# Experimental Investigation of Innovative Internal Trailing Edge Cooling Configurations with Pentagonal Arrangement and Elliptic Pin Fin

Authors: L. Tarchi; B. Facchini; S. Zecchi
Journal: International Journal of Rotating Machinery
 (2008)

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## Abstract

This paper describes a heat transfer experimental study
of four different internal trailing edge cooling configurations
based on pin fin schemes. The aim of the study is the
comparison between innovative configurations and standard
ones. So, a circular pin fin configuration with an innovative
pentagonal scheme is compared to a standard staggered
scheme, while two elliptic pin fin configurations are compared
to each other turning the ellipse from the streamwise
to the spanwise direction. For each configuration, heat transfer
and pressure loss measurements were made keeping the
Mach number fixed at 0.3 and varying the Reynolds number
from 9000 to 27000. In order to investigate the overall behavior
of both endwall and pedestals, heat transfer measurements
are performed using a combined transient technique.
Over the endwall surface, the classic transient technique
with thermochromic liquid crystals allows the measurement
of a detailed heat transfer coefficient (HTC) map. Pin fins
are made of high thermal conductivity material, and an inverse
data reduction method based on a finite element code
allows to evaluate the mean HTC of each pin fin. Results
show that the pentagonal arrangement generates a nonuniform
HTC distribution over the endwall surface, while, in
terms of average values, it is equivalent to the staggered
configuration. On the contrary, the HTC map of the two
elliptic configurations is similar, but the spanwise arrangement
generates higher heat transfer coefficients and pressure
losses.


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## Body

## 1. Introduction

The
trailing  edge is  one of the most critical parts of
gas turbine blades and vanes since it is exposed to very high thermal loads. A
very efficient cooling system is, therefore, required so as to keep metal
temperature below critical values. Inline and staggered arrays of
short cylindrical pin fins are one of the most common types of cooling devices
used in turbine blades. Such  arrays enhance the heat
transfer levels mainly increasing the heat transfer coefficient and, forH/D>0.5,
the wet surface. Being easier to manufacture, pin fins with circular
cross-sections are the most used and investigated.
The first experimental investigations on circular pin fins were carried out by
[1–3]. They measured row by row
heat transfer coefficients and pressure losses for inline and staggered
configurations. Reference [4]
investigated the influence of accelerating flow in a wedge-shaped duct on heat
transfer. Their results showed that flow acceleration decreases the influence
of Reynolds number on Nusselt number. By means of the transient TLC technique,
[5, 6] studied the effects of the
fillet radii on the endwall heat transfer, while [7–9] studied the effects of turning flow in a wedge-shaped
duct with circular, elliptical, and diamond cross-section pin fins. It has been
demonstrated by various authors [23, 24] that cylinders with
streamline-shaped cross-section have much less flow resistance than circular
ones, while they have about the same behavior in terms of heat transfer. The
work in [10] also
investigated the partial length circular pin fin concept and found that both
the array averaged-heat transfer and friction factor
decrease with increasing gap distance.Even if streamwise-oriented elliptic pin fins show an
overall better behavior than other shapes, devices with a non-aerodynamic shape
are employed in gas turbine airfoils too. In modern multipass cooling systems,
the airflow approaches the trailing edge region from the hub or from the tip of
the airfoil; hence, the implementation of cooling devices with low pressure
losses could lead to nonuniform coolant distribution in the radial direction and
then to higher differences in airfoil temperature. That is the reason why
cooling devices with high pressure losses have been implemented and
investigated. Reference [8]
studied the effects of diamond pin fins and turning flow on heat transfer. Pin
fins with oblong cross-section were investigated by [11] for various pin
orientations with respect to the main flow. Their results indicate that the use
of elongated pin fins (oblong shape) increases endwall heat transfer
and also causes higher levels of aerodynamic
penalty than the circular pin fins when the main flow direction deviates from
the direction of the major axis of the oblong pin fin. When the main flow
approaches zero incidence, the pressure loss levels
become lower than circular pin fins ones.In the present paper, the differences between
streamwise- and spanwise-oriented elliptic cross-section pin fins are
investigated. Pin fins are inserted in a wedge-shaped duct in order to
replicate a typical trailing edge cooling system. Then, two geometries with
circular cross-section are investigated: one is a standard staggered array,
while the other consists of an innovative array based on a pentagonal scheme.
As already mentioned, in modern cooling systems, the flow does not approach the
pin fin array in the axial direction, but in a mixed axial-radial direction. In
this case, a staggered pin fin array works as an in line configuration, leading
to lower heat transfer capability. Hence, the idea is to develop an innovative
array insensitive to the mainstream direction. The aim of this paper is then
the comparison in terms of heat transfer and pressure losses between the
standard staggered array and the innovative pentagonal scheme, with a
mainstream flow oriented in the axial direction. An experimental survey with
mixed axial-radial flow is planned as well.About the experimental techniques, in the pioneering
works of [1, 3], an average HTC
row by row value was evaluated employing copper test articles and a
steady-state technique. Afterwards, [12, 13] used the naphthalene sublimation method, based on
heat-mass transfer analogy, to investigate the separate contribution of endwall
and pin fin. The work in [5, 6] performed detailed heat transfer measurements on the
endwall surface of pedestals array with TLC transient technique. With the same
experimental method, [7, 9, 14] evaluated heat transfer and pressure losses in
trailing edge cooling geometries typical of real blades: wedge and trapezoidal
ducts, pin shape, and lateral flow effects were investigated. Lately, [15], besides the endwall HTC
measurements with TLC, evaluated the pin fin contribution to heat transfer using
high conductivity pedestals and an inverse data reduction method based on a
finite element simulation of the transient test. Results shown that pin fins
have higher HTC than the surrounding endwall surface. On the contrary,
[16], using the
so-called “lumped heat capacity method” to estimate the pin fin contribution,
measured lower heat transfer values over the pin fin surface.


