Stereoscopic PIV Measurements of Swirling Flow Entering a Catalyst Substrate T. Persoons * , Trinity College Dublin, Mechanical Engineering Department, Parsons Building, Dublin 2, Ireland, tel: +353-1-8968503, fax: +353-1-6795554 M. Vanierschot and E. Van den Bulck Katholieke Universiteit Leuven, Department of Mechanical Engineering, Celestijnenlaan 300A, 3001 Leuven, Belgium Abstract This experimental study investigates the stagnation region of a swirling flow entering an automotive catalyst substrate. A methodology is established using stereoscopic particle image velocimetry (PIV) to determine three-component velocity distribu- tions up to 0.2 mm from the catalyst entrance face. In adverse conditions of strong out-of-plane velocity, PIV operating parameters are adjusted for maximum spatial correlation strength. The measurement distance to the catalyst is sufficiently small to observe radial flow spreading. A scaling analysis of the stagnation flow region provides a model for the flow uniformization as a function of the catalyst pressure drop. Key words: swirling, oblique, inclined flow, catalyst, entrance, stereoscopic particle image velocimetry, correlation strength, out-of-plane velocity PACS: 44.15.+a, 47.32.Ef, 47.80.Cb Nomenclature D, d hydraulic diameter of annular duct and substrate channel, m E beam expansion ratio F loss of spatial correlation factor f focal length, m * Corresponding author. Email address: [email protected](T. Persoons). Preprint submitted to Exp. Therm. Fluid Sci. 1 May 2008
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Stereoscopic PIV Measurements of Swirling
Flow Entering a Catalyst Substrate
T. Persoons ∗,Trinity College Dublin, Mechanical Engineering Department, Parsons Building,
Katholieke Universiteit Leuven, Department of Mechanical Engineering,Celestijnenlaan 300A, 3001 Leuven, Belgium
Abstract
This experimental study investigates the stagnation region of a swirling flow enteringan automotive catalyst substrate. A methodology is established using stereoscopicparticle image velocimetry (PIV) to determine three-component velocity distribu-tions up to 0.2 mm from the catalyst entrance face. In adverse conditions of strongout-of-plane velocity, PIV operating parameters are adjusted for maximum spatialcorrelation strength. The measurement distance to the catalyst is sufficiently smallto observe radial flow spreading. A scaling analysis of the stagnation flow regionprovides a model for the flow uniformization as a function of the catalyst pressuredrop.
D, d hydraulic diameter of annular duct and substrate channel, mE beam expansion ratioF loss of spatial correlation factorf focal length, m
∗ Corresponding author.Email address: [email protected] (T. Persoons).
Preprint submitted to Exp. Therm. Fluid Sci. 1 May 2008
K pressure loss, relative to the dynamic head in the substratechannel
L substrate channel length, mM2 spatial mode of laser headN number of particles per interrogation windowR, Ri outer and inner radius of the annular duct, mS, SW swirl number and swirl vane settingU , V , W axial, radial and tangential velocity, m/st, ts beam diameter and sheet thickness, mx, r axial and radial coordinate, mGreek symbolsα incidence angle of the oblique flow (tanα = Ut/U ), ◦
ε open frontal area ratioλ wavelength, mψ camera elevation angle, ◦
τ laser pulse separation time, sθ tangential coordinate, ◦
ρ density, kg/m3
Subscripts0, 1, 2, 3 laser head, lenses 1 through 3c substrate channelI interrogation windowm cross-sectional average
t transverse velocity component (e.g. Ut =√V 2 +W 2)
1 Introduction1
Devices for exchange of mass or heat (e.g. catalytic converter, heat exchanger,2
particulate filters) operate optimally when the flow is uniformly distributed3
over the cross-section. In this case, the pressure loss is minimal and the effi-4
ciency of mass or heat exchange is maximal. For a catalyst, a uniform flow5
distribution avoids local degradation or ageing [1].6
The flow distribution across such devices is largely determined by the upstream7
flow conditions. For the specific case of automotive catalysts, an additional8
pressure loss is caused by oblique or swirling flow entrance. Since the flow in9
the catalyst is laminar (typically 200 < Re < 2000), the pressure loss in the10
channel is approximately linearly proportional to the axial velocity, whereas11
the additional pressure loss is proportional to the square of the tangential12
approach velocity. This effect is not negligible and has been shown to strongly13
affect the flow distribution [2, 3, 4] and as such, the mass or heat exchange14
2
efficiency.15
Kuchemann and Weber [5] proposed two models for the oblique inlet pressure16
