This paper focuses on a wall-resolved Large Eddy Simulation (LES) of an isothermal round submerged air jet impinging on a heated flat plate, at a Reynolds number of 23 000 (based on the nozzle diameter and the bulk velocity at the nozzle outlet) and for a nozzle to plate distance of two jet diameters. This specific configuration is known to lead to a non-monotonic variation of the temporal-mean Nusselt number as a function of the jet center distance, with the presence of two distinct peaks located on the jet axis and close to two nozzle diameters from the jet axis. The objectives are here twofold: first, validate the LES results against experimental data available in the literature and second to explore this validated numerical database by the use of high order statistics such as skewness and probability density functions of the temporal distribution of temperature and pressure to identify flow features at the origin of the second Nusselt peak. Skewness (Sk) of the pressure temporal distribution reveals the rebound of the primary vortices located near the location of the secondary peak and allows to identify the initiation of the unsteady separation linked to the local minimum in the mean heat transfer distribution. In the region of mean heat transfer enhancement, joint velocity-temperature analyses highlight that the most probable event is a cold fluid flux towards the plate produced by the passage of the vortical structures. In parallel, heat transfer distributions, analyzed using similar statistical tools, allow to connect the above mentioned events to the heat transfer on the plate. Thanks to such advanced analyses, the origin of the double peak is confirmed and connected to the flow dynamics.

1.
J.-C.
Han
and
L. M.
Wright
, “
Enhanced internal cooling of turbine blades and vanes
,” in
The Gas Turbine Handbook
(
U.S. National Energy Technology Laboratory
,
Morgantown, WV
,
2007
), pp.
321
352
.
2.
K.
Jambunathan
,
E.
Lai
,
M. A.
Moss
, and
B. L.
Button
, “
A review of heat transfer data for single circular jet impingement
,”
Int. J. Heat Fluid Flow
13
,
106
115
(
1992
).
3.
R.
Viskanta
, “
Heat transfer to impinging isothermal gas and flame jets
,”
Exp. Therm. Fluid Sci.
6
,
111
134
(
1993
).
4.
A.
Dewan
,
R.
Dutta
, and
B.
Srinivasan
, “
Recent trends in computation of turbulent jet impingement heat transfer
,”
Heat Transfer Eng.
33
,
447
460
(
2012
).
5.
H.
Martin
, “
Heat and mass transfer between impinging gas jets and solid surfaces
,” in
Advances in Heat Transfer
(
Elsevier Ltd.
,
New york
,
1977
), Vol.
13
, pp.
1
60
.
6.
S. C.
Crow
and
F. H.
Champagne
, “
Orderly structure in jet turbulence
,”
J. Fluid Mech.
48
,
547
591
(
1970
).
7.
C.
Popiel
and
O.
Trass
, “
Visualization of a free and impinging round jet
,”
Exp. Therm. Fluid Sci.
4
,
253
264
(
1991
).
8.
C.
Cornaro
,
A. S.
Fleischer
, and
R. J.
Goldstein
, “
Flow visualization of a round jet impinging on cylindrical surfaces
,”
Exp. Therm. Fluid Sci.
20
,
66
78
(
1999
).
9.
A.
Yule
, “
Large-scale structure in the mixing layer of a round jet
,”
J. Fluid Mech.
89
,
413
(
1978
).
10.
A. K. M. F.
Hussain
and
K. B. M. Q.
Zaman
, “
The ‘preferred mode’ of the axisymmetric jet
,”
J. Fluid Mech.
110
,
39
71
(
1981
).
11.
C.
Chu
,
C.
Wang
, and
C.
Hsieh
, “
An experimental investigation of vortex motions near surfaces
,”
Phys. Fluids A
5
,
662
676
(
1993
).
12.
J. D. A.
Walker
,
C. R.
Smith
,
A. W.
Cerra
, and
T. L.
Doligalski
, “
The impact of a vortex ring on a wall
,”
J. Fluid Mech.
41
,
99
140
(
1987
).
