection angles, we can also relate the deﬂection angle to the apparent displacement
Δy of the background pattern using equation 3.
εy = tan(

Δy
Δy
)≈
Zd
Zd

(3)

Combining equations 2 and 3 and considering deﬂection in x direction analogously, expressions for the ﬁrst spatial
gradients of refractive index as a function of the apparent pattern displacement are obtained:∂ n n0 Δx=∂ x W Zd
∂ n n0 Δ y=∂ y W Zd

(4)

Since we can assume parallel projection in this telecentric optical system, the scaling between background and image
sensor plane is deﬁned only by the focal lengths f 1 and f 2 of the two lenses [9]. 3.
f 2 Δy== Mtelef 1 Δy(5)

Practically, correct scaling is ensured using a calibration target on the background plane and the displacement Δy
is obtained directly using the cross-correlation algorithm of Lavision DAVIS 8.4. Classically, the BOS methods

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Light Source

Entropy wave

Backgroundο௬Lens 1

Aperture

Lens 2

Camera Sensor

ߝ

οᇱ௬
y
z

ܼௗ

݂ଵ

ܼ௔

݂ଶ

݈௜

Figure 3. Telecentric BOS principle
requires a reference image of the background taken with clean optical path, meaning a homogenous medium inthe observation area and therefore ε = 0. This reference is then compared to snapshots later in time using crosscorrelation when the optical path is affected by refractive index gradients. In highly vibrating environments andthermally unsteady experiments this can be a problem because high bias errors arise [13]. Even in a less harshexperimental environment, so called spurious displacements [14] can cause signiﬁcant errors in the displacement
quantiﬁcation. Overall it is best to minimize the time between the recording of the reference image and the actual
measurement. In this work, only moving fast moving gradient structures are considered, therefore a different strategy
is employed. For each measurement, data sets of 5000 images were recorded at a frame-rate of 12.5 kHz and an
average image was calculated to serve as reference. The slight blurriness resulting from this strategy was handled
well by the cross-correlation algorithm.
The δx and δy ﬁelds were calculated employing a multi-pass strategy with decreasing correlation window size of 48 by
48 pixel with 75% overlap in the ﬁrst pass and 16 by 16 pixel with 50% overlap in the second pass. Despite the very
luminous LED light source (Model IL-106, HARDsoft Inc.), there is a trade-off between gathering enough light andimproved depth of ﬁeld due to a small aperture. An aperture diameter of d = 4 mm was found to allow for sufﬁcient
illumination even at this high frame-rate.
3.2 Processing
The telecentric BOS system described in section 3.1 yields instantaneous displacement ﬁelds Δx and Δy of the camera
FOV. Using the velocity information obtained by PIV, these ﬁelds are spatially connected since the frame-rate is
sufﬁciently high to have overlapping
areas within the individual snapshots. Figure 4 a) shows such snapshots of thethe total displacement Δxy = Δ2x + Δ2y . Visually it is already obvious that there is signiﬁcant overlap between theindividual frames since the gradient structure that is advected through the FOV has an almost identical shape in all
the displayed snapshots. The overlap d(φ ) is estimated using a phase-averaged spatial average of the axial velocity
at this instant. In the next step the overlapping areas are continuously averaged, as displayed in ﬁgure 4 b). Since theaxial velocity is not constant over the acoustic cycle, the overlap d varies as well. This process is repeated over all
available acoustic cycles to get the displacement ﬁeld depicted in ﬁgure 4 c). Since the overlap is not constant, but
the phase angle increases linearly with time, new coordinates x̃ and ỹ are needed:x̃ = xs +

T0
2π

 φ
0

ũ(φ )dφỹ = ys

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(6)

‫ݔ‬௦

‫ ݐ‬ൌ ‫ݐ‬ଵ ൅ ͵ο‫ݐ‬‫ ݐ‬ൌ ‫ݐ‬ଵ ൅ ʹο‫ݐ‬

‫ݔ‬௦

‫ݔ‬௦

‫ݔ‬௦

‫ݔ‬௦

݀ሺ߮ሻ ൌ ‫ݑ‬ሺ߮ሻ ȉ ο‫ݐ‬

‫ݕ‬෤

݀

‫ ݐ‬ൌ ‫ݐ‬ଵ ൅ Ͷο‫ݐ‬

‫ݕ‬௦

‫ݕ‬௦

‫ݕ‬௦

‫ ݐ‬ൌ ‫ݐ‬ଵ ൅ ο‫ݐ‬

‫ݕ‬௦

‫ݕ‬௦

‫ ݐ‬ൌ ‫ݐ‬ଵ

‫ݕ‬෤

‫ݔ‬෤

‫ݔ‬෤

Figure 4. a) Instantaneous displacement ﬁelds of camera FOV b) Using the velocimetry data obtained by PIV, anoverlap is calculated and the displacement ﬁelds are stacked on top of each other accordingly. In the overlapping area,
the displacement ﬁelds are averaged. c) Resulting phase-averaged displacement ﬁeld representing one acoustic cycle(here 240 Hz)
The displacement ﬁelds obtained by applying this method represent the phase-averaged mean of an entire convective
wavelength, but captured sequentially at the camera position since the FOV is not wide enough to capture an instantaneous convective wave in one shot.
The same approach may also be used with instantaneous velocity data to get several instantaneous cycles. The axial
coordinate would in that case change to:x̃inst = xs +tu(t)dt(7)

