A large-eddy simulation is used to assess the Reynolds-stress budgets of a round impinging jet in the context of a second-moment closure of turbulence. The present work focuses on the stagnation region where no data are available in the literature except in the wall vicinity. Inside the stagnation region, it is shown that the pressure terms are dominant in the budgets. They balance the Reynolds-stress production and the convective fluxes. A visualization of this equilibrium through a specific indicator reveals that impingement effects extend to less than one nozzle diameter in the wall-normal direction and to about one diameter radially. This study underlines the role of the pressure diffusion term that conveys energy to the wall, balancing the high production rates (both positive or negative). Finally, the failure of turbulence models is explained by the absence of appropriate modeling of this pressure diffusion term leading to excessive Reynolds-stress values inside the impingement region.

1.
J.
Baughn
and
S.
Shimizu
, “
Heat transfer measurements from a surface with uniform heat flux and an impinging jet
,”
J. Heat Transfer
111
,
1096
(
1989
).
2.
P.
Aillaud
,
F.
Duchaine
,
L.
Gicquel
, and
S.
Didorally
, “
Secondary peak in the Nusselt number distribution of impinging jet flows: A phenomenological analysis
,”
Phys. Fluids
28
,
095110
(
2016
).
3.
K.
Nishino
,
M.
Samada
,
K.
Kasuya
, and
K.
Torii
, “
Turbulence statistics in the stagnation region of an axisymmetric impinging jet flow
,”
Int. J. Heat Fluid Flow
17
,
193
201
(
1996
).
4.
L.
Geers
,
M.
Tummers
, and
K.
Hanjalić
, “
Experimental investigation of impinging jet arrays
,”
Exp. Fluids
36
,
946
958
(
2004
).
5.
C.
Shekhar
and
K.
Nishino
, “
Turbulence energetics in an axisymmetric impinging jet flow
,”
Phys. Fluids
31
,
055111
(
2019
).
6.
J.
Lee
and
S.-J.
Lee
, “
Stagnation region heat transfer of a turbulent axisymmetric jet impingement
,”
Exp. Heat Transfer
12
,
137
156
(
1999
).
7.
P.
Brevet
,
E.
Dorignac
, and
J.
Vullierme
, “
Mach number effect on jet impingement heat transfer
,”
Ann. N. Y. Acad. Sci.
934
,
409
416
(
2006
).
8.
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
).
9.
M.
Tummers
,
J.
Jacobse
, and
S.
Voorbrood
, “
Turbulent flow in the near field of a round impinging jet
,”
Int. J. Heat Mass Transfer
54
,
4939
4948
(
2011
).
10.
M.
Fénot
,
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
).
11.
N.
Kim
, “
Analyse exp érimentale d'un jet turbulent impactant sur un plaque plane et sur un obstacle de section carrée
,” Ph.D. thesis (
Université Paul Sabatier Toulouse III
,
Toulouse
,
2005
).
12.
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
).
13.
M.
Hadžiabdić
and
K.
Hanjalić
, “
Vortical structures and heat transfer in a round impinging jet
,”
J. Fluid Mech.
596
,
221
260
(
2008
).
14.
T.
Dairay
,
V.
Fortuné
,
E.
Lamballais
, and
L.
Brizzi
, “
Direct numerical simulation of a turbulent jet impinging on a heated wall
,”
J. Fluid Mech.
764
,
362
394
(
2015
).
15.
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
).
16.
P.
Grenson
and
H.
Deniau
, “
Large-eddy simulation of an impinging heated jet for a small nozzle-to-plate distance and high Reynolds number
,”
Int. J. Heat Fluid Flow
68
,
348
363
(
2017
).
17.
H.
Yadav
and
A.
Agrawal
, “
Effect of vortical structures on velocity and turbulent fields in the near region of an impinging turbulent jet
,”
Phys. Fluids
30
,
035107
(
2018
).
18.
S.
Ashforth-Frost
and
K.
Jambunathan
, “
Numerical prediction of semi-confined jet impingement and comparison with experimental data
,”
Int. J. Numer. Methods Fluids
23
,
295
306
(
1996
).
19.
M.
Behnia
,
S.
Parneix
, and
P.
Durbin
, “
Prediction of heat transfer in an axisymmetric turbulent jet impinging on a flat plate
,”
Int. J. Heat Mass Transfer
41
,
1845
1855
(
1998
).
20.
T.
Craft
,
L.
Graham
, and
B.
Launder
, “
Impinging jet studies for turbulence model assessment-II. An examination of the performance of four turbulence models
,”
Int. J. Heat Mass Transfer
36
,
2685
2697
(
1993
).