## 2. Experiments

### 2.1. Test Facility

The experimental survey was performed at the
Dipartimento di Energetica of the University of Florence. The final aim of this
activity is the measurement of the HTC over the whole internal surfaces of four
different geometries using a transient technique.The test rig (Figure1) consists of a suction-type
circuit that allows complete control of the air stream in terms of both
temperature and mass flow rate. The mainstream air passes through a 9.0kW electronically controlled electric heater;
then, the flow rate is measured by an orifice. A three-way valve, with
pneumatic actuator, assures the sample at room temperature, as required by
transient technique, while the other components of the test rig are warming up.
Two rotary vane vacuum pumps, powered by two 7.5kW electric motors, blow air outside and provide
the suction for a maximum mass flow rate of 0.10kg/s.
The flow rate is set up by guiding the motor speed between 300 rpm and 1300 rpm
and by throttling the remote-controlled-motorized valve; the air temperature
exiting the heater is controlled by means of a four-wire RTD (Pt100). Two
pressure scanners Scanivalve DSA 3017 with temperature-compensated
piezoresistive relative pressure sensors allow us to measure the total or
static pressure in 32 different locations with an accuracy of 6.9Pa.
Several T-type thermocouples connected to a data acquisition/switch unit
(HP-Agilent 34970A) measure the mainstream temperature and the aluminum pin fin
temperature. A digital three-charge-coupled-device (3CCD) camcorder (Canon
XM-2) records a sequence of color bitmap images (720×576pixel, 25 frames/s) from the thermochromic
liquid crystal- (TLC-) painted surface on a PC (IEEE-1394 standard). The
illuminating system (Shott-Fostec KL1500 LCD) uses an optical fiber ring light
to ensure a uniform illumination on the test surface, and it allows us to keep
both color temperature and light power constant. In order to reduce any
undesired polymethyl methacrylate (PMMA) reflections, two polarized lens
filters are fitted on both ring light and camcorder lenses. TLCs are the
devices used to evaluate surface temperature and, consequently, the heat
transfer coefficient. For our purpose, we used the 40C5W formulation of
Hallcrest active from 40C° to 45C°. Crystals are
thinned with water and sprayed with an airbrush on the test surface, then a
black background paint is applied. TLCs have been calibrated, replicating the
same optic conditions of the real test: the peak value of the green intensity
was found at 42.3C°,
so it has been used in the data reduction procedure.Figure 1
Experimental setup.


### 2.2. Geometries

Four different pin fin configurations are investigated
in this paper. In Figure2, a sketch of the two elliptic configurations is
shown. In the first one (G2.1), the major axis of the ellipse is oriented
in the airflow direction (i.e., streamwise), while in the other configuration (G2.2),
the ellipse is rotated 90 degrees, so in spanwise direction. Both the arrays
are fitted in a 10-degree wedge-shaped duct (L1 region), replicating the
typical trailing edge shape. Ahead of that region, the test article starts with
a settling chamber, a grid, and then a smooth constant height duct (L0 region). L1 region is 200mm wide and 5Sx=72.75mm long. Height varies from HL0=19.65mm to HL2=H=6.72mm.
Each pin fin row is composed of 12 or 11 pin fins
with diameter D=H.
Spanwise pitch is S/D=2.5 and the array is made by equilateral
triangles, so Sx/D=2.17.
The L2 region consists of a constant height duct with a single row of
circular pin fin with fillet radius r=H/2 and the minimum diameter
being equal to the L1 pins diameter. The
fillet radius was introduced because it represents with more accuracy a typical
configuration used in the outlet of trailing edge cooling systems of
high-pressure stages.Figure 2
Streamwise and
spanwise staggered elliptical pin fin configurations.The two other configurations are composed by circular
pin fins (Figure3). The geometry G2.5 consists of 7 rows of staggered
pin fins with diameter D=H=5.6mm,
spanwise pitch S/D=2.3 and streamwise pitch Sx/D=1.86.
Endwall dimensions are the same of the elliptic geometries while the height is
different (HL0=18.51mm−HL2=H=5.6mm). Each row presents 15 pins, thus over the
whole L1 region, there are 105 pedestals. In the G2.6 configuration, there are 106 pin fins arranged in a pentagonal scheme. The
design of such innovative geometry starts from the idea to develop a repeatable
pin fin array capable of good heat transfer performance in presence of mixed
axial-radial coolant flows as well. As a matter of fact, the standard staggered
array works very well once the airflow is orthogonal to the array, while in
presence of inclined airflow, the array works as an inline configuration, and
cooling performance decreases. Results reported in this paper intend to verify
the behavior of the pentagonal scheme considering an axial coolant flow in
comparison with the standard staggered scheme, keeping practically constant the
overall pin fin density ratio (105 or 106 pin fins over the L1 region).
In the L2 region, there are no pin fins because G2.5 and G2.6 configurations represent a real cooling system where along the L2 region
a cutback is present.Figure 3
Circular pin
fin geometries with staggered (G2.5) and pentagonal arrangement (G2.6).As required by the transient technique, models are
made of transparent PMMA, and the TLC were applied over the whole endwall fromL0 to L2. On the contrary, pin fins are made of
aluminum and their temperature was measured with a small thermocouple inside
one pin for each row. Air temperature is also measured at the inlet with two
miniaturized thermocouples that allow a fast response for the transient test.
The inlet temperature profile was verified during the commissioning of the test
article and it is uniform in the whole test section. As
regarding pressure measurements, static pressure is
measured in various sections from L0 to L2. In Figures 2 and 3,
the position of thermocouples and pressure taps for each model is depicted with
white and black circles (G2.1 instrumentation is exactly in the same
position of G2.2 geometry).


