AIAA 2002–2925
EXPERIMENTAL AND
COMPUTATIONAL INVESTIGATION
OF FLOW IN GAS TURBINE BLADE
COOLING PASSAGES
Harald Roclawski, Jamey D. Jacob, Tiangliang Yang,
& James M. McDonough
Mechanical Engineering Dept.
University of Kentucky
31st AIAA Fluid Dynamics
Conference and Exhibit
June 11-14, 2002/Anaheim, CA
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191–4344
June 7, 2001
EXPERIMENTAL AND COMPUTATIONAL
INVESTIGATION OF FLOW IN GAS
TURBINE BLADE COOLING PASSAGES
Harald Roclawski,∗ Jamey D. Jacob,† Tiangliang Yang,‡ & James M. McDonough§
Mechanical Engineering Dept.
University of Kentucky
Results of experimental and numerical investigations into gas turbine cooling passage
flows are presented. EXPAND ONCE ENTIRE PAPER IS COMPLETE.
Nomenclature
b
cf
D
FFP
h
H
Re
U∞
ν
ρ
Turbulators
Film−Cooling
Bleed Holes
Tip Bleed Air
Film−Cooling
Bleed Holes Trailing−Edge
Region
Turbulators
Bar height, 25.4mm
Skin friction coefficient
Channel width, 406mm
Forward flow probability
Backward facing step height, 28.6mm
Channel height, 203mm
Reynolds number
Freestream velocity
Viscosity
Density, kg/m3
Introduction
Continuing requirements for ever increasing
thrust/weight ratio in high-performance aircraft gas
turbine engines necessitates increasing operating temperatures to gain improved thermodynamic efficiency.
Even a fractional improvement in performance can
offer significant savings (see, for example, Mayle1 ).
Currently available materials for turbine blades are
unable to withstand long periods of exposure to
these high temperatures while maintaining structural
integrity, even with thermal barrier coatings (TBC),
implying need for active cooling strategies. Over
the past 30 years turbine temperatures have been
continually increased, and continuing improvements
in cooling techniques have been a major contribution
to this.
Several different approaches to cooling are usually
employed in cooling even a single turbine blade, as can
be inferred from a sample blade circuit shown in figure 1. In general, high-performance turbine blades are
cooled by a combination of exterior flow film cooling
which limits the heat flux from the combustion gases to
the blade material and interior cooling air circuit flows
which extract heat from the interior surfaces of the
∗ M.S.
student; member AIAA.
Professor; senior member AIAA.
‡ Post-doctoral Fellow; member AIAA.
§ Professor; senior member AIAA.
† Assistant
c 2002 by the authors. Published by the American
Copyright °
Institute of Aeronautics and Astronautics, Inc. with permission.
Incoming Cooling Air
Fig. 1 Typical turbine blade cooling circuit (after
Han et al., 1986).
blade. A key factor in this interior heat removal process is maintaining turbulent flow. At the same time
this results in greater pressure losses, so there must always be a tradeoff between cooling circuit heat transfer
effectiveness and pressure loss in turbine blade design
studies. A significant portion of the design effort is devoted to this problem, and it is especially difficult for
both experimental and computational fluid dynamics
(CFD) because of the highly complex geometries of
interior cooling air circuits, the turbulent flow, and in
the case of experiments, the need to account for high
rates of blade rotation.
Past experiments on turbine blade cooling have fo-
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American Institute of Aeronautics and Astronautics Paper 2002–2925
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cused on the flows within simple or complex channels
and the effect of turbulence generating devices on the
flow field and heat transfer rates. The effect of rotation, which is a requisite parameter in turbine flows,
has generally been ignored due to the complexity of
the experimental apparatus. This has proved to be a
major gap in in experimental testing. Also, the majority of experimental measurements have been single
point measurements, not allowing a full field analysis.
This point has proved particular difficulty when trying
to validate numerical simulations which benefit from
full field data. The maturation of modern optical field
measurements have allowed these hurdles to be overcome, though any experiments must require extreme
care in their formulation.
