Large Eddy Simulation
of
Impinging Jets
with
Heat Transfer
Thomas Hällqvist
KTH / Scania CV AB
1
Outline
• Background
• Project description
• Computational method
and cases
• Results
• Summary
2
Background
• Project initiated in year 2000 by KTH and Scania CV AB
• Industrial goal: Improve the cooling capacity of
Scania heavy trucks
– Increase of the engine power.
– Decrease of available space.
900
y = 11.598x - 22585
800
Engine power [hp]
700
600
500
400
300
200
100
0
1975
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
Year
3
Outline
• Background
• Project description
• Computational method
and cases
• Results
• Summary
4
Project description
• To capture basic physical features
 a simplified geometry is studied
– The under-hood flow is approximated by an impinging jet
• Scientific goal: To enhance the understanding of the
flow and dynamics of impinging jets; including
– Impinging jet flow and related heat transfer.
– Turbulence and its modeling for such flows.
– Utilizing modern computational tools.
5
The Impinging Jet
(I)
Impinging jets are common in engineering
applications
– Processing of metal, glass and paper.
– Cooling applications: electronics, gasturbine combustion chambers, mechanical
devices.
Other more indirect application areas
– VTOL aircrafts, rockets (when close to the ground).
– High pressure washers.
6
The Impinging Jet
(II)
The impinging jet is characterized by
three flow regions
a)
b)
c)
The free jet region.
The stagnation region.
The wall jet region.
Geometrical parameters
D: Nozzle diameter
H: Impingement distance
W: Width
Nozzle outlet conditions
V0: Mean axial velocity
C0: Mean concentration
k0: Turbulent kinetic energy
7
The Impinging Jet
Impingement wall heat transfer
depends on
– Nozzle conditions.
– Impingement distance (H/D).
(III)
Nozzle
condition A
Nozzle
condition B
For small H/D
– Minimum of Nu at r/D=0.
– Two maximums of Nu.
H/D=2
For large H/D
– Maximum of Nu at r/D=0.
– Monotone decrease with r/D.
hD
k
 k (T / y ) y 0
Nu 
h
Tw  T0
Nusselt number (Nu)
Maximum in stagnation Nu
– Depends on the nozzle
conditions.
– Within the range: H/D=3-8.
– End of the potential core.
H/D=4
H/D=6
0
r/D
R
hypothetical
impingement wall
8
Outline
• Background
• Project description
• Computational method
and cases
• Results
• Summary
9
Computational method
•
Impinging jet simulated by large-eddy simulation (LES).
•
Space-filtering to reduce the number of degrees of freedom.
•
The effects
fromspectrum
the unresolved
Turbulent
velocity
scales
must
be modeled
Velocity
signal
E()
– Dissipation of energy.
():
– Backscatter, structural information. ():
•
Unfiltered signal
Filtered signal
Despite the filtering LES is computationally highly expensive.
large scales,
small scales, flows.
– Particularly for wall-bounded
resolved
unresolved
•
As LES is an unsteady approach
”SGS”
– Correct inflow conditions.
– Flow development region.
•
LES must be conducted in a 3-D domain
cut-off, c
– No symmetry-planes.
– Turbulence 
is three-dimensional.
x
10
Main computational cases
• Paper 1 & Paper 2: Basics of impinging jets
– Basic characters of an impinging circular jet using top-hat inflow
velocity profile. Paper 1: flow; Paper 2: heat transfer.
• Paper 3 & Paper 4: Swirling impinging jets
– Swirl effects on the flow and wall heat transfer for circular and
annular impinging jets.
• Paper 5: Inflow profile effects
– Radial distribution of the axial mean inflow velocity and from
periodic forcing.
• Paper 6: Parametric studies
– Nozzle-to-plate spacing effects.
– Reynolds number effects.
– Fully developed turbulent inflow condition for circular nonswirling and swirling impinging jets.
Data normalized by:
Mean inflow velocity (V0), nozzle diameter (D0) and mean inflow temperature (C0).
( Re=V0D0/ )
11
Outline
• Background
• Project description
• Computational method
and cases
• Results
• Summary
12
Dynamical character
From Paper 5
Instantaneous vorticity in the xy-plane
2
nozzle outlet, D
Inviscid
instability
y/D
Roll-up and
shedding of
natural vortices,
Stn
Vortex pairing
1
Shedding of
primary vortices,
Stn/2
shed vortices
Convection of
primary vortices
Formation of
secondary vortices
1  v u 
 
2  x y 
 z  
0
Separation
and breakdown
impingement wall
2
1
0
r/D
1
2
13
Dynamical character
From Paper 1 & 5
Spectrum at r/D=0.5, y/D=1
Dominant modes and energy at r/D=0.5
y/D
PSD
VP
St
•
•
Two dominant modes.
Sharp decrease of PSD for
higher St.
St
E
• Natural mode initially dominant.
• Delayed amplification of the
subharmonic mode.
• Vortex pairing (VP) between:
E(Stn)=E(Stn/2) and max[E(Stn/2)].