### 2.3. Experimental Procedure

Heat transfer tests were performed using a combined
transient technique that allows the measurement of HTC on both endwall and pin
fin surfaces with a single transient test. During the warm up of the rig, the
test model is kept at constant temperature. When air temperature reaches about70–80C° in the bypass circuit, the 3-way valve is
switched making the air passing through the test model; automatically air
temperature, aluminum pin fin temperature, and air pressure values are recorded
and the camcorder starts acquiring frames of the TLC-coated surface. The
transient test is finished when the liquid crystal reaches the blue color over
the whole surface.Pressure losses are evaluated with a cold test.


## 2.1. Test Facility

The experimental survey was performed at the
Dipartimento di Energetica of the University of Florence. The final aim of this
activity is the measurement of the HTC over the whole internal surfaces of four
different geometries using a transient technique.The test rig (Figure1) consists of a suction-type
circuit that allows complete control of the air stream in terms of both
temperature and mass flow rate. The mainstream air passes through a 9.0kW electronically controlled electric heater;
then, the flow rate is measured by an orifice. A three-way valve, with
pneumatic actuator, assures the sample at room temperature, as required by
transient technique, while the other components of the test rig are warming up.
Two rotary vane vacuum pumps, powered by two 7.5kW electric motors, blow air outside and provide
the suction for a maximum mass flow rate of 0.10kg/s.
The flow rate is set up by guiding the motor speed between 300 rpm and 1300 rpm
and by throttling the remote-controlled-motorized valve; the air temperature
exiting the heater is controlled by means of a four-wire RTD (Pt100). Two
pressure scanners Scanivalve DSA 3017 with temperature-compensated
piezoresistive relative pressure sensors allow us to measure the total or
static pressure in 32 different locations with an accuracy of 6.9Pa.
Several T-type thermocouples connected to a data acquisition/switch unit
(HP-Agilent 34970A) measure the mainstream temperature and the aluminum pin fin
temperature. A digital three-charge-coupled-device (3CCD) camcorder (Canon
XM-2) records a sequence of color bitmap images (720×576pixel, 25 frames/s) from the thermochromic
liquid crystal- (TLC-) painted surface on a PC (IEEE-1394 standard). The
illuminating system (Shott-Fostec KL1500 LCD) uses an optical fiber ring light
to ensure a uniform illumination on the test surface, and it allows us to keep
both color temperature and light power constant. In order to reduce any
undesired polymethyl methacrylate (PMMA) reflections, two polarized lens
filters are fitted on both ring light and camcorder lenses. TLCs are the
devices used to evaluate surface temperature and, consequently, the heat
transfer coefficient. For our purpose, we used the 40C5W formulation of
Hallcrest active from 40C° to 45C°. Crystals are
thinned with water and sprayed with an airbrush on the test surface, then a
black background paint is applied. TLCs have been calibrated, replicating the
same optic conditions of the real test: the peak value of the green intensity
was found at 42.3C°,
so it has been used in the data reduction procedure.Figure 1
Experimental setup.