In the case of numerical simulations, turbulence
modeling based on Reynolds-averaged Navier-Stokes
(RANS) approaches has generally proven inadequate
for this problem, and typical Reynolds numbers (Re)
encountered in internal cooling air flows (∼ O(105 ))
preclude use of direct numerical simulation (DNS) in
most cases. But recent advances in computing power
and in numerical procedures associated with largeeddy simulation (LES) suggest that certain forms of
this approach may be applicable. However, a significant amount of laboratory experimentation is needed
for their validation, and (probably) tuning. In the
present paper we will focus on one particular aspect
of constructing synthetic velocity models. We remark
that there are many alternative approaches,15, 16 and
we shall not attempt a thorough review of the subject. Instead, we will concentrate on the Hylin and
McDonough17 formalism.
Previous Work
Previous experimental research in turbine blade
cooling has been primarily focused on the external
cooling effects (e.g., Wang et. al2 ). This is due to
the relative ease of the external measurements as compared to the complex apparatus or gross simplifications required for internal duct measurements, particularly when it applies to measurements of the flow
field. Previous research efforts on internal cooling
have been limited in scope, typically focusing on a single aspect of the multivariant problem. Bunker and
Metzger3 examined the local heat transfer from internal impingement cooling using temperature sensitive
paint. General relations showed increased heat transfer with increased jet Reynolds number. Bohn et. al4
numerically and experimentally examined trailing edge
cooling in turbine blades. The experiments were conducted in a scaled test rig and showed anisotropic turbulence profiles resulting in non-symmetrical coolant
distribution. The numerical predictions compared reasonably well with the experimental data. Johnson et.
al5 examined the heat transfer within rotating serpentine passages. Geometry and orientation were found
to have large effects on the maximum local heat transfer. Specifically, the angle to which the passage was
inclinded respective to the axis of rotation was found
to vary the heat transer ratio up to 50%. Flannery
et. al6 examined the heat transfer properties of various
heat transfer enhancement devices within a cooling circuit using napthalene sublimation. Dimensional analysis and scale modeling showed improvement in heat
transfer in vortex flow cavities and sand-dune shaped
turbulators, though actual measurements in a channel or rotating cavity were not performed. Morris and
Chang7 investigated the heat transfer properties of a
circular cooling channel. Full field heat transfer data
were obtained through a combination of measurements
and solution of the channel wall heat conduction equation. The resulting internal heat flux distribution over
the full inner surface was subsequently used to determine the local variation of heat transfer coefficient.
Effects of the Coriolis force and centripetal buoyancy
on the forced convection mechanism were investigated
and found to be of sufficient order to warrent consideration in further experimental and numerical studies.
Cakan and Arts8 studied the flow in a straight, rectangular, rib-roughened internal cooling channel. At a
Reynolds number of 6500 and 30000 and a rib blockage
ratio of 0.133, DPIV measurements were taken. They
found that the flow through the ribbed channel can be
characterized by a series of accelerations, decelerations
with separation, reattachment and redevelopment due
to the sudden changes in cross-section. The ribs induce
a separation and recirculation bubble. The flow reattaches at X/e = 4.5 (Re = 6500). Comparing both
studies, they claim that the reattachment distance is
not strongly dependent on the Reynolds number. Upstream of the ribs, the flow impinges on the rib, moves
to the sidewalls of the channel and produces to vortices. Behind the rib a similar motion occurs due to the
recirculation region. In the span wise flow direction;
two counter rotating secondary flow cells are observed.
The flow in a straight, rectangular channel with ribs
on two opposite walls was investigated by Lio et. al9
by means of LDV. The Reynolds number based on the
channel hydraulic diameter was 33000. The ribs were
perforated and the effect of the rib open area ratio was
investigated. They also found a periodic accelerating
and decelerating flow behavior. In contrast to the previous paper, only one secondary flow cell is observed in
the span wise flow direction. Furthermore, it was discovered that the reattachment length downstream of a
rib pair is shorter than in the case of a backward-facing
step. The maximum heat transfer rate was found to
be dependent upon a critical range of the open area
ratio governed by whether the flow treated the ribs as
permeable or impermeable. A PIV Investigation of the
flow in a rectangular channel with a 90◦ and 45◦ rib
arrangement and a 180◦ bend was done by Schabacker
and Bölcs10 at Re = 45700 and a rib height equal to
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0.1 hydraulic diameters. Two counter rotating vortices
in the span wise flow direction were observed. The development length to achieve a fully developed flow condition is longer for the case of a 45◦ rib arrangement.