13.
N.
Uddin
,
S.
Neumann
, and
B.
Weigand
, “
LES simulations of an impinging jet: On the origin of the second peak in the Nusselt number distribution
,”
Int. J. Heat Mass Transfer
57
,
356
368
(
2013
).
14.
N.
Didden
and
C.-M.
Ho
, “
Unsteady separation in a boundary layer produced by an impinging jet
,”
J. Fluid Mech.
160
,
235
(
1985
).
15.
M.
Angioletti
,
R.
Di Tommaso
,
E.
Nino
, and
G.
Ruocco
, “
Simultaneous visualization of flow field and evaluation of local heat transfer by transitional impinging jets
,”
Int. J. Heat Mass Transfer
46
,
1703
1713
(
2003
).
16.
J. W.
Baughn
and
S.
Shimizu
, “
Heat transfer measurements from a surface with uniform heat flux and an impinging jet
,”
J. Heat Transfer
111
,
1096
1098
(
1989
).
17.
R.
Gardon
and
J.
Akfirat
, “
The role of turbulence in determining the heat-transfer characteristics of impinging jets
,”
Int. J. Heat Mass Transfer
8
,
1261
1272
(
1965
).
18.
K.
Kataoka
,
R.
Sahara
,
H.
Ase
, and
T.
Harada
, “
Role of large scale coherent structures in impinging jet heat transfer
,”
J. Chem. Eng. Jpn.
20
,
71
76
(
1987
).
19.
T.
O’Donovan
and
D.
Murray
, “
Jet impingement heat transfer Part I: Mean and root-mean-square heat transfer and velocity distributions
,”
Int. J. Heat Mass Transfer
50
,
3291
3301
(
2007
).
20.
S.
Roux
,
M.
Fenot
,
G.
Lalizel
,
L. E.
Brizzi
, and
E.
Dorignac
, “
Evidence of flow vortex signatures on wall fluctuating temperature using unsteady infrared thermography for an acoustically forced impinging jet
,”
Int. J. Heat Fluid Flow
50
,
38
50
(
2014
).
21.
T.
Dairay
,
V.
Fortuné
,
E.
Lamballais
, and
L.-E.
Brizzi
, “
Direct numerical simulation of a turbulent jet impinging on a heated wall
,”
J. Fluid Mech.
764
,
362
394
(
2015
).
22.
M.
Hadžiabdić
and
K.
Hanjalić
, “
Vortical structures and heat transfer in a round impinging jet
,”
J. Fluid Mech.
596
,
221
260
(
2008
).
23.
H.
Hattori
and
Y.
Nagano
, “
Direct numerical simulation of turbulent heat transfer in plane impinging jet
,”
Int. J. Heat Fluid Flow
25
,
749
758
(
2004
).
24.
F.
Shum-kivan
,
F.
Duchaine
, and
L.
Gicquel
, “
Large-eddy simulation and conjugate heat transfer in a round impinging jet
,” in
ASME Turbo Expo 2014: Turbine Technical Conference and Exposition
(
ASME
,
2014
).
25.
J.
Lee
and
S.-J.
Lee
, “
Stagnation region heat transfer of a turbulent axisymmetric jet impingement
,”
Exp. Heat Transfer
12
,
137
156
(
1999
).
26.
N. T.
Obot
,
A. S.
Majumdar
, and
W. J. M.
Douglas
,
The Effect of Nozzle Geometry on Impingement Heat Transfer Under a Round Turbulent Jet
(
American Society of Mechanical Engineers
,
1979
).
27.
S.
Roux
,
M.
Fénot
,
G.
Lalizel
,
L.-E.
Brizzi
, and
E.
Dorignac
, “
Experimental investigation of the flow and heat transfer of an impinging jet under acoustic excitation
,”
Int. J. Heat Mass Transfer
54
,
3277
3290
(
2011
).
28.
D. W.
Colucci
and
R.
Viskanta
, “
Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet
,”
Exp. Therm. Fluid Sci.
