The paper presents a novel view on the absolute instability phenomenon in heated variable density round jets. As known from literature the global instability mechanism in low density jets is released when the density ratio is lower than a certain critical value. The existence of the global modes was confirmed by an experimental evidence in both hot and air-helium jets. However, some differences in both globally unstable flows were observed concerning, among others, a level of the critical density ratio. The research is performed using the Large Eddy Simulation (LES) method with a high-order numerical code. An analysis of the LES results revealed that the inlet conditions for the velocity and density distributions at the nozzle exit influence significantly the critical density ratio and the global mode frequency. Two inlet velocity profiles were analyzed, i.e., the hyperbolic tangent and the Blasius profiles. It was shown that using the Blasius velocity profile and the uniform density distribution led to a significantly better agreement with the universal scaling law for global mode frequency.

1.
P.
Huerre
and
P. A.
Monkewitz
, “
Local and global instabilities in spatially developing flows
,”
Annu. Rev. Fluid Mech.
22
,
473
(
1990
).
2.
P. A.
Monkewitz
and
K. D.
Sohn
, “
Absolute instability in hot jets
,”
AIAA J.
26
(
8
),
911
916
(
1988
).
3.
R. J.
Briggs
,
Electron-Stream Interaction with Plasmas
,
Research Monograph
Vol.
29
(
The MIT Press
,
1964
).
4.
S.
Jendoubi
and
P.
Strykowski
, “
Absolute and convective instability of axisymmetric jets with external flow
,”
Phys. Fluids
6
,
3000
(
1994
).
5.
l.
Lesshafft
,
P.
Huerre
,
P.
Sagaut
, and
M.
Terracol
, “
Nonlinear global modes in hot jets
,”
J. Fluid Mech.
554
,
393
409
(
2006
).
6.
P. A.
Monkewitz
,
D. W.
Bechert
,
B.
Barsikow
, and
B.
Lehmann
, “
Self-excited oscillations and mixing in a heated round jet
,”
J. Fluid Mech.
213
,
611
639
(
1990
).
7.
K. R.
Sreenivasan
,
S.
Raghu
, and
D.
Kyle
, “
Absolute instability in variable density round jets
,”
Exp. Fluids
7
,
309
(
1989
).
8.
D. M.
Kyle
and
K. R.
Sreenivasan
, “
The instability and breakdown of a round variable density jet
,”
J. Fluid Mech.
249
,
619
664
(
1993
).
9.
S.
Russ
and
P. J.
Strykowski
, “
Turbulent structure and entrainment in heated jets: The effect of initial conditions
,”
Phys. Fluids
5
(
12
),
3216
3225
(
1993
).
10.
A.
Michalke
, “
Survey on jet instability theory
,”
Prog. Aeronaut. Sci.
2
,
159
199
(
1984
).
11.
B. S.
Yildirim
and
A. K.
Agrawal
, “
Full-field measurements of self-excited oscillations in momentum-dominated helium jets
,”
Exp. Fluids
38
,
161
173
(
2005
).
12.
C. D.
Richards
,
B. D.
Breuel
,
R. P.
Clark
, and
T. R.
Troutt
, “
Concentration measurements in a self-excited jet
,”
Exp. Fluids
21
,
103
109
(
1996
).
13.
M. P.
Hallberg
and
P. J.
Strykowski
, “
On the universality of global modes in low-density axisymmetric jets
,”
J. Fluid Mech.
569
,
493
507
(
2006
).
14.
X.
Zhou
,
K. H.
Luo
, and
J. J. R.
Williams
, “
Study of density effects in turbulent buoyant jets using large-eddy simulation
,”
Theor. Comput. Fluid Dyn.
15
,
95
120
(
2001
).
15.
A.
Tyliszczak
and
A.
Boguslawski
, “
LES of variable density bifurcating jets
,” in
Complex Effects in Large Eddy Simulations
, edited by
G.
Iacarrino
,
S. C.
Kassinos
,
C. A.
Langer
, and
P.
Moin
,
Lecture Notes in Computational Science and Engineering
Vol.
56
(
Springer
,
2007
), pp.
273
288
.
16.
P.
Wang
,
J.
Fröhlich
,
V.
Michelassi
, and
W.
Rodi
, “
Large-eddy simulation of variable-density turbulent axisymmetric jets
,”
Int. J. Heat Fluid Flow
29
,
654
664
(
2008
).
17.
A.
Tyliszczak
,
A.
Boguslawski
, and
S.
Drobniak
, “
Quality of LES predictions of isothermal and hot round jet
,” in
Quality and Reliability of Large Eddy Simulations
, edited by
J.
Meyers
,
B. J.
Geurts
, and
P.
Sagaut
,
ERCOFTAC Series
Vol.
12
(
Springer
,
2008
), pp.
259
270
.
18.