Furthermore, the 45◦ ribs prevent the development of
zones of recirculating flow in the upstream outer corner of the bend and the curvature-induced secondary
flows a weakened in this section of the channel. Compared to a smooth channel, the flow recovers faster
from the bend effect. Results for the case of a stationary and rotating, rectangular, ribbed channel with a
180◦ bend were obtained by Servouze11 using LDV.
The flow conditions were Re=5000, Ro=0.33 and a
rib aspect ratio of 10. In the stationary case a periodic accelerating and decelerating flow behavior was
found. In contrast to other papers, secondary flow
structures (vortices) in the span wise flow direction
were not observed. Iacovides12 did an LDA study
on the flow in a ribbed channel with a 180◦ bend.
He investigated a staionary case at a Re=100000 and
two rotating cases at Ro=(+-)0.2. The rib-height to
duct diameter ratio was 0.1 He also observes a periodic flow behavior. Because of the ribs, turbulence
increases at the bend entry and an additional separation bubble over the first rib interval downstream of
the bend exit is formed. Nevertheless, in agreement
with Schabacker and Bölcs, it is claimed that the flow
recovers faster from the bend effect in a ribbed channel. Especially the separation bubble along the inner
wall is reduced. Lastly, Hwang and Lai14 examined
laminar flow within a rotating multiple-pass channel
with bends from a computational standpoint. Rotation was found to have a large impact on the wall
friction factor. Validations were only made with stationary experiments, however. Heat transfer rate or
turbulators were not examined.
Previous Modeling Efforts
Put previous modeling in here.
Experimental Portion
Setup & Diagnostics
The wind tunnel arrangements for the backward
facing step and turbulator experiments are shown in
figure 11(a) and 11(c), respectively. Both test sections
were installed in a low-turbulence open-circuit blowdown wind tunnel. A 7.5 hp motor powers a radial
fan at the inlet. A vibration damper, flow straightener,
and turbulence dampening screens precede the nozzle
which has a contraction ratio of 6.7. The maximum
test section velocity is 35 m/s with an open exhaust
and approximately 10 m/s when a filter is installed
to capture seeding particles. The test sections have
a channel height H of 0.2 m (203 mm) and width D
of 0.4 m (406 mm). The backward facing step has a
step height h of 28.6 mm. The turbulator test section is arranged so that multiple square ribs of various
Geometry
BFS
Turbulator
Table 1
Scale
h
H
b
H
Re Range
2.0 · 103 − 1.7 · 104
1.4 · 104 − 1.2 · 105
1.8 · 103 − 1.8 · 104
1.4 · 104 − 1.4 · 105
Experimental Parameters
sizes can be placed in different locations in the channel. The current paper presents results for ribs of equal
sizes with sides b = 24.5 mm. Ribs arrangements of 1,
2, 3, and 4 bars are examined with equal separation
distances of 152 mm in the multiple turbulator runs.
Re based on channel height, step size, and rib size are
reported in table 1.
In both the backward facing step and turbulator
test sections, PIV, HWA, and static pressure measurements were made along the tunnel centerline downstream of the step and last rib, respectively. For PIV,
the laser sheet was generated by a 25 mJ double-pulsed
Nd:YAG laser with a maximum repetition rate of 15
Hz. Pulse separations varied from 100 µs to 1 ms
based upon the tunnel velocity. A 10 bit CCD camera with a 1008×1018 pixel array was used to capture
images. Uniform seeding was accomplished using either zinc stearate or talc injected at the fan inlet; a 1
micron filter at the tunnel exhaust was required to capture the particles thus reducing the maximum tunnel
velocity during PIV. A predictor-corrector algorithm
with an interrogation area of 32×32 was used to generate displacement vectors and velocity gradients.13 For
the hot-wire measurements, which are required to obtain details of random fluctuations in velocity for the
modeling efforts, a single-component boundary layer
hot-wire probe was used capable of wall measurements
within 0.3 mm of the surface. 40,000 points or greater
were recored at a sampling rate 10 kHz. For the static
pressure measurements, pressure taps were placed 25.4
mm apart downstream of the backward facing step and
slightly upstream and downstream of the last turbulator. Pressure measurements were made up to 14.5 b
downstream of the turbulator in the results presented
here.
