scispace - formally typeset

Proceedings ArticleDOI

Estimation of convection speed in underexpanded jets from schlieren pictures

30 May 2016-pp 1-14

Abstract: In this paper, the quality of the estimation of the convection velocity in jet shear layers using schlieren pictures is investigated. The aim is to discuss whether the convection velocity is likely to be biased if determined from schlieren images obtained at a high framerate, as in previous experiments using the phase shift method. For this, a numerical procedure is developed in order to generate schlieren-like images on the basis of simulation data, and applied to the results provided by the large-eddy simulation (LES) of an under-expanded round jet at an ideally expanded Mach number of 1.56. The results obtained from the schlieren pictures are compared with those obtained directly from the LES density fields. It is notably found that the location of the maximum of gray level fluctuations in the schlieren pictures corresponds well to that of the maximum of density fluctuations, and that the convection velocity estimated for low frequencies using schlieren pictures is underestimated for small separation distances between the two points used for the phase shift calculation.
Topics: Schlieren (65%), Jet (fluid) (51%)

Content maybe subject to copyright    Report










          


 






 
an author's
https://oatao.univ-toulouse.fr/27038
https://doi.org/10.2514/6.2016-2984
Castelain, Thomas and Gojon, Romain and Mercier, Bertrand and Bogey, Christophe Estimation of convection speed
in underexpanded jets from schlieren pictures. (2016) In: 22nd AIAA/CEAS Aeroacoustics Conference, 30 May 2016 -
1 June 2016 (Lyon, France).

Estimation of convection speed in underexpanded jets
from schlieren pictures
Thomas Castelain
1,2,
, Romain Gojon
1,
, Bertrand Mercier
1,
& Christophe Bogey
1, §
1- Univ Lyon, Laboratoire de ecanique des Fluides et d’Acoustique, UMR 5509,
´
Ecole Centrale de Lyon, 36 av. Guy de Collongue, F-69134 Ecully C´edex, France
2- Univ Lyon, Universit´e Lyon 1, 43 Bd du 11 Novembre 1918, F-69622 Villeurbanne edex, France
In this paper, the quality of the estimation of the convection velocity in jet shear layers
using schlieren pictures is investigated. The aim is to discuss whether the convection ve-
locity is likely to be biased if determined from schlieren images obtained at a hi gh frame
rate, as in previous experiments using the phase shift method. For this, a numerical pro-
cedure is developed in order to generate schlieren-like images on the basis of simulation
data, and applied to the results provided by the large-eddy simulation (LES) of an under-
expanded round jet at an ideally expanded Mach number of 1.56. The results obtained
from the schlieren pictures are compared with those obtained directly from the LES den-
sity fields. It is notably found that the location of the maximum of gray level fluctuations
in the s chlieren pictures corresponds well to that of the maximum of density fluctuations,
and that the convection velocity estimated for low frequencies using schlieren pictures is
underestimated for small separation distances between the two points used for the phase
shift cal culation.
I. Introduction
In aeroac oustics models for supersonic jet noise,
1, 2
one input parameter related to the flow itself is the
convection velocity of the turbulence in the jet shear layer. In recent years, different experimental methods
3–8
were applied to measure the convection velocity in high-speed jets, and when possible, its de pendency on
the frequency. In s everal studies, a schlieren system is set up together with imaging optics so that the
light intensity in the image plane of the jet is measured by use of two combined photodiodes
6, 9, 10
or of a
high speed camera.
7, 8
The data analysis seeks for instance at determining the phase difference between two
signals from a couple of sens ors. This phase s hift is related (at least partly) to c onvec tion and hence, an
estimate of the convection velocity is obtained as soon as the distance b etween the two sensors is known.
Conventional schlieren imaging is known to provide pictures whose c ontrast results from the integration of
all the light beam perturba tions from the light source to the sensor. Sharp-focusing systems
11, 12
can provide
two-dimensional slices of a flow, with a focus depth depending on the exper imental apparatus chosen. In
practical,
11
the focus depth is of the order of the diameter of the Lab-scale round supersonic jets.
This paper is an attempt to determine if the characteristics of conventional schlieren imaging (space
integration over the light path, sensitivity to gr adients of density rather than the density itself) can affect
the convection velocity estimation.
In this purpose, experimental s chlieren images of an underexpanded jet at M
j
= 1.50 are first exploited.
To estimate the convection velocity, the phase shift method is applied by using two time signals extra cted
from the time-series of schlieren pictures a cquired at a high frame ra te. The distance between the two points
is varied and its influence on the convection velocity e stimation is highlighted. To go further, a study base d
on synthetic schlieren pictures processed from 3-D data o btained by Large Eddy Simulation (les) of a round
underexpanded M
j
= 1.56 jet is presented. These pictures, obtained by using a specific numerical proce dure,
Assistant Professor, Universit´e Lyon 1, France
PhD, currently Post-doctoral student at KTH Royal Institute of Technology, Sweden
PhD student, Univ Lyon,
´
Ecole Centrale de Lyon
§
CNRS Research Scientist, AIAA Senior Member and Associate Fel low
22nd AIAA/CEAS Aeroacoustics Conference
30 May - 1 June, 2016, Lyon, France
Aeroacoustics Conferences