21.
N.
Zuckerman
and
N.
Lior
, “
Jet impingement heat transfer: Physics, correlations, and numerical modeling
,”
Adv. Heat Transfer
39
,
565
631
(
2006
).
22.
M.
Kato
and
B.
Launder
, “
The modelling of turbulent flow around stationary and vibrating square cylinders
,” in
9th Symposium on Turbulent Shear Flows
(
1993
), pp.
10
14
.
23.
F.
Menter
, “
Improved two-equation k-ω turbulence models for aerodynamic flows
,”
Report No. N93-22809
(NASA,
1992
).
24.
P.
Durbin
, “
On the k-ε stagnation point anomaly
,”
Int. J. Heat Fluid Flow
17
,
89
90
(
1996
).
25.
V.
Guimet
and
D.
Laurence
, “
A linearised turbulent production in the k-ε model for engineering applications
,” in
Engineering Turbulence Modelling and Experiments
(
Elsevier
,
2002
), Vol.
5
, pp.
157
166
.
26.
C.
Yap
, “
Turbulent heat and momentum transfer in recirculating and impinging flows
,” Ph.D. thesis [University of Manchester Institute of Science and Technology (UMIST),
1987
].
27.
T.
Craft
,
B.
Launder
, and
K.
Suga
, “
Development and application of a cubic eddy-viscosity model of turbulence
,”
Int. J. Heat Fluid Flow
17
,
108
115
(
1996
).
28.
P. A.
Durbin
, “
Near-wall turbulence closure modeling without ‘damping functions
,’”
Theor. Comput. Fluid Dyn.
3
,
1
13
(
1991
).
29.
R.
Manceau
,
R.
Perrin
,
M.
Hadžiabdić
, and
S.
Benhamadouche
, “
Investigation of the interaction of a turbulent impinging jet and a heated, rotating disk
,”
Phys. Fluids
26
,
035102
(
2014
).
30.
T.
Craft
and
B.
Launder
, “
New wall-reflection model applied to the turbulent impinging jet
,”
AIAA J.
30
,
2970
2972
(
1992
).
31.
N.
Uddin
, “
Turbulence modeling of complex flows in CFD
,” Ph.D. thesis (
Institute of Aerospace Thermodynamics, Universität Stuttgart
,
2008
).
32.
M.
Hadžiabdić
, “
LES, RANS combined simulation of impinging flows and heat transfer
,” Ph.D. thesis (
University of Sarajevo
,
Bosnia and Herzegovina
,
2006
).
33.
S.
Alekseenko
,
A.
Bilsky
,
V.
Dulin
,
B.
Ilyushin
, and
D.
Markovich
, “
Non-intrusive determination of turbulent energy balance in free and confined jet flows
,” in
TSFP Digital Library ONLINE
(
Begel House Inc
.,
2005
).
34.
S.
Alekseenko
,
A.
Bilsky
,
V.
Dulin
, and
D.
Markovich
, “
Experimental study of an impinging jet with different swirl rates
,”
Int. J. Heat Fluid Flow
28
,
1340
1359
(
2007
).
35.
J.
Lumley
, “
Computational modeling of turbulent flows
,” in
Advances in Applied Mechanics
(
Elsevier
,
1979
), Vol.
18
, pp.
123
176
.
36.
Z.
Xiong
and
S.
Lele
, “
Stagnation-point flow under free-stream turbulence
,”
J. Fluid Mech.
590
,
1
33
(
2007
).
37.
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
).
38.
R.
Kraichnan
, “
Diffusion by a random velocity field
,”
Phys. Fluids
13
,
22
31
(
1970
).
39.
T. J.
Poinsot
and
S.
Lele
, “
Boundary conditions for direct simulations of compressible viscous flows
,”
J. Comput. Phys.
101
,
104
129
(
1992
).
40.
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
).
41.
O.
Colin
and
M.
Rudgyard
, “
Development of high-order Taylor-Galerkin schemes for LES
,”
J. Comput. Phys.
162
,
338
371
(
2000
).
42.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based square velocity gradient tensor
,”
Flow, Turbul. Combust.
62
,
183
200
(
1999
).
43.
S.
Toutiaei
,
R.
Semaan
, and
J.
Naughton
, “
Reynolds stress and turbulence kinetic energy balances in swirling jets
,” in
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
(
AIAA
,
2010
), p.
105
.
44.
R.
Manceau
and
K.
Hanjalić
, “
Elliptic blending model: A new near-wall Reynolds-stress turbulence closure
,”
Phys. Fluids
14
,
744
754
(
2002
).
You do not currently have access to this content.