Results
Backward Facing Step
insert discussion files
Turbulators
insert discussion files
Discussion
Modeling
In the present paper we will focus on one particular aspect of constructing synthetic velocity models. We remark that there are many alternative approaches,15, 16 and we shall not attempt a thorough
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review of the subject. Instead, we will concentrate on
the Hylin and McDonough17 formalism.
We begin by noting that synthetic velocity turbulence models offer the potential of a much closer connection to laboratory measurements than can be obtained with other modeling approaches because primitive variables (e.g., velocity components) are directly
modeled and used instead of attempting to model flow
statistics—Reynolds stresses.
Within the Hylin and McDonough framework, a
subgrid-scale quantity is expressed as a product of
three factors, e.g.,
u ∗ = A u ζu Mu .
(1)
in McDonough and Huang.24, 25 The other two parameters are most closely associated with shear stress: uy
and vx in 2D. As noted in McDonough and Huang,25
in order to construct reliable synthetic velocities by
employing nonlinear DDSs it is essential to find a mapping between physical parameters, say Re and ∇U and
the above bifurcation parameters of the map(s). The
present paper documents our initial attempts to accomplish this for a specific flow geometry.
We begin by noting that in order to establish such
a mapping we must first be able to accurately express
any appropriate set of physical data in terms of bifurcation parameters of the DDS. This is nothing more
than a curve-fitting problem, and McDonough et al.26
and Mukerji et al.27 provided an approach to solving
it. This consists of first recognizing that an “exact”
polynomial fit is not appropriate (cf., Casdagli and Eubank,28 for examples where it is appropriate), and that
a global least-squares fit is needed. The next step is to
determine a set of data characterizations by means of
which to compare the fit with the original data. McDonough et al.26 provide a long list of these but make
no claims as to either the necessity of any single one,
or sufficiency of the set as a whole.
Once such a set of characterizations is chosen, we
construct the model in the form given in McDonough
et al.:26
Here u∗ is a SGS velocity component; Au is an amplitude factor; ζu is an anisotropy correction, and Mu is
a temporal fluctuation. Each of the three factors on
the right-hand side of (1) varies across the spatial grid,
and from one resolved-scale time step to the next.
Expressions for the first two factors have been derived from first principles employing the Kolmogorov
theory of homogeneous turbulence (see Frisch,18
for a good overview), as given in Hylin and McDonough17, 19, 20 ) and Sagaut.21 The third factor received little specific attention in early investigations.
Hylin22 associated this factor with Kolmogorov’s
“stochastic variable,” and considered the logistic map,
“absolute value” logistic map and tent map for realizations. All appear to give similar results when the
same map is used for all velocity components.
Two-dimensional simulations of turbine blade cooling presented by McDonough et al.23 suggest that
using the same map for all solution components is not
correct (especially for passive scalars). McDonough
and Huang24 provide a derivation of appropriate maps
for use in (1) for reduced-kinetics H2 –O2 combustion
and show that the maps (discrete dynamical systems,
DDSs) arising from the Navier–Stokes equations are
basically logistic maps while those corresponding to
thermal energy and species concentrations are not.