loss in finned heat exchangers, depending on the flow conditions near the17
entrance. (i) The first model assumes no suction can be sustained on the18
leeward side of the channel walls, which is equivalent to a total loss of the19
transverse dynamic head. (ii) The second model (Kα = tan2 α, where α is20
the flow incidence angle) assumes lossless flow if α < αcrit. The critical angle21
αcrit depends on the overall pressure loss in the entire channel. Kuchemann and22
Weber [5] present experimental data that confirm the validity of the first model23
for laminar flow, and the second model for turbulent flow, since turbulent flow24
can sustain stronger suction without leading to full flow separation.25
Persoons et al. [6] discuss the available literature on the oblique inlet pressure26
loss. The findings vary between the limiting cases outlined by Kuchemann27
and Weber [5]. Using the same experimental rig as presented in this study,28
Persoons et al. [6] have derived a correlation for the oblique inlet pressure loss29
for an unwashcoated automotive catalyst (cell density 400 cells per square30
inch, wall thickness 4.3× 10−3 inch):31
Kα =Kα,1 tan2 α, where Kα,1 = 0.459 (1)
(±13%, R2 = 0.81)
which is valid for different substrate lengths (4.3 6 L/d 6 44). This correla-32
tion resembles the first model of Kuchemann and Weber [5], however with a33
[14] A. Gupta, G. Lilley, N. Syred, Swirl Flows, Abacus Press, Tunbridge375
Wells, UK, 1984.376
[15] C. Willert, Stereoscopic digital particle image velocimetry for applications377
in wind tunnel flows, Measurement Science and Technology 8 (12) (1997)378
1465-1479.379
[16] B. Wieneke, Stereo-PIV using self-calibration on particle images, Exper-380
iments in Fluids 39 (2) (2005) 267-280.381
[17] R.D. Keane, R.J. Adrian, Theory of cross-correlation analysis of PIV382
images, Applied Scientific Research 49 (3) (1992) 191-215.383
[18] J. Westerweel, Fundamentals of digital particle image velocimetry, Mea-384
13
surement Science and Technology 8 (12) (1997) 1379-1392.385
[19] M. Raffel, C. Willert, J. Kompenhans, Particle image velocimetry, a prac-386
tical guide, Springer-Verlag, 1998.387
[20] J. Westerweel, Theoretical analysis of the measurement precision in par-388
ticle image velocimetry, Experiments in Fluids 29 (Suppl.) (2000) S3-S12.389
14
Figure captions390
(a)Roots
blower
pp , t
flow rate
orifice
adjustable swirl
swirl generator + annular duct
L L
L
poo o
a
p
*
(b)
θ
x
r
V
U
Wpositive
swirl viewing glass
L
RRi
W
U
r
x
rx
2ψ
V
Fig. 1. Annular swirling flow rig: (a) overview and (b) detail of the measurementsection
15
3
(top view)
(side view)
PIV laser
PIV laser
viewingglass
swirlgenerator
catalystsubstrate (view A)
2ψ
two high-speed camerasin Scheimpflug arrangement
laser light sheet
A
2 1
32 1
s ∆xx s
Fig. 2. Optical arrangement of laser light sheet and cameras
16
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
U/Um
(L/d = 10.3, SW = 1.00, Um
= 16.4 m/s)
Ri
R
0.60.7 0.70.8 0.80.9
1 1 1 1
1 1
1
1.1
1.1
1.1
0.9
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
V/Um
(L/d = 10.3, SW = 1.00, Um
= 16.4 m/s)
Ri
R
−0.040.04
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
W/Um
(L/d = 10.3, SW = 1.00, Um
= 16.4 m/s)
Ri
R
0.2 0.20.3 0.30.4 0.40.50.5
0.6
0.6
0.60.6
0.6
Fig. 3. {U, V, W} velocity distribution for L = 12 mm substrate, swirl setting 100%
17
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
U/Um
(L/d = 10.3, SW = 0.00, Um
= 16.4 m/s)
Ri
R
0.7 0.7 0.7 0.80.8 0.9 0.9
1 1
1 1
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
V/Um
(L/d = 10.3, SW = 0.00, Um
= 16.4 m/s)
Ri
R
−0.04
−2 −1.5 −1 −0.5 0
x/D, axial
r, r
adia
l
W/Um
(L/d = 10.3, SW = 0.00, Um
= 16.4 m/s)
Ri
R
Fig. 4. {U, V,W} velocity distribution for L = 12 mm substrate, swirl setting 0%
18
0.75 0.8 0.85 0.9 0.95 10
0.5
1
1.5
r / R (−)
Vel
ocity
(−
)
L / d = 22.4, SW = 1.00, x = −0.5 D
U/Um
(Um
= 14.4 ± 0.05 m/s)
W/Um
(Wm
= 9.1 ± 0.04 m/s), S = 0.56 ± 0.01
(a)
−2 −1.5 −1 −0.5 00
0.5
1
1.5
x / D (−)
Vel
ocity
(−
)
L / d = 22.4, SW = 1.00, r = R*
U/Um
(Um
= 15.3 ± 0.14 m/s)
W/Um
(Wm
= 9.3 ± 0.13 m/s)
(b)
Fig. 5. (a) Radial and (b) axial velocity profile for L = 26 mm substrate, swirlsetting 100% at (a) x = −0.5D and (b) r = R∗ = (Ri + R)/2: PIV (lines) versusLDA (white markers)
19
R
R
Ri
*
r
Vmax
D/2
U∞∆U
x → −∞m
r
U0∆U
x = 0m
(a)
10−1
100
101
0
0.2
0.4
0.6
0.8
1
K (−)
∆U0 /
∆U∞ (
−)
x0,U
= cst
x0,U
~ K1/2
measurements
(b)
Fig. 6. Scaling analysis in the flow stagnation region: (a) definitions and (b) flowuniformization versus pressure drop K
20
Tables391
Table 1Velocity profile characteristics for 4.3 6 L/d 6 22, 0 6 tanα 6 0.7 and 850 6Red 6 2100