13
,
71
80
(
1996
).
29.
L. F. G.
Geers
,
K.
Hanjalic
, and
M. J.
Tummers
, “
Wall imprint of turbulent structures and heat transfer in multiple impinging jet arrays
,”
J. Fluid Mech.
546
,
255
284
(
2006
).
30.
D.
Lytle
and
B.
Webb
, “
Air jet impingement heat transfer at low nozzle-plate spacings
,”
Int. J. Heat Mass Transfer
37
,
1687
1697
(
1994
).
31.
Y. M.
Chung
,
K. H.
Luo
, and
N. D.
Sandham
, “
Numerical study of momentum and heat transfer in unsteady impinging jets
,”
Int. J. Heat Fluid Flow
23
,
592
600
(
2002
).
32.
W.
Rohlfs
,
H.
Haustein
,
O.
Garbrecht
, and
R.
Kneer
, “
Insights into the local heat transfer of a submerged impinging jet: Influence of local flow acceleration and vortex-wall interaction
,”
Int. J. Heat Mass Transfer
55
,
7728
7736
(
2012
).
33.
M.
Fenot
,
J. J.
Vullierme
, and
E.
Dorignac
, “
Local heat transfer due to several configurations of circular air jets impinging on a flat plate with and without semi-confinement
,”
Int. J. Therm. Sci.
44
,
665
675
(
2005
).
34.
P.
Grenson
,
O.
Léon
,
P.
Reulet
, and
B.
Aupoix
, “
Investigation of an impinging heated jet for a small nozzle-to-plate distance and high Reynolds number: An extensive experimental approach
,”
Int. J. Heat Mass Transfer
102
,
801
815
(
2016
).
35.
M. J.
Tummers
,
J.
Jacobse
, and
S. G. J.
Voorbrood
, “
Turbulent flow in the near field of a round impinging jet
,”
Int. J. Heat Mass Transfer
54
,
4939
4948
(
2011
).
36.
T.
Schonfeld
and
M.
Rudgyard
, “
Steady and unsteady flows simulations using the hybrid flow solver AVBP
,”
AIAA J.
37
,
1378
1385
(
1999
).
37.
O.
Colin
and
M.
Rudgyard
, “
Development of high-order Taylor–Galerkin schemes for LES
,”
J. Comput. Phys.
162
,
338
371
(
2000
).
38.
J.
Donea
and
A.
Huerta
,
Finite Element Methods for Flow Problems
(
John Wiley & Sons, Ltd.
,
2003
).
39.
F.
Duchaine
,
N.
Maheu
,
V.
Moureau
,
G.
Balarac
, and
S.
Moreau
, “
Large-eddy simulation and conjugate heat transfer around a low-Mach turbine blade
,”
J. Turbomach.
136
,
051015
(
2013
).
40.
C.
Koupper
, “
Unsteady multi-component simulations dedicated to the impact of the combustion chamber on the turbine of aeronautical gas turbines
,” Ph.D. thesis,
INP Toulouse
,
2015
.
41.
R.
Fransen
, “
LES based aerothermal modeling of turbine blade cooling systems
,” Ph.D. thesis,
INP Toulouse
,
2013
.
42.
D.
Papadogiannis
, “
Coupled large eddy simulations of combustion - turbine interactions
,” Ph.D. thesis,
INP Toulouse
,
2015
.
43.
L. Y. M.
Gicquel
,
G.
Staffelbach
, and
T.
Poinsot
, “
Large eddy simulations of gaseous flames in gas turbine combustion chambers
,”
Prog. Energy Combust. Sci.
38
,
782
817
(
2012
).
44.
S.
Mendez
and
F.
Nicoud
, “
Large-eddy simulation of a bi-periodic turbulent flow with effusion
,”
J. Fluid Mech.
598
,
27
65
(
2008
).
45.
S. B.
Pope
,
Turbulent Flows
(
Cambridge University Press
,
New York
,
2000
).
46.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,”
Flow, Turbul. Combust.