## 2.2. Geometries

Four different pin fin configurations are investigated
in this paper. In Figure2, a sketch of the two elliptic configurations is
shown. In the first one (G2.1), the major axis of the ellipse is oriented
in the airflow direction (i.e., streamwise), while in the other configuration (G2.2),
the ellipse is rotated 90 degrees, so in spanwise direction. Both the arrays
are fitted in a 10-degree wedge-shaped duct (L1 region), replicating the
typical trailing edge shape. Ahead of that region, the test article starts with
a settling chamber, a grid, and then a smooth constant height duct (L0 region). L1 region is 200mm wide and 5Sx=72.75mm long. Height varies from HL0=19.65mm to HL2=H=6.72mm.
Each pin fin row is composed of 12 or 11 pin fins
with diameter D=H.
Spanwise pitch is S/D=2.5 and the array is made by equilateral
triangles, so Sx/D=2.17.
The L2 region consists of a constant height duct with a single row of
circular pin fin with fillet radius r=H/2 and the minimum diameter
being equal to the L1 pins diameter. The
fillet radius was introduced because it represents with more accuracy a typical
configuration used in the outlet of trailing edge cooling systems of
high-pressure stages.Figure 2
Streamwise and
spanwise staggered elliptical pin fin configurations.The two other configurations are composed by circular
pin fins (Figure3). The geometry G2.5 consists of 7 rows of staggered
pin fins with diameter D=H=5.6mm,
spanwise pitch S/D=2.3 and streamwise pitch Sx/D=1.86.
Endwall dimensions are the same of the elliptic geometries while the height is
different (HL0=18.51mm−HL2=H=5.6mm). Each row presents 15 pins, thus over the
whole L1 region, there are 105 pedestals. In the G2.6 configuration, there are 106 pin fins arranged in a pentagonal scheme. The
design of such innovative geometry starts from the idea to develop a repeatable
pin fin array capable of good heat transfer performance in presence of mixed
axial-radial coolant flows as well. As a matter of fact, the standard staggered
array works very well once the airflow is orthogonal to the array, while in
presence of inclined airflow, the array works as an inline configuration, and
cooling performance decreases. Results reported in this paper intend to verify
the behavior of the pentagonal scheme considering an axial coolant flow in
comparison with the standard staggered scheme, keeping practically constant the
overall pin fin density ratio (105 or 106 pin fins over the L1 region).
In the L2 region, there are no pin fins because G2.5 and G2.6 configurations represent a real cooling system where along the L2 region
a cutback is present.Figure 3
Circular pin
fin geometries with staggered (G2.5) and pentagonal arrangement (G2.6).As required by the transient technique, models are
made of transparent PMMA, and the TLC were applied over the whole endwall fromL0 to L2. On the contrary, pin fins are made of
aluminum and their temperature was measured with a small thermocouple inside
one pin for each row. Air temperature is also measured at the inlet with two
miniaturized thermocouples that allow a fast response for the transient test.
The inlet temperature profile was verified during the commissioning of the test
article and it is uniform in the whole test section. As
regarding pressure measurements, static pressure is
measured in various sections from L0 to L2. In Figures 2 and 3,
the position of thermocouples and pressure taps for each model is depicted with
white and black circles (G2.1 instrumentation is exactly in the same
position of G2.2 geometry).


## 2.3. Experimental Procedure

Heat transfer tests were performed using a combined
transient technique that allows the measurement of HTC on both endwall and pin
fin surfaces with a single transient test. During the warm up of the rig, the
test model is kept at constant temperature. When air temperature reaches about70–80C° in the bypass circuit, the 3-way valve is
switched making the air passing through the test model; automatically air
temperature, aluminum pin fin temperature, and air pressure values are recorded
and the camcorder starts acquiring frames of the TLC-coated surface. The
transient test is finished when the liquid crystal reaches the blue color over
the whole surface.Pressure losses are evaluated with a cold test.


## 3. Data Reduction

### 3.1. Reynolds and Nusselt Numbers Definition

Reynolds and Nusselt numbers for data reduction are
defined in two different ways: the first is based on the inlet section (L0) hydraulic diameter, the second on the pin
fin diameter D.
In both the elliptic configurations, the minor axis length is used as reference
diameter: (1)ReL0=m˙DL0AL0μ,NuL0=h¯DL0k,(2)Red=m˙DAminμ,Nud=h¯Dk.DL0 is the hydraulic diameter of the inlet duct
with cross-section area AL0; μ and k are evaluated at the total temperature
measured in the L0 region; and Amin is the minimum passage area between two pins
and it is variable row by row. In order to compare directly the two elliptic
configurations, the minimum passage area of the streamwise configuration (G2.1)
is used in the data reduction of the spanwise (G2.2) too. Similarly, the
pentagonal geometry (G2.6) results were postprocessed using the minimum
passage area of the staggered configuration (G2.5).The overall average HTCh¯ is defined as follows: (3)h¯=∑i=1NhEWi⋅AEWi+hPINi⋅APINiAEWi+APINi, where AEW takes into account the lower and the upper
endwall surfaces. In the definition of the row by row Nusselt number (2), the
average HTC is based on single-row data.


### 3.2. Heat Transfer Coefficient Evaluation

Detailed heat transfer coefficient distribution on the
endwall surface is obtained assuming one-dimensional conduction over a
semi-infinite solid [17, 18]. The “series of steps” method
[19] is used to take into account the air temperature time history.Because of the high heat transfer coefficients
achieved during the test and the quite high wet surface, the mainstream
temperature decreases between the inlet and the
outlet section is not negligible; thus the use of the inlet temperature
measured inL0 as reference temperature leads to underestimate the HTC.
Solving such a problem makes necessary to take into account the variation of
the local bulk mean temperature in time and space. Reference [20] evaluate four different
approaches and their theoretical background for determining the local bulk mean
temperature and the sensible local heat transfer coefficient. These authors
assert that the invariant local heat flux method is the best choice as
it produces very accurate results, with a very little
processing time and implementation effort; so, such method was applied in the
data reduction procedure.Pin fin heat transfer coefficients are evaluated by
means of an inverse data reduction method. Such method is based on a full 3D
transient FEM simulation of the experiment and an iterative procedure. The HTC
of each pin fin is updated using the Newton convergence criterion, iterating
until the temperature history evaluated with the FEM code matches the measured
temperature history inside each pin. A more-detailed description of this
procedure was reported by [15].