~z
~y
Figure 1. Single-frame schlieren image for M
j
= 1.50. The w hite dashed area indicates the field of view
recorded at a high frame rate; the symbols indicate the typical locations where the data are extracted to appl y
the convecti on velocity estimation procedure by two-poi nt phase difference, the ax ial distance between the two
points ranging from 2δ
z
= 8 px (ie 2δ
z
/D = 0 .055) to 2δ
z
= 6 4 px (ie 2δ
z
/D = 0.44)
are validated aga inst reference quasi-analytic solutions. The convection velocity is es tima ted again using the
phase shift method, as for the experiments. The results are compared with those derived from the same
metho dology applied to the density field - the raw data provided by the numerical s imulations. The analysis
aims to show that the spacing between the two points affects the convection velocity estimation from the
schlieren pictures. Before presenting these results, the parameters and methods used in the experiments and
in the simulation a re first given.
II. Jets parameters and methods used
A. Experimental set-up
The experiments were done in the 10 m×8 m×8 m anechoic r oom of the Centre Acoustique, Laborato ire
de eca nique des Fluides et d’Acoustique at
´
Ecole Centrale de Lyon. A contoured convergent nozzle of
diameter D = 38 mm, is continuously supplied by a centrifugal compressor in unheated dry air. The wall
static pressure is measured 15 nozzle diameters upstream of the exit. Stagnation pressure is then retrieved
from the wall static pressure value thr ough the estimate of the local Mach number in the measurement
section. The superso nic jet s tudied here is associated to an ideally expanded Mach number M
j
= 1.50 and a
total temperature around 30
C. The associa ted Reynolds number based on the fully expanded velocity and
the nozzle diameter D is Re
D
= 2×10
6
. A representative view of the choked jet is provided in Figure 1 using
a conventional Z-type schlieren system. The imaging system used in the following consists of a continuous
Cree XHP LED light source, a knife edge set perpendicular to the jet axis , and two f /8, 203.2-mm-diam
parabolic mirro rs arranged so that the off-axis setting is limited to 10 deg. The schlieren images are rec orded
by a high-speed P hantom V12 CMOS camera whose fra me rate is set to 430 769 Hz, with an exposur e time o f
1.87 µs. The total length of one recording is 1.21 s which corres ponds to 521472 successive images. To ensure
the high acquisition frame rate, the recorded image area is limited to a 640 px×16 px region centered on the
upper jet shear layer. Using appropriate collimating optics, the ima ge resolution is set to 0.261 mm/px.
With these settings, the field of vie w corres ponds to 4.4D in the longitudinal direction and to 0.11D in the
radial direction, as can be observed in the typical image depicted in Figure 1. In this Figure the location of
the couple points used for the estimations of co nvection velocity, arbitrary placed on the nozzle lipline and
in the middle of the third shock cell, is also represented. This position is noted x
0
in the following. Similar
results as thos e presented in section III were also obtained for other locations at various distances to the
nozzle exit along the lipline.
B. Numerical simulation of a round underexpanded M
j
=1.56 jet
A supersonic round jet has been computed by s olving the unstea dy compressible Navier-Stokes equations
using low-dispersion and low-dissipation schemes
13–15
. Further details on the simulation are provided in a
previous paper.
16
The jet is underexpanded, and is characterized by a Nozzle Pres sur
e Ratio of NPR =
P
r
/P
amb
= 4.03, where P
r
is the stagnation press ure and P
amb
is the ambient pressure. The fully expanded