62
,
183
200
(
1999
).
47.
J.
Smagorinsky
, “
General circulation experiments with the primitive equations. I. The basics experiment
,”
Mon. Weather Rev.
91
,
99
164
(
1963
).
48.
T. J.
Poinsot
and
S. K.
Lele
, “
Boundary conditions for direct simulations of compressible viscous flows
,”
J. Comput. Phys.
101
,
104
129
(
1992
).
49.
G.
Lodato
,
L.
Vervisch
, and
P.
Domingo
, “
A compressible wall-adapting similarity mixed model for large-eddy simulation of the impinging round jet
,”
Phys. Fluids
21
,
035102
(
2009
).
50.
D.
Cooper
,
D.
Jackson
,
B.
Launder
, and
G.
Liao
, “
Impinging jet studies for turbulence model assessment. I. Flow field experiments
,”
Int. J. Heat Mass Transfer
36
,
2675
2684
(
1993
).
51.
N.
Guézennec
and
T.
Poinsot
, “
Acoustically nonreflecting and reflecting boundary conditions for vortcity injection in compressible solvers
,”
AIAA J.
47
,
1709
1722
(
2009
).
52.
V.
Granet
,
O.
Vermorel
,
T.
Léonard
,
L.
Gicquel
, and
T.
Poinsot
, “
Comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids
,”
AIAA J.
48
,
2348
2364
(
2010
).
53.
P.
Sagaut
,
Large Eddy Simulation for Incompressible Flows
(
Springer-Verlag
,
2000
).
54.
M.
Bovo
and
L.
Davidson
, “
Direct comparison of les and experiment of a single-pulse impinging jet
,”
Int. J. Heat Mass Transfer
88
,
102
110
(
2015
).
55.
F.
Nicoud
,
H. B.
Toda
,
O.
Cabrit
,
S.
Bose
, and
J.
Lee
, “
Using singular values to build a subgrid-scale model for large eddy simulations
,”
Phys. Fluids
23
,
085106
(
2011
).
56.
C.
Koupper
,
L.
Gicquel
,
F.
Duchaine
, and
G.
Bonneau
, “
Advanced combustor exit plane temperature diagnostics based on large eddy simulations: Going further than the radial temperature distribution factor
,”
Flow, Turbul. Combust.
95
,
79
96
(
2015
).
57.
K. P.
Balanda
and
H. L.
MacGillivray
, “
Kurtosis: A critical review
,”
Am. Stat.
42
,
111
119
(
1988
).
58.
L. T.
DeCarlo
, “
On the meaning and use of kurtosis
,”
Psychol. Methods
2
,
292
307
(
1997
).
59.
K. D.
Hopkins
and
D. L.
Weeks
, “
Tests for normality and measures of skewness and kurtosis: Their place in research reporting
,”
Educ. Psychol. Meas.
50
,
717
729
(
1990
).
60.
H.
Tennekes
and
J. L.
Lumley
,
A First Course in Turbulence
(
MIT Press
,
1972
).
61.
C.-M.
Ho
and
N. S.
Nosseir
, “
Dynamics of an impinging jet. I. The feedback phenomenon
,”
J. Fluid Mech.
105
,
119
(
1981
).
62.
K. B. M. Q.
Zaman
and
a. K. M. F.
Hussain
, “
Taylor hypothesis and large-scale coherent structures
,”
J. Fluid Mech.
112
,
379
396
(
1981
).
63.
D. J. C.
Dennis
and
T. B.
Nickels
, “
On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer
,”
J. Fluid Mech.
614
,
197
(
2008
).
64.
A.
Cerra
and
C. R.
Smith
,
Experimental observation of vortex ring interaction with the fluid adjacent to a surface, Technical Report
,
Lehigh University
,
1983
.
65.
P.
Orlandi
and
R.
Verzicco
, “
Vortex rings impinging on walls: Axisymmetric and three-dimensional simulations
,”
J. Fluid Mech.
256
,
615
646
(
1993
).
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