### 3.3. Pressure Drops Evaluation

Pressure drops were measured across the duct in
adiabatic conditions (mainstream flow at ambient temperature). Static pressure
was measured in various points, starting from the inlet, until the end of theL2 region (Figures 2 and 3). The pressure values at the end of each region were
used to evaluate the friction factor defined as (4)f=Δp0(1/2)ρv2, where Δp0 is the total pressure difference between the
beginning and the end of the L1 region; the total pressure is calculated
summing up the dynamic pressure to the average static pressure of each section. ρ and v are average values measured in the L0 region.


### 3.4. Experimental Uncertainty

The uncertainty
analysis was performed following the standard PTC 19.1 [21] based on the
Kline and McClintock method [22]. Typical uncertainties of the most important
parameters are HTC=12.2%, Re=2.8%, f=5.4%.
More details about the individual contributions to the uncertainties of the
single parameters for each of the measured physical properties are reported by
[15].


## 3.1. Reynolds and Nusselt Numbers Definition

Reynolds and Nusselt numbers for data reduction are
defined in two different ways: the first is based on the inlet section (L0) hydraulic diameter, the second on the pin
fin diameter D.
In both the elliptic configurations, the minor axis length is used as reference
diameter: (1)ReL0=m˙DL0AL0μ,NuL0=h¯DL0k,(2)Red=m˙DAminμ,Nud=h¯Dk.DL0 is the hydraulic diameter of the inlet duct
with cross-section area AL0; μ and k are evaluated at the total temperature
measured in the L0 region; and Amin is the minimum passage area between two pins
and it is variable row by row. In order to compare directly the two elliptic
configurations, the minimum passage area of the streamwise configuration (G2.1)
is used in the data reduction of the spanwise (G2.2) too. Similarly, the
pentagonal geometry (G2.6) results were postprocessed using the minimum
passage area of the staggered configuration (G2.5).The overall average HTCh¯ is defined as follows: (3)h¯=∑i=1NhEWi⋅AEWi+hPINi⋅APINiAEWi+APINi, where AEW takes into account the lower and the upper
endwall surfaces. In the definition of the row by row Nusselt number (2), the
average HTC is based on single-row data.


## 3.2. Heat Transfer Coefficient Evaluation

Detailed heat transfer coefficient distribution on the
endwall surface is obtained assuming one-dimensional conduction over a
semi-infinite solid [17, 18]. The “series of steps” method
[19] is used to take into account the air temperature time history.Because of the high heat transfer coefficients
achieved during the test and the quite high wet surface, the mainstream
temperature decreases between the inlet and the
outlet section is not negligible; thus the use of the inlet temperature
measured inL0 as reference temperature leads to underestimate the HTC.
Solving such a problem makes necessary to take into account the variation of
the local bulk mean temperature in time and space. Reference [20] evaluate four different
approaches and their theoretical background for determining the local bulk mean
temperature and the sensible local heat transfer coefficient. These authors
assert that the invariant local heat flux method is the best choice as
it produces very accurate results, with a very little
processing time and implementation effort; so, such method was applied in the
data reduction procedure.Pin fin heat transfer coefficients are evaluated by
means of an inverse data reduction method. Such method is based on a full 3D
transient FEM simulation of the experiment and an iterative procedure. The HTC
of each pin fin is updated using the Newton convergence criterion, iterating
until the temperature history evaluated with the FEM code matches the measured
temperature history inside each pin. A more-detailed description of this
procedure was reported by [15].


## 3.3. Pressure Drops Evaluation

Pressure drops were measured across the duct in
adiabatic conditions (mainstream flow at ambient temperature). Static pressure
was measured in various points, starting from the inlet, until the end of theL2 region (Figures 2 and 3). The pressure values at the end of each region were
used to evaluate the friction factor defined as (4)f=Δp0(1/2)ρv2, where Δp0 is the total pressure difference between the
beginning and the end of the L1 region; the total pressure is calculated
summing up the dynamic pressure to the average static pressure of each section. ρ and v are average values measured in the L0 region.


## 3.4. Experimental Uncertainty

The uncertainty
analysis was performed following the standard PTC 19.1 [21] based on the
Kline and McClintock method [22]. Typical uncertainties of the most important
parameters are HTC=12.2%, Re=2.8%, f=5.4%.
More details about the individual contributions to the uncertainties of the
single parameters for each of the measured physical properties are reported by
[15].