0

To further process the obtained gradient ﬁelds, one needs to perform 2D spatial integration. This can be achieved bysolving the system shown in equation 4. In this study the integration was done by taking the partial derivative in x andy respectively and adding the 2 equations which results in equation 8∂ 2n ∂ 2nn0  ∂ Δx ∂ Δy ++=
∂ x2 ∂ y2 W Zd ∂ x∂y(8)

The two dimensional line-of-sight integrated refraction index ﬁeld can then be obtained using a poisson solver.
[14] The line-of-sight integrated density is obtained via the Gladstone-Dale equation shown below with G being
the Gladstone-Dale constant [3].
n−1
(9)
ρ=
G
Using the ideal gas law, one can then calculate the line-of-sight integrated temperature ﬁeld, using the gas constant of
air R and the static pressure ps .
ps
T=
(10)
ρR

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4

RESULTS

4.1 Temperature and Mie scattering ﬁelds
Experiments were conducted at various excitation temperatures and frequencies. The mass ﬂow rate of the cold main
ﬂow was kept at 150 g/s, while the overall mass ﬂow of the oscillating hot jet-in-crossﬂow was kept at 10 % of themain ﬂow. The temperature of the hot jet-in-crossﬂow was varied from 321K to 519K while the cold main ﬂow was
kept at 300K. Figure 5 shows the obtained line-of-sight integrated temperature ﬁelds for two siren frequencies andﬁve amplitudes each. The increase in excitation temperature is easily visible, which is a good indication that thepresented results are physical and entropy waves survive the advection process from siren injection to the test section.
This also means that these waves would be relevant for indirect noise production, if an area change would be added
to the channel. To support the claim of having measured the entropy waves correctly, the same processing algorithmb)

480 HzExcitation temperature

a)

min

max

min
min

max
max

240 HzExcitation temperature

[K]

[K]

Figure 5. a) Phase-averaged amplitude ﬁelds of the ﬂuctuating temperature component for increasing siren amplitudes
and two frequencies b) Phase-averaged Mie scattering images
detailed in section 3.2 was applied to the Mie scattering images of the seeded ﬂow, recorded to perform PIV. Since
only the cold main ﬂow was subject to particle seeding, one can qualitatively identify hot regions by looking at theintensity of this Mie scattering signal. Low luminosity corresponds therefore to a hot region and higher higher luminosity to a colder region where less or no mixing with the hot air, injected by the siren, has happened. The resultspresented in ﬁgure 5 b) are in good agreement with the BOS results.

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4.2 Validation against LES
To validate the measured temperature amplitudes, large-eddy simulations (LES) were performed using the explicit
parallel code AVBP [4], employing the second order numerical scheme Lax-Wendroff. Five simulations with similar
conditions for mass ﬂows, temperatures and pressure were performed in a domain representative of the experimental
facilities. The intention was not to achieve a perfect match, but to show that the obtained BOS results are reasonable.

Figure 6. Phase-locked amplitudes of temperature obtained by experiments and LES as a function of Strouhal number
Figure 6 shows phase-locked amplitudes of the line-of-sight integrated temperature, extracted from the LES, as afunction of the Strouhal number Str = fu¯·Lc . L respresents the axial distance from the siren injection hole, f theexcitation frequency and u¯a the average advection velocity present in the channel. The agreement for low Str is quite
good, but at higher Str, the LES consequently predicts a higher temperature ﬂuctuation amplitude. This experimental
method relies on spatial integration, which increases the difﬁculty to get a clean measurement when spatial separationof the entropy waves becomes smaller. This is the case for high Str numbers, especially since these points were
measured using a higher excitation frequency, rather than increased distance. A large variation of L is difﬁcult toachieve with this experimental facility, because the optical access is limited to the test section.
This issue and also the shape of the amplitude decay in the LES will be discussed in depth in a separate publication.

5

CONCLUSION

An experimental method to measure the temperature amplitude of advected entropy waves in the region of several
hundred Hz has been presented. The 2D distribution of line-of-sight integrated temperature agrees well with thequalitative information in the Mie scattering signal of the imaged seeding particles.
The agreement with LES is quite good for lower frequencies. In the higher frequency range further investigations areneeded. After the addition of a nozzle, the measured temperature ﬂuctuations will be used to study indirect noise,
which is the main motivation of the future work.

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