14
Unsteady heat transfer
From Paper 2
Instantaneous vorticity in the xy-plane, Nu and Cf plots
nozzle outlet, D
Attached
vortices
PV
V0
A: mean flow
convection
B: coherent heat
transfer
C: incoherent
heat transfer
PV : Primary vortex
SV : Secondary vortex
Conv. vel. Uc  V0 / 2
(—): Cf
(—): Nu
impingement wall
C
B
Stagnation point
A
B
C
SV, separation
15
From Paper 2
Unsteady heat transfer
Instantaneous vorticity in the xy-plane, Nu and Cf plots
(—): Cf
(—): Nu
separation point
reattachment point
16
Unsteady heat transfer
From Paper 2
Vorticity,
z
Velocity vectors
PV
hot fluid
SV
Separation
point
Reattachment
point
PV: counter-clockwise rotating
SV: clockwise rotating
1  v u 
 z    
2  x y 
(---): Cf
17
From Paper 2
Unsteady wall heat transfer
Wall friction
convective wave
Red color: high wall friction
Blue color: low wall friction, separation
Wall heat transfer
convective spot
Red color: high wall heat transfer
Blue color: low wall heat transfer
18
Mean inflow profile effects
From Paper 6
Instantaneous temperature distribution in the xy-plane (H/D=4)
top-hat
”fully turbulent” (ref. case)
mollified
•
Top-hat: irregular flow character, coherent
structures only close to the nozzle outlet.
Qualitatively similar to the reference case.
•
Mollified: distinct axisymmetric ring vortices
 large-scale mixing, delayed transition.
19
Mean flow character
From Paper 1 & 6
Mean axial velocity decay
Radial velocity at r/D=1
y/D
():
():
(О):
():
V/VCL
•
•
•
Potential core extends to
y/D≈1.
Top-hat: earlier decay.
Pipe: later decay  high
correlation with Geers et al.
LES (pipe)
LES (top-hat)
Cooper et al.
Geers et al.
Inflow:
”Fully developed ”
turb. pipe flow.
Top-hat mean
velocity profile.
Fully developed
turb. pipe flow.
U
•
•
•
•
Top-hat: low axial momentum
 low peak velocity.
Pipe: stronger wall shear-layer,
high peak velocity.
High correlation with Cooper et
al.
Experimental discrepancy:
–
–
Measurement technique.
Nozzle conditions.
20
Turbulence statistics
From Paper 1 & 6
urms (vrms) at r/D=0
Production of k at r/D=0
():
():
(О):
():
y/D
(vrms)
urms
•
•
•
Top-hat: negligible
level of fluctuations.
Pipe: Urms≈0.04,
sharp increase close to
the wall.
High correlation with
Geers et al.
urms at r/D=1
LES (pipe)
LES (top-hat)
Cooper et al.
Geers et al.
urms
Pk
•
•
•
•
Pk=0 for y/D>1.
•
Pipe: as the gradient
increases so does Pk.
Close to the wall Pk<0 as •
Pk (vrms2 - urms2).
•
Top-hat: overall zero
production.
•
As r/D increases:
inflow conditions less
important.
Pipe: clear near-wall
peak of Urms.
Overall good agreement
with experiments
(within tolerance for the
two exp. setups).
Top-hat: weaker wallshear  no distinct nearwall peak.
21
Effect from swirl
From Paper 3 & 6
Mean axial velocity decay
•
S=Ut/V0
Nu
y/D
•
Nusselt number
k
V/VCL
•
k at y/D=0.15
Jet spreading increases •
with swirl.
Top-hat: significant
increase 
•
recirculation bubble.
The bubble reaches
downstream to r/D≈1.
•
r/D
r/D
At small r/D k is
strongly influenced by
top-hat case,
swirl.
Less influence at larger
radius.
Significant influence from the
character of the inflow
– Radial distribution of the axial and
azimuthal velocity components.
– Swirl generator structures.
•
Pipe:( 
high
level
k
): LES
S=0of(pipe)
 high
(- - Nu.
-): LES S=1 (pipe)
S=1
(  ): Nu
LESis
S=0
(top-hat)
• Top-hat:
low,
despite
- -): of
LES
high (level
k.S=1 (top-hat)
(): Geers et al.
• Negligible rate of mean
flow convection.
(  ):
(- - -):
(  ):
(- - -):
():
LES S=0 (pipe)
LES S=1 (pipe)
LES S=0 (top-hat)
LES S=1 (top-hat)
Geers et al.
22
Outline
• Background
• Project description
• Computational method
and cases
• Results
• Summary
23
Summary
1. The inflow boundary conditions is of significant importance for
the development of the flow and scalar fields.
2. The underlying mechanisms of impinging jet heat transfer have
been identified, discussed and visualized.
3. The dynamics of non-swirling and swirling impinging jets have
been studied in some detail. Swirl has large effect on the wall
heat transfer. The swirl generating method is crucial.
4. The LES approach provides accurate results in an efficient
manner. The simulation method is not problem dependent.
24
Possible extensions
1. Study and explore (new) SGS models for the near-wall
region.
2. Determine quantitatively the sensitivity of the Nusselt
number from inflow condition uncertainties.
3. Study the effects of blade generated flow.
4. Determine the flow due to wall porosity.
5. Flow induces acoustics.
Instantaneous velocity field
Acoustics source distribution
25
Thank you!
26
27
Summary: wall heat transfer
From Paper 2 & 5
Correlation between Nu and Cf
Nu, Cf , k, 
Trends of: mean Nu, Cf , k, 
III
I
IV
Ruc
():
():
():
():
Nu
Cf
k

II
r/D
r/D
•
Nu: Local peak at r/D≈0.6.
•
•
Cf: Strong accelerating wall jet,
local peak at r/D≈0.7.
I: Low level of k, laminar-like wall jet 
high Ruc.
•
•
k: Zero in the core region, local
peak at r/D≈1.75.
II: Vortical structures penetrates the
wall boundary layer  low Ruc.
•
•
: Indicates formation of counter
rotating secondary vortices  high
k and local increase of Nu.
III: Convective structured primary
vortices  high Ruc.
•
IV: Influence from secondary vortices
and increasing level of irregular
structures, i.e. eddies  low Ruc.
28