## 4. Results

### 4.1. Elliptic Pin Fin Configurations

For each configuration, five
tests were performed at different Reynolds numbers
(9000<Red5<27000), keeping constant the Mach number at 0.3.
Both Ma and Red are evaluated in the minimum passage area
between two pins of the fifth row (i.e., in the throat section).  Figure 4 shows
a detailed map of the heat transfer coefficient of the two elliptic
configurations at Red5=18000.
The colors inside the pins correspond to the average HTC measured over the pin
fin surface with the inverse data reduction. As the local HTC peak values show,
a stagnation area is present in both configurations ahead of each pin fin,
while the recirculation zone presents slight differences especially in the
first row: in G2.1, the recirculation area is small and does not lead to
a large increase of HTC, whereas, in G2.2, the larger recirculation
generated by the wake of the first pin enhances the heat transfer. For a deeper
insight into the surface flow structure, a surface flow visualization of this
configuration was done using the oil and dye technique. The endwall flow
pattern in Figure 5 shows a large stagnation region ahead of the first pin,
with the saddle point located at 1D upstream the pin. The two counter-rotating vortexes in the recirculation downstream the first pin cover a quite large area
and they spread up to second row, interacting with the stagnation region of such row that is not present on
the endwall. As from the following rows, the flow pattern becomes more
periodic,  the recirculation is smaller, and the saddle point is always located
at about D/2 upstream the pin leading edge.HTC [W/m2K] map of elliptic configurations—Red5=18000.
(a)(b)Figure 5
Surface flow
visualization ofG2.2.Figure6 reports the spanwise-averaged values of HTC
together with the pin fin surface average values. First of all, it is evident
how the spanwise-oriented pin fins (G2.2) generate a more turbulent flow
and then higher heat transfer rates over the whole endwall. Moreover, the
increase in streamwise direction due to the combined effect of pin fin and
convergence is clearly visible for both configurations in the L1 region (0<x/Sx<5), while endwall values are quite constant
over the L2 region (x/Sx>5). About this region, we have to point out
that HTC values are very similar for both configuration, showing that the high
turbulence generated by the streamwise pin fins quickly vanishes.Figure 6
Endwall
spanwise averaged and pin fin HTC—Red5=18000.A final important issue to be discussed concerns with
the different contribution to heat transfer of pin fins and endwall. Looking at
Figures4 and 6, it is noticeable that pin fin HTC is always higher than the
surrounding endwall one, and always very close to
the peak value located upstream each pin. For the first row pin fin, HTC are
about twice  than the endwall ones; according to the authors, this trend can be
explained thinking  over the flow field of such region. Only a portion of the
endwall is covered by the horseshoe vortex generated by the pin, while between
the pins, specially in the streamwise configuration (G2.1), there are
some areas with the same HTC of the upstream flow. On the contrary, the pin fin
surface is fully covered by flow structures with high heat transfer: a
stagnation region over the leading edge and a recirculation over the back side.
In the following rows, the differences between pin fin HTC and endwall is
slightly lower as the first are 50–90% higher than the latter. This behavior
was reported by various researchers that investigated the separate contribution
to heat transfer of pin fin and endwall. Reference [3] reported that, for a staggered array, the HTC on the
pin surface is 35% higher than the endwall values. Reference [11] found that the ratio hPIN/hEW varies from 1.8 to 2.1, depending on steamwise
pitch (Sx). Reference [13], using the naphthalane sublimation technique, measured
that HTC over the pin fin surfece is 10–20% higher than the endwall values.
Finally, [15], using
the same combined data reduction method reported in this paper, showed that the
pin HTC is always higher than the endwall. Recently, [16], using a “lumped heat
capacity method” for the pin fins, reported an inverse result; they mesured a
higher HTC over the endwall by about 3–40% than that on the corresponding pin
fin of the same row.Figures7 and 8 present all the experimental data in
the two different definitions of Reynolds and Nusselt number reported in (1) and
(2).Figure 7
Row by row heat
transfer data.Figure 8
G2.1 and G2.2 data—NuL0 versus ReL0.The general trend of the experimental data confirms
the results of the already discussedRed5=18000 test, so the spanwise configuration (G2.2)
reveals higher heat transfer values at the same mass flow rate. Moreover, data
scattering of such configuration is higher; such behavior is mainly due to the
steep increase of heat transfer capability between the first and the third
rows, while values are quite constant between the
third and the fifth rows.Such trend is present in theG2.1 configuration
too, even if it is hardly visible. Reference [4] in a 10 row-staggered pin fin configuration with
constant height found that the average heat transfer increases up to the 4th−5th row, then decreases up to the 10th row. In the present results, the general trend
is the same measured by [4], but taking also into account the row by row
increasing Red,
the local maximum is reached at the 3rd row and is much more enhanced in the
spanwise-oriented geometry.L2 region
values (PIN6) of both configurations are in line with the G2.1 data, showing that the very high turbulence levels generated by the spanwise-oriented
elliptic fins decrease very quickly without affecting the heat transfer
behavior of the L2 region.The comparison with the correlation proposed by
[4] (Figure 7) for a
10-row-staggered array with 1.5<Sx/D<5.0, S/D<2.5 and H/D=1.0 shows the effect of the elliptic pin fins on
heat transfer. This correlation showed also a good agreement with a circular
pin fin array inserted in a wedge-shape duct similar to the present work
[15]. Looking at the graph, it is clearly visible that the
streamwise-oriented pin fins experience lower heat transfer coefficients than
the circular ones. Such result, as also described by other authors
[23, 24], is mainly due to the different wake behavior of the two
devices: while circular pin fins produce a wake with two large counter-rotating
vortexes, for the elliptic pin fin configurations, such vortexes usually are
not present. Hence, streamwise elliptic pin fins produce less turbulence and
then lower HTC values. On the contrary, in the spanwise-oriented configuration,
the wakes cover a large part of the endwall surface (see Figure 5), and then
the heat transfer is highly enhanced.In order to have a general overview about the cooling
performance of the two elliptic geometries, Figure8 shows the experimental
data of the whole L1 region, together with L0 and L2 values. As expected, the entrance region (L0) is not affected by the pin
fin orientation, while in the L1 region, the higher Nusselt number
values of the spanwise configuration are evident.As already highlighted in the row by row data
reduction (Figure7), in the constant height region (L2) with circular filleted pin fins, the
elliptic pin orientation does not have a large effect on the heat transfer
behavior.