Mach number is M
j
= 1.56, the exit Mach number M
e
= 1, and the Reynolds number is Re
D
= 5 × 10
4
.
The mesh contains 400 million points, with mesh spacings allowing acoustic waves with Strouhal numbers
up to St
D
= 5.6 to be well propagated. The 3-D flow density of the simulation is recorded at a sampling
frequency of St
D
= 6.4, over a volume defined in cylindrical coordinates by 200 points in the radial direction
with a maximum radial position of r = 1.5 D, 512 points in the azimuthal direction covering 2π and 491
points along the jet axis ranging up to z = 5.15D. In the following, a light beam along the Cartesian ~x axis
is supposed to go through the underexpanded jet, as represented in the figur e 2. The equations governing
refractions of the light beam due to the variations in the flow density, derived from Fermat’s principle, are
provided in the next section.
~x
~y
~z
Figure 2. Time-averaged density field o f an underexpanded, M
j
= 1.56 and Re
D
= 5 × 10
4
, jet, obtained by
simulation.
16
Isovalues of density f rom 1 to 2.6 kg.m
3
, by step 0.2 kg.m
3
, are presented.
C. Two-point method for convection velocity estimation
The convection velocity may be estimated from the phase lag between two signals represe ntative of the flow,
recorded at two different points in the jet shear layer. These could be density signals,
3
velocity signals
4, 5
or
optical signals depe nding on density gradients.
6, 7, 9, 10
For one physical position x within the flow, let g(x,t)
be the signal measured by the sensor used at the time t. Calling G(x,f) the Fourier transform of g(x,t) and
taking the x location as a r eference point, the cross-spec trum G
δz
(x, f) between the signal coming fro m x +
δz~z and the one coming from x - δz~z is computed using :
G
δz
(x, f) = G(x + δz~z, f) × G
(x δz~z, f) (1)
where the
denotes complex conjugate.
The estimation o f the convection velocity U
c
is derived from the phase Φ
δz
(x, f) of the cross- spectrum
G
δx
(x, f) using :
U
c
(x, f) = 2πf
2δz
Φ
δz
(x, f)
=
4πfδz
Φ
δz
(x, f)
(2)