Finally, McDonough and Huang25 present a detailed
analysis of the 2-D “poor man’s N.–S. equations” derived as in the previous reference. They show that
essentially every temporal behavior seen in actual N.–
S. flows can be produced by this simple 2-D DDS:
³
´
a(n+1) = β1 a(n) ³ 1 − a(n)´ − γ1 a(n) b(n) ,
b(n+1) = β2 b(n) 1 − b(n) − γ2 a(n) b(n) ,
(2)
Details of this expression can be found in the cited
references, but we briefly note the following. The parameters θ, αk , βk , ωk , dk and K must all be found
in the course of the curve-fitting process. The αk are
amplitude factors and can be considered analogous to
Fourier coefficients (although they do not arise from a
formal inner product). Sk is a nonlinear discontinuous
function of the behavior of the map; its purpose is to
allow existence of frequencies of oscillation not found
in the DDS, itself (i.e., lower frequencies) in addition
to permitting modeling of very irregular intermittencies. The parameters ωk are the frequencies at which
iterations of the k th map will be initiated; dk is the
duration of evaluation once initiated; βk is the bifurcation parameter, and for purposes herein, the form of
the k th map is
³
´
(n+1)
(n)
(n)
mk
= β k mk
1 − mk
,
(3)
where (a, b)T can be viewed as high-wavenumber
Fourier coefficients of the velocity field, U = (U, V )T .
This DDS contains four bifurcations parameters (β1 ,
β2 , γ1 , γ2 ). The first two are directly related to the
Reynolds number, Re, or possibly the integral scale or
Taylor microscale Re, depending on details of implementation,17 and thus might reasonably be set equal as
the basic logistic map (see, e.g., May, 1976, for an
interesting and detailed treatment).
We will use the scalar map (3) in the present study,
rather than the 2-D map described above, because the
temporal resolution of the current 2-D PIV data is
insufficient for capturing details of subgrid-scale turbulent fluctuations. On the other hand, the single
M (n+1) = (1−θ)M (n) +θ
K
X
(n+1)
α k Sk
(dk , ωk , mk (βk )) .
k=1
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velocity component obtained from hot-wire measurements at 10 KHz is sufficient. Our goal is thus to
determine the variation of each of the parameters in
Eq. (2) at a specific location in the physical flow field
as a function of Re.
For each value of Re considered we will construct
two separate curve fits of the data. The first will be
based on the complete velocity signal and thus, up to
subtracting out the mean, corresponds to a Reynoldsaveraged N.–S. (RANS) quantity:
u0 (x, t) = U (x, t) − u(x),
where the overbar denotes time average. The second
will be obtained from high-pass filtered data analogous
to the SGS behavior in a LES formalism. In this case
u∗ (x, t) = U (x, t) − ũ(x, t),
where tilde denotes (formally) a spatial filtering.
Both cases are of interest because the ability to fit
both types of data shows that synthetic velocity fields
are applicable to both LES and RANS models. But
in addition, with both fits available we will see that
they are very different—as one should expect. This
raises very serious questions regarding validity of certain forms of “very” large-eddy simulation (VLES)
in which “time-accurate” RANS equations are solved,
and conversely to forms of LES in which RANS formalisms are employed to construct the SGS models.
At the fundamental mathematical level RANS and
LES are quite different, and the results we present below provide a direct empirical demonstration of this.
Thus, considrable care must be taken when attempting to bridge the gap between these two modeling
approaches.
The cases we consider correspond to Re = 4 × 104
and Re = 1 × 105 for the turbulator flows discussed
above in the section on experiments. For both values
of Re the measurement location was ?? mm upstream
of reattachment, and at a height of 3.5 mm, behind the
first turbulator. The curve-fitting process was carried
out essentially as described in McDonough et al.26 and
Mukerji et al. ,27 and as in those references once the
process is complete we compare three additional features: i) the “appearance” of the time series, ii) the
power spectral density, and iii) the delay map.
As emphasized in these references, we consider the
appearance of the modeled time series to be essential
to a good fit of the data (just as would be the case
in an exact fit), and the characterizations employed
in the least-squares fit are selected to guarantee this.
But appearance in this case is a nontrivial notion, first
because it is difficult to define precisely, and second
because the objective function for the least-squares fit
is highly nonlinear, discontinuous, contains both real
and integer variables, and thus generally has multiple
local minima.
McDonough et al.26 discuss appearance of the time
series in some detail, indicating that close examination of most such data will lead to identification of a
finite number of types of “structures.” The number of
these is typically used as the initial guess for the value
of K, the number of terms in the model representation, Eq. (2). In comparing the model with the data
it is important to observe, as already noted, that the
fit is not intended to be exact because an exact fit is
intrinsically incompatible with the physics (and mathematics) of a turbulent flow. Our rule of thumb for
checking that the model has preserved the appearance
of the data is that if the modeled time series and data
are juxtaposed, it should be impossible to determine
where the data ends and the model begins.