J. W.
Nichols
,
P. J.
Schmid
, and
J. J.
Riley
, “
Self-sustained oscillations in variable-density round jets
,”
J. Fluid Mech.
582
,
341
376
(
2007
).
19.
L.
Lesshafft
,
P.
Huerre
, and
P.
Sagaut
, “
Frequency selection in globally unstable round jets
,”
Phys. Fluids
19
,
054108
(
2007
).
20.
H.
Foysi
,
J. P.
Mellado
, and
S.
Sarkar
, “
Large-eddy simulation of variable-density round and plane jets
,”
Int. J. Heat Fluid Flow
31
,
307
314
(
2010
).
21.
L.
Raynal
,
J.-L.
Harion
,
M.
Favre-Marinet
, and
G.
Binder
, “
The oscillatory instability of plane variable-density jets
,”
Phys. Fluids
8
(
4
),
993
(
1996
).
22.
L.
Kuban
,
J.-P.
Laval
,
W.
Elsner
,
A.
Tyliszczak
, and
M.
Marquillie
, “
LES modeling of converging-diverging turbulent channel flow
,”
J. Turbul.
13
,
1
19
(
2012
).
23.
A.
Boguslawski
,
A.
Tyliszczak
,
S.
Drobniak
, and
D.
Asendrych
, “
Self-sustained oscillations in a homogeneous-density round jet
,”
J. Turbul.
14
(
4
),
25
52
(
2013
).
24.
A.
Tyliszczak
, “
A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows
,”
J. Comput. Phys.
276
,
438
467
(
2014
).
25.
A.
Tyliszczak
, “
Multi-armed jets: A subset of the blooming jets
,”
Phys. Fluids
27
,
041703
(
2015
).
26.
A.
Tyliszczak
and
B. J.
Geurts
, “
Parametric analysis of excited round jets—Numerical study
,”
Flow, Turbul. Combust.
93
,
221
247
(
2014
).
27.
K.
Wawrzak
,
A.
Boguslawski
, and
A.
Tyliszczak
, “
LES predictions of self-sustained oscillations in homogeneous density round free jet
,”
Flow, Turbul. Combust.
95
,
437
459
(
2015
).
28.
A.
Tyliszczak
and
B. J.
Geurts
, “
Controlled mixing enhancement in turbulent rectangular jets responding to periodically forced inflow conditions
,”
J. Turbul.
16
(
8
),
742
771
(
2015
).
29.
A.
Tyliszczak
, “
Assessment of implementation variants of conditional scalar dissipation rate in LES-CMC simulation of auto-ignition of hydrogen jet
,”
Arch. Mech.
65
(
2
),
97
129
(
2013
).
30.
A.
Tyliszczak
, “
LES-CMC and LES-flamelet simulation of non-premixed methane flame (Sandia F)
,”
J. Theor. Appl. Mech.
51
(
4
),
859
871
(
2013
).
31.
A.
Tyliszczak
, “
LES-CMC study of an excited hydrogen flame
,”
Combust. Flame
162
,
3864
3883
(
2015
).
32.
T.
Poinsot
and
D.
Veynante
,
Theoretical and Numerical Combustion
(
Edwards
,
2001
).
33.
A.
Tyliszczak
, “
High-order compact difference algorithm on half-stagered meshes for low Mach number flows
,”
Comput. Fluids
127
,
131
145
(
2016
).
34.
B. J.
Geurts
,
Elements of Direct and Large-Eddy Simulation
(
Edwards Publishing
,
2003
).
35.
A. W.
Vreman
, “
An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications
,”
Phys. Fluids
16
,
3670
3681
(
2004
).
36.
M.
Klein
,
A.
Sadiki
, and
J.
Janicka
, “
A digital filter based generation of inflow data for spatially developing direct numerical and large eddy simulations
,”
J. Comput. Phys.
186
,
652
665
(
2003
).
37.
H.
Schlichting
,
Boundary Layer Theory
(
McGraw-Hill Book Company
,
New York
,
1979
).
38.
L. P.
Chua
and
A.
Antonia
, “
Turbulent Prandtl number in a circular jet
,”
Int. J. Heat Mass Transfer
33
(
2
),
331
339
(
1990
).
39.
P. A.
Monkewitz
,
D. W.
Bechert
,
B.
Bariskow
, and
B.
Lehmann
, “
The spreading of self-excited hot jets by side jets
,”
Phys. Fluids
3
,
446
447
(
1989
).
40.
A.
Couiron
and
J.-M.
Chomaz
, “
Fully nonlinear global modes in slowly varying flows
,”
Phys. Fluids
11
,
3688
3703
(
1999
).
41.
C.
Canuto
,
M. Y.
Hussaini
,
A.
Quarteroni
, and
T. A.
Zang
,
Spectral Methods in Fluid Dynamics
(
Springer-Verlag
,
1988
).
You do not currently have access to this content.