0
5
10
15
20
0 5 10 15
St
D
(a)
Φ
δz
(x
0
) [rad]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5 10 15
St
D
(b)
U
c
/U
j
Figure 3. (a ) Phase lag Φ
δz
(x
0
for different couples of points centered on x
0
: δ
z
= 4 px; δ
z
= 8 px;
δ
z
= 12 px; δ
z
= 16 px; δ
z
= 32 px, (b) Estimation o f the non-dimensio ned convection velocity U
c
/U
j
for
the same couples of points centered on x
0
III. Experimental results for an underexpanded M
j
=1.50 jet
High-speed schlieren cinematography has previous ly been proposed using the Cranz-Schardin principle,
17
which a llowed for up to 4 c onsecutive schlieren images with a minimum time separ ation of 1 µs. The idea
proposed here is to use the tr emendous capac ities of high-speed digital cameras to construct time signals
extracted from a sequence of several hundreds of thousands consecutive images. Grayscale time signals
from the schlieren images would then be used as the input signals for cross- spectrum computation as in (1).
Because of the knife-edge orientation, orthogonal to the jet axis in this experimental study, the signal will
be deno ted as g
z
, w he re the subscript z is used to indicate that the contrast in these experimental schlieren
images is due to density gradients along the ~z axis.
In this study, the e xperimental signa ls were segmented into 9997 blocks of 104 p oints, obtained using a
50% overlap, to compute the mean cross-spectrum of w hich the phase is extracted. C onsidering in Figure
3(a) the evolution of the phase Φ
δz
(x
0
) as a function of the Strouhal number St
D
= f D/U
j
based o n the
nozzle diameter and the perfectly expanded jet velocity U
j
, one notices that the phase delay mo notonically
increases with St
D
for the tes ted values of δz. For the two largest values of δz, the phase shift is limited
to approximately 20 radians because noise limits the e stimation accuracy for larger values. The convection
velocity, estimated using (2) and given in Figur e 3(b), follows the behavior obtained in previo us studies,
by globally incr easing monotonically with St
D
and reaching values around 0.7U
j
or 0.8U
j
. Nevertheless, as
pointed out earlier,
3, 6, 7
the distance δz be tween the probes a ffects the estimation of the convection velocity
over the whole range of St
D
.
This influence must be taken into acc ount also becaus e the differences in U
c
are noticeable (around 10%)
for the smallest separations 2δz= 8 px and 16 px (respectively 2δz/D= 0.055 a nd 0.110, which corresponds
to 2δz= 2.1 mm and 4.2 mm), tha t are of the order of the local shear layer momentum thickness (δ
θ
3.3
mm for x
0
=(3.8D,0.5D) as mentioned in Fig 3.42 of a previous study
7
) and thus small with respect to the
jet diameter D. Panda
3
reminds us that the distor tion of the eddies that occurs over the s eparation distance
also influences in the phase, thus there should be at least one part of the error in the estimation of the
convection velocity that comes from the phase lag method itself. This effect is noticeable in Panda
3
for the
case of a round M
j
= 0.95 jet; for a s eparation between the two probes of around one jet diameter D at
St
D
= 1.6, the lack of coherence b etween the two experimental signals induces errors in the phase estimate.
For smaller pro bes separations, the linear dependency of the cros s-spectral phase with the probes se paration
is remarkable, which indicates that the separation between the probes induces only a small, if any, bias in
the convection velocity estimate.
To summarize, probes separation in high-speed conventional schlieren imaging affects the convection
velocity estimation, as it is also the case in previous studies
3, 6
where it is proposed to calculate this qua ntity
by averaging over multiple separation points. Considering the large differe nc e be tween these estimations

Figures (12)
Citations
More filters

Journal ArticleDOI
Romain Gojon1, Christophe Bogey1Institutions (1)
Abstract: The flow and near acoustic fields of a supersonic round free jet are explored using a compressible large eddy simulation. At the exit of a straight pipe nozzle, the jet is underexpanded, and is characterized by a Nozzle Pressure Ratio of 4.03 and a Temperature Ratio of 1. It has a fully expanded Mach number of 1.56, an exit Mach number of 1, and a Reynolds number of 60000. Flow snapshots, mean flow fields and convection velocity in the jet shear layers are consistent with experimental data and theoretical results. Furthermore, two screech tones are found to emerge in the pressure spectrum calculated close to the nozzle. Using a Fourier decomposition of the pressure fields, the two screech tones are found to be associated with anticlockwise helical oscillation modes. Besides, the frequencies of the screech tones and the associated oscillation modes both agree with theoretical predictions and measurements. Moreover, pressure fields filtered at the screech frequencies reveal the presence of hydrodynamic-acoustic standing waves. In those waves, the regions of highest amplitude in the jet are located in the fifth and the sixth cells of the shock cell structure. The two screech tones therefore seem to be linked to two different loops established between the nozzle and the fifth and sixth shock cells, respectively. In the pressure fields, three other acoustic components, namely the low-frequency mixing noise, the high-frequency mixing noise and the broadband shock-associated noise, are noted. The directivity and frequency of the mixing noise are in line with numerical and experimental studies. A production mechanism of the mixing noise consisting of sudden intrusions of turbulent structures into the potential core is discussed. Then, the broadband shock-associated noise is studied. This noise component is due to the interactions between the turbulent structure in the shear layers and the shocks in the jet. By analyzing the near pressure fields, this noise component is found to be produced mainly in the sixth shock cell. Finally, using the size of this shock cell in the classical theoretical model of this noise component, a good agreement is found with the simulation results.