Use of power spectra and delay maps as additional
tests of goodness of fit is recommended because appearance is at best only semi-quantitative. On the
other hand, neither of these characterizations alone
will guarantee a good fit. Many different time series
exhibit very similar power spectra, and the delay map
provides only basic topological information associated
with the underlying attractor (if there is one). Nevertheless, both of these can be of value in “fine tuning”
a fit of data.
Results for Complete Velocity
Figure ? displays three complete velocity time series in parts (a) through (c). The first corresponds to
experimental data for Re = 4 × 104 ; the second represents evaluation of the model, Eq. (2), with and initial
guess of the parameters to be determined in the leastsquares fit, and the third shows the final fit of data.
We display part (b) of the figure to emphasize that
finding the correct parameters is a nontrivial process
(and one which requires considerable CPU time). Table ? displays the initial guess of the parameter values
and the associated objective function value, as well as
the same data for the final fit, for both values of Re
considered. Part (c) of the figure indicates a significant improvement over the initial guess, and in fact a
fairly good representation of the data.
Figures ?? and ??? display comparisons of power
spectra and delay maps, respectively, with part (a)
corresponding to measured data and part (b) to modeled results in both cases.
Similar results are presented in Figs. ????, ?????
and ?????? for the Re = 1 × 105 case, except that
we have not shown the initial guess result in Fig. ????.
[Give comparative discussion of these results,
and indicate dependence on Re from Table ?.
Discuss application to RANS modeling.]
Results for High-Pass Filtered Velocity
[Repeat above figures (no Fig. ?(b)); indicate
suitability for LES SGS models. Discuss Re dependence of data.]
[Compare model results in the two cases
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emphasizing differences between complete and
high-pass filtered behaviors—e.g., variation of
parameters with Re.]
Discussion
Continuing Work
Acknowledgements
12
H. Iacovides, D.C. Jackson, H.Ji, G.Kelemenis,
B.E.Launder, K.Nikas LDA Study of the Flow Development Through an Orthogonally Rotating U-Bend
of Strong Curvature and Rib-Roughened Walls, Journal of Turbomachinery, April 1998 Vol.120 p. 386391.
13
Raffel, M., Willert, C., and Kompenhans, J. Particle Image Velocimetry: A Practical Guide, SpringerVerlag, 1998.
This work is supported by AFOSR grant F4962000-1-0258 under the supervision of Dr. Tom Beutner.
REFERENCES
14
Note : CHECK ALL REFERENCES HERE AND
IN TEXT FOR CONSISTENCY, ACCURACY, and
TIMELINESS. THEY WILL BE UNIFORMLY REFORMATTED ONCE COMPLETE.
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E. C. Hylin, J. M. McDonough (1999). Int. J. Fluid
Mech. Res., 26, 539-567.
M. Marion, R. Temam (1989). SIAM J. Numer. Anal.
26, 1139–1157.
J. M. McDonough (1995). Int. J. Fluid Mech. Res. 22,
27–55
J. M. McDonough (1997). In Parallel Computational
Fluid Dynamics: Algorithms and Results Using Advanced Computers, Schiano, et al. (Eds.) Elsevier
Science B. V. Amsterdam, 92–99
J. M. McDonough, R. C. Bywater (1986). AIAA J.
24, 1924–1930.
J. M. McDonough, R. C. Bywater (1989). In Forum on
Turbulent Flows–1989. Bower, Morris (Eds.), ASMEFED 76, ASME, NY, 7–12.
J. M. McDonough, J. C. Buell, R. C. Bywater (1984a).
ASME Paper 84-WA/HT-16,
J. M. McDonough, R. C. Bywater, J. C. Buell (1984b).
AIAA Paper 84-1674.
J. M. McDonough, S. Mukerji and S. Chung (1998b).
Appl. Comput. Math. 95, 219–243.