### 4.2. Staggered and Pentagonal Scheme Configurations

For each configuration, five
tests were performed at different Reynolds
numbers (9000<Red7<27000), once again keeping the Mach number at 0.3.
Both Ma and Red evaluated in the minimum passage
are between two pins of the seventh row (i.e., in the throat section). Figure 9
depicts a detailed map of the heat transfer coefficient of the standard
staggered configuration and of the innovative configuration with pentagonal
arrangement at Red7=18000.
The colors inside the pins correspond to the average HTC measured over the pin
fin surface with the inverse data reduction, in the G2.6 geometry, such
measurement was performed in only 8 of the 29 pins that make up a repeatable
array.G2.5 and G2.6 endwall HTC [W/m2K] map—Red7=18000.
(a)(b)The two HTC maps in Figure9 clearly show the
different flowfield induced by the different pin fin
arrangements. As expected, the HTC distribution is symmetric in the staggered configuration (G2.5), a stagnation region is present in
front of each pin fin and the spanwise averaged HTC increases row by row. The pentagonal configuration shows a
nonuniform development of the HTC map, actually there are noticeable
differences in the spanwise direction. Due to pin fin distribution, in some
areas they work as an inline array, while in other areas as staggered. For
instance, for y/Sy=0.9−1,
there are no pin fins over the endwall and
then the HTC are lower. On the contrary, for −1<y/Sy<0,
pin fins arrangement is similar to a staggered configuration and then heat
transfer in that area is higher.The surface flow visualization in Figure10 confirms
the nonuniform flowfield. Anyway, the stagnation point and the recirculation
ahead and behind each pin are almost always in line with the mainstream
direction, while when two pin are in line, they are
not clearly distinguishable. In this visualization, the low HTC area present at y/Sy=0.9−1 is depicted by a single streamline that runs
along the streamwise direction.Figure 10
Surface flow
visualization ofG2.6.The spanwise-averaged endwall HTC values presented in
Figure11 show the heat transfer enhancement in the streamwise direction of
both configurations. In the staggered array (G2.5),
the stagnation ahead each pin fin row is visible, while for the pentagonal
arrangement, it is noticeable only for x/Sx=0.4 where there are three aligned pin fins.
Finally, looking at the spanwise-averaged endwall values, the G2.6 configuration always shows higher HTC values, especially for x/Sx>5.
On the other hand, the pin fin HTC values are always slightly higher in the
staggered configuration (G2.5), with the consequence that the overall
heat transfer performance of both geometries is the same (Figure 12).Figure 11
G2.5 and G2.6 endwall spanwise averaged and pin fin HTC—Red7=18000.Figure 12
G2.5 and G2.6 data—NuL0 versus ReL0.As for the elliptic configurations, in Figure12, the
overall Nusselt number of the L1 region of both configurations is
compared to the L0 values. The entrance region values are, as expected,
the same for both configurations, while it is
surprising that the two pin fin arrangements generate an equal heat transfer
enhancement too.Some interesting considerations can be drawn looking at the
row by row Nusselt values of the staggered configuration reported in Figure13
(having a nonuniform arrangement, the definition of row by row values is not
possible for the pentagonal array). Due to the higher number of rows, the
aforesaid behavior for the spanwise elliptic geometry G2.2 is now more
evident. The heat transfer capability of each row increases quickly up to the
third row, then it is quite constant up to the fifth, increasing once again in
the last two rows. Finally, the comparison with the correlation proposed by
[4] for a constant
height duct shows a general good agreement even if the flow acceleration due to
the wedge-shaped duct leads to a lower dependence on the Reynold number, as was
already reported once again by [4].Figure 13
G2.5 row by row heat transfer data.Figure 14
Pressure losses.


### 4.3. Pressure Losses

In order to complete the experimental investigation,
pressure losses of the four configurations were calculated using the definition
of (4).Due to the non-aerodynamic shape and to the very high
flow velocity between the pin fins, the elliptic spanwise configurationG2.2 generates pressure losses up to seven times higher than the streamwise one.
Such difference, also compared to the heat transfer enhancement capability that
is only twice, demonstrates that the spanwise-oriented pin fins are not the
optimal arrangement to be implemented in a trailing edge cooling system. Anyway,
they can be employed in all the situations where low pressure losses are not
required, while very high heat transfer coefficients are necessary.Regarding the two circular configurations, the
pentagonal arrangementG2.6 generates lower pressure losses than the
standard staggered one. This result, considering that the two configurations
showed the same heat transfer capabilities as well, proves the good
capabilities of such innovative arrangement.