19 citations


Dissertation
06 Dec 2017
Abstract: Dans ce travail de recherche, on presente des developpements specifiques de diagnostiques optiques et leur application a l’etude aeroacoustique des jets rapides a haut nombre de Reynolds. Les resultats experimentaux presentes ici resultent de visualisation par strioscopie et, de maniere preponderante dans ce manuscrit, de mesure de masse volumique par diffusion Rayleigh. Ces methodes de caracterisation d’ecoulement, appliquees aux jets subsoniques ou supersoniques, ont ete associees a des mesures de bruit en champ lointain. La mesure par diffusion Rayleigh, qui repose sur la lumiere diffusee par les molecules constituantes du gaz, et n’est donc pas intrusive. Des difficultes apparaissent neanmoins pour exploiter les resultats lorsque le milieu diffusant contient des poussieres. Bien que l’air des ecoulements obtenu en soufflerie soit filtre, la quantite residuelle de poussieres a rendu necessaire le developpement d’une methode de nettoyage du signal en post-traitement. Le niveau des signaux obtenus par diffusion Rayleigh est tres faible, et domine par du bruit appele shot noise. Un gain significatif sur le niveau de ce bruit a ete obtenu en optimisant la chaine d’acquisition apres analyse des systemes existants. De plus une methode de traitement du signal derivee d’une methode existante a permis de calculer des spectres de masse volumique malgre le shot noise avec un seul capteur, la ou il en fallait deux auparavant. Les profils de p obtenus par cette technique ont montre qu’il existe une loi de similarite permettant de superposer les profils mesures a differentes positions axiales. Cette loi est identique pour les jets issus de trois tuyeres aux geometries differentes, et a des nombres de Mach de 0.7 et 0.9. Une loi de similarite est egalement observee pour p’rms si les profils sont mesures suffisamment loin de la tuyere. L’etude des spectres dans la couche de melange a mis en evidence un maximum faiblement marque autour d’une frequence centrale comprise entre St = 0:2 et St = 2 dans les regions mesurees, plus marque que dans les spectres de vitesse, et dont le comportement differe selon l’etat initialement laminaire ou turbulent du jet. L’evolution de la forme des spectres en fonction de la difference de masse volumique entre le jet et le milieu ambiant, ainsi qu’en fonction du nombre de Mach, a egalement ete etudiee. Une loi permettant de superposer les spectres a ete definie empiriquement sur la plage de variation des differents parametres. Des mesures simultanees entre l’acoustique en champ lointain et la masse volumique dans l’ecoulement ont ete realisees pour un jet a Mj = 0:9 et un jet a Mj = 1:32. Ces resultats ont permis l’estimation de coherences spectrales et de moyennes conditionnelles. Les resultats obtenus mettent en evidence la presence de structures liees au rayonnement acoustique dans une region situee proche de l’axe du jet en aval du cone potentiel. Pour finir, une etude a ete realisee sur le screech dans les jets supersoniques sous-detendus. Elle a permis d’identifier la position de la source de la retroaction acoustique pour les modes A1, A2, et B, ainsi que la structure du cycle de la boucle qui determine les changements de frequences observes aux sauts de modes.