J. M. McDonough, K. Saito (1994). Fire Sci. and
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J. M. McDonough, D. Wang (1995). In Parallel Computational Fluid Dynamics: New Algorithms and Applications. N. Satofuka et al. (Eds.), Elsevier Science
B. V. Amsterdam, 129–136.
S. Mukerji, J. M. McDonough, M. P. Mengüç, S. Manickavasagam and S. Chung (1998). Int. J. Heat Mass
Transfer 41, 4095–4112.
M. J. Sholl, Ö. Savaş (1997). AIAA Paper 97-0493.
E. F. C. Somercales (1974). In Flow: Its Measurement
and Control in Science and Industry, 1, Instrument
Society of America, 795–808.
R. Temam (1996). J. Comput. Phys. 127, 309–315.
Y. Yang, J. M. McDonough (1992). In Bifurcation
Phenomena and Chaos in Thermal Convection. Bau
et. al. (Eds.). ASME-HTD 214, ASME, NY, 85–92.
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June 7, 2001
U
PIV
regi
on 1
PIV
regi
on 2
(H−h)
HWA
regi
on
H
h
D
a) Backward facing step geometry.
U
PIV
regi
on 1
PIV
HWA
regi
on 2
regi
on
H
s
b
D
b) Turbulator geometry.
Fig. 2
Channel geometry for experimental studies.
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Velocity Magnitude
5
2.5
4.5
2
4
y/h
3.5
1.5
3
2.5
1
2
1.5
0.5
1
0
−1
0
1
2
3
4
x/b
RMS Turbulence
2.5
0.9
0.8
2
y/h
0.7
1.5
0.6
0.5
1
0.4
0.3
0.5
0.2
0
−1
0
1
2
3
4
x/b
Fig. 3
Channel geometry for experimental studies.
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0.1
June 7, 2001
12
y/h
Velocity Magnitude
10
2
8
1
6
0
0
2
4
6
x/b
8
10
12
4
2
0.8
RMS Turbulence
y/h
2
0.6
1
0.4
0
0
2
4
Fig. 4
6
x/b
8
10
12
0.2
Channel geometry for experimental studies.
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u/U
2.5
y/h
2
1.5
1
0.5
0
−1
0
1
2
3
4
5
6
4
5
6
7
11
12
13
14
x/b
a) Backward facing step geometry.
2.5
y/h
2
u/U
1.5
1
0.5
0
0
1
2
3
x/b
2.5
y/h
2
1.5
1
0.5
0
7
8
9
10
x/b
b) Turbulator geometry.
Fig. 5
Channel geometry for experimental studies.
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2.5
u/U
y/h
2
1.5
1
0.5
0
−1
0
1
2
3
4
5
6
7
x/b
2.5
y/h
2
1.5
1
0.5
0
7
8
9
10
11
12
13
x/b
Fig. 6
Channel geometry for experimental studies.
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American Institute of Aeronautics and Astronautics Paper 2002–2925
14
15
June 7, 2001
1 bar
y/h
2
1
0
−1
0
1
2
3
4
2 bars
5
6
7
8
9
0
1
2
3
4
4 bars
5
6
7
8
9
0
1
2
3
4
x/b
5
6
7
8
9
y/h
2
1
0
−1
y/h
2
1
0
−1
Fig. 7
Channel geometry for experimental studies.
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American Institute of Aeronautics and Astronautics Paper 2002–2925
June 7, 2001
1 bar
y/h
2
1
0
0
2
4
6
8
10
12
6
8
10
12
6
8
10
12
2 bars
y/h
2
1
0
0
2
4
4 bars
y/h
2
1
0
0
2
4
x/b
Fig. 8
Channel geometry for experimental studies.
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American Institute of Aeronautics and Astronautics Paper 2002–2925
June 7, 2001
1 bar
y/h
2
1
0
0
2
4
6
8
10
12
6
8
10
12
6
8
10
12
2 bars
y/h
2
1
0
0
2
4
4 bars
y/h
2
1
0
0
2
4
x/b
Fig. 9
Channel geometry for experimental studies.