## 4.1. Elliptic Pin Fin Configurations

For each configuration, five
tests were performed at different Reynolds numbers
(9000<Red5<27000), keeping constant the Mach number at 0.3.
Both Ma and Red are evaluated in the minimum passage area
between two pins of the fifth row (i.e., in the throat section).  Figure 4 shows
a detailed map of the heat transfer coefficient of the two elliptic
configurations at Red5=18000.
The colors inside the pins correspond to the average HTC measured over the pin
fin surface with the inverse data reduction. As the local HTC peak values show,
a stagnation area is present in both configurations ahead of each pin fin,
while the recirculation zone presents slight differences especially in the
first row: in G2.1, the recirculation area is small and does not lead to
a large increase of HTC, whereas, in G2.2, the larger recirculation
generated by the wake of the first pin enhances the heat transfer. For a deeper
insight into the surface flow structure, a surface flow visualization of this
configuration was done using the oil and dye technique. The endwall flow
pattern in Figure 5 shows a large stagnation region ahead of the first pin,
with the saddle point located at 1D upstream the pin. The two counter-rotating vortexes in the recirculation downstream the first pin cover a quite large area
and they spread up to second row, interacting with the stagnation region of such row that is not present on
the endwall. As from the following rows, the flow pattern becomes more
periodic,  the recirculation is smaller, and the saddle point is always located
at about D/2 upstream the pin leading edge.HTC [W/m2K] map of elliptic configurations—Red5=18000.
(a)(b)Figure 5
Surface flow
visualization ofG2.2.Figure6 reports the spanwise-averaged values of HTC
together with the pin fin surface average values. First of all, it is evident
how the spanwise-oriented pin fins (G2.2) generate a more turbulent flow
and then higher heat transfer rates over the whole endwall. Moreover, the
increase in streamwise direction due to the combined effect of pin fin and
convergence is clearly visible for both configurations in the L1 region (0<x/Sx<5), while endwall values are quite constant
over the L2 region (x/Sx>5). About this region, we have to point out
that HTC values are very similar for both configuration, showing that the high
turbulence generated by the streamwise pin fins quickly vanishes.Figure 6
Endwall
spanwise averaged and pin fin HTC—Red5=18000.A final important issue to be discussed concerns with
the different contribution to heat transfer of pin fins and endwall. Looking at
Figures4 and 6, it is noticeable that pin fin HTC is always higher than the
surrounding endwall one, and always very close to
the peak value located upstream each pin. For the first row pin fin, HTC are
about twice  than the endwall ones; according to the authors, this trend can be
explained thinking  over the flow field of such region. Only a portion of the
endwall is covered by the horseshoe vortex generated by the pin, while between
the pins, specially in the streamwise configuration (G2.1), there are
some areas with the same HTC of the upstream flow. On the contrary, the pin fin
surface is fully covered by flow structures with high heat transfer: a
stagnation region over the leading edge and a recirculation over the back side.
In the following rows, the differences between pin fin HTC and endwall is
slightly lower as the first are 50–90% higher than the latter. This behavior
was reported by various researchers that investigated the separate contribution
to heat transfer of pin fin and endwall. Reference [3] reported that, for a staggered array, the HTC on the
pin surface is 35% higher than the endwall values. Reference [11] found that the ratio hPIN/hEW varies from 1.8 to 2.1, depending on steamwise
pitch (Sx). Reference [13], using the naphthalane sublimation technique, measured
that HTC over the pin fin surfece is 10–20% higher than the endwall values.
Finally, [15], using
the same combined data reduction method reported in this paper, showed that the
pin HTC is always higher than the endwall. Recently, [16], using a “lumped heat
capacity method” for the pin fins, reported an inverse result; they mesured a
higher HTC over the endwall by about 3–40% than that on the corresponding pin
fin of the same row.Figures7 and 8 present all the experimental data in
the two different definitions of Reynolds and Nusselt number reported in (1) and
(2).Figure 7
Row by row heat
transfer data.Figure 8
G2.1 and G2.2 data—NuL0 versus ReL0.The general trend of the experimental data confirms
the results of the already discussedRed5=18000 test, so the spanwise configuration (G2.2)
reveals higher heat transfer values at the same mass flow rate. Moreover, data
scattering of such configuration is higher; such behavior is mainly due to the
steep increase of heat transfer capability between the first and the third
rows, while values are quite constant between the
third and the fifth rows.Such trend is present in theG2.1 configuration
too, even if it is hardly visible. Reference [4] in a 10 row-staggered pin fin configuration with
constant height found that the average heat transfer increases up to the 4th−5th row, then decreases up to the 10th row. In the present results, the general trend
is the same measured by [4], but taking also into account the row by row
increasing Red,
the local maximum is reached at the 3rd row and is much more enhanced in the
spanwise-oriented geometry.L2 region
values (PIN6) of both configurations are in line with the G2.1 data, showing that the very high turbulence levels generated by the spanwise-oriented
elliptic fins decrease very quickly without affecting the heat transfer
behavior of the L2 region.The comparison with the correlation proposed by
[4] (Figure 7) for a
10-row-staggered array with 1.5<Sx/D<5.0, S/D<2.5 and H/D=1.0 shows the effect of the elliptic pin fins on
heat transfer. This correlation showed also a good agreement with a circular
pin fin array inserted in a wedge-shape duct similar to the present work
[15]. Looking at the graph, it is clearly visible that the
streamwise-oriented pin fins experience lower heat transfer coefficients than
the circular