5 citations


Journal ArticleDOI
Abstract: The primary objective of the present study was to develop a quantitative schlieren-imaging technique that can be used to study the dynamics of instability waves. The technique was initially validated by optically capturing a controlled acoustic wave generated by a compression driver and excellent agreement was obtained with microphone measurements. An underexpanded jet was considered as an ideal test case due to the complexity and multitude of instability mechanism. Further analysis of the underexpanded jet demonstrated that this technique can be used to capture the very high frequency mode related to the phenomenon of screech.

4 citations


Cites background from "Estimation of convection speed in u..."

  • ...[4], Panda and Seasholtz [5], to cite a few)....

    [...]


Proceedings ArticleDOI
Thomas Knast1, Lee Mears2, Nishal Arora2, Tufan Kumar Guha2  +4 moreInstitutions (2)
25 Jun 2018

References
More filters

Journal ArticleDOI
Christophe Bogey1, Christophe Bailly1Institutions (1)
Abstract: Explicit numerical methods for spatial derivation, filtering and time integration are proposed. They are developed with the aim of computing flow and noise with high accuracy and fidelity. All the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to kΔx = π/2 corresponding to four points per wavelength. They are shown to be more accurate, and also more efficient numerically, than most of the standard explicit high-order methods, for uniform and slowly non-uniform grids. Two problems involving long-range sound propagation are resolved to illustrate their respective precisions. Remarks about their practical applications are then made, especially about the connection with the boundary conditions. Finally, their relevance for the simulation of turbulent flows is emphasized.

815 citations


Journal ArticleDOI

727 citations


Journal ArticleDOI
TL;DR: A shock-capturing methodology is developed for non-linear computations using low-dissipation schemes and centered finite differences that allows in particular to distinguish shocks from linear waves, and from vortices when it is performed from dilatation rather than from pressure.
Abstract: A shock-capturing methodology is developed for non-linear computations using low-dissipation schemes and centered finite differences. It consists in applying an adaptative second-order filtering to handle discontinuities in combination with a background selective filtering to remove grid-to-grid oscillations. The shock-capturing filtering is written in its conservative form, and its magnitude is determined dynamically from the flow solutions. A shock-detection procedure based on a Jameson-like shock sensor is derived so as to apply the shock-capturing filtering only around shocks. A second-order filter with reduced errors in the Fourier space with respect to the standard second-order filter is also designed. Linear and non-linear 1D and 2D problems are solved to show that the methodology is capable of capturing shocks without providing dissipation outside shocks. The shock detection allows in particular to distinguish shocks from linear waves, and from vortices when it is performed from dilatation rather than from pressure. Finally the methodology is simple to implement and reasonable in terms of computational cost.

297 citations


Journal ArticleDOI
Ganesh Raman1Institutions (1)
Abstract: Under certain conditions, shock-containing jets produce an intense tone referred to as screech. Screech was discovered about half a century ago by Alan Powell in England. Here I recount developments in supersonic jet screech — from Powell's first observation in 1951 to now. During this period more than 200 papers have been published — many offering only incremental advances. This paper provides a concise screech resource including a historical perspective, a summary of recent developments and a critical assessment of the state of the art. Topics include modulation of instability waves by shocks, shock-cell models and screech frequency prediction models, unsteady shock motions and clues about their role in shock noise generation. Also, detailed nearfield measurements and computer simulation methods now available are discussed. However, despite the advances, screech amplitude prediction remains an elusive but increasingly important goal not only due to concerns about sonic fatigue failure of aircraft structures but because knowledge gained by the study of screech can be applied to a variety of resonant flow situations, including jet impingement, cavity resonance, and closed-loop active flow control.

225 citations


Proceedings ArticleDOI
01 Jan 1970
Abstract: Acoustic power output from supersonic jets, considering aerodynamic and acoustic characteristics for supersonic exhaust velocities

151 citations


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
20182
20172