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1 bar
y/h
2
1
0
−1
0
1
2
3
4
2 bars
5
6
7
8
9
0
1
2
3
4
4 bars
5
6
7
8
9
0
1
2
3
4
x/b
5
6
7
8
9
y/h
2
1
0
−1
y/h
2
1
0
−1
Fig. 10
Channel geometry for experimental studies.
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June 7, 2001
1
Cp
Cp
1
0
0
1 bar
−2
0
2
4
1 bar
6
8
10
12
14
−1
−4
16
−2
0
2
4
−2
0
2
4
−2
0
2
4
6
0
0
2
4
8
10
12
14
−1
−4
1
16
6
0
2
4
16
8
10
12
14
16
8
10
12
14
16
8
10
12
14
16
3 bars
6
8
10
12
14
−1
−4
1
16
Cp
−2
0
6
0
4 bars
0
2
4
4 bars
6
x/b
8
10
12
14
−1
−4
16
−2
0
a) Backward facing step geometry.
2
4
6
x/b
b) Turbulator geometry.
Cp
1
0
1 bar
−1
−4
−2
0
2
4
−2
0
2
4
−2
0
2
4
−2
0
2
4
6
8
10
12
14
16
8
10
12
14
16
8
10
12
14
16
8
10
12
14
16
Cp
1
0
2 bars
−1
−4
6
1
Cp
−2
0
3 bars
−1
−4
6
1
Cp
Cp
14
0
3 bars
−1
−4
12
2 bars
6
Cp
Cp
−2
0
−1
−4
1
10
0
2 bars
−1
−4
1
8
1
Cp
Cp
−1
−4
1
0
4 bars
−1
−4
6
c) Turbulator geometry.
Fig. 11
Channel geometry for experimental studies.
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m/s
s
−1
60
0.8
40
Velocity: BFS
0.7
Vorticity: BFS
20
0.6
0
0.5
−20
0.4
0.3
−40
0.2
−60
0.1
−80
a) Velocity.
b) Vorticity.
0.16
0.9
0.14
RMS Turbulence Intensity: BFS
FFP: BFS
0.12
0.8
0.7
0.1
0.6
0.5
0.08
0.4
0.06
0.3
0.04
0.2
0.02
c) RMS turbulence intensity.
Fig. 12
0.1
d) Forward flow probability.
Backward facing step PIV: U∞ =0.89 m/s, Re =1,702.
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m/s
s−1
200
2.5
150
Velocity: BFS
Vorticity: BFS
2
100
50
1.5
0
−50
1
−100
−150
0.5
−200
a) Velocity.
b) Vorticity.
0.9
0.3
RMS Turbulence Intensity: BFS
FFP: BFS
0.25
0.8
0.7
0.6
0.2
0.5
0.15
0.4
0.3
0.1
0.2
0.05
0.1
c) RMS turbulence intensity.
Fig. 13
d) Forward flow probability.
Backward facing step PIV: U∞ =2.56 m/s, Re =4,880.
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m/s
s−1
8
600
7
Velocity: BFS
Vorticity: BFS
400
6
200
5
4
0
3
−200
2
−400
1
a) Velocity.
b) Vorticity.
0.4
RMS Turbulence Intensity: BFS
0.35
0.9
FFP: BFS
0.8
0.7
0.3
0.6
0.25
0.5
0.2
0.4
0.15
0.3
0.1
0.2
0.05
c) RMS turbulence intensity.
Fig. 14
Fig. 15
0.1
d) Forward flow probability.
Backward facing step PIV: U∞ =7.69 m/s, Re =14,657.
Detail of reattachment for backward facing step: U∞ =2.56 m/s, Re =4,880..
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m/s
s
40
0.7
0.6
Velocity: BFS
−1
Vorticity: BFS
20
0.5
0
0.4
−20
0.3
−40
0.2
−60
0.1
a) Velocity.
b) Vorticity.
0.12
0.9
0.8
FFP: BFS
RMS Turbulence Intensity: BFS
0.1
0.7
0.08
0.6
0.5
0.06
0.4
0.04
0.3
0.2
0.02
0.1
c) RMS turbulence intensity.
Fig. 16
d) Forward flow probability.
Turbulator - single rub PIV: U∞ =0.71 m/s, Re =1,350.
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CFD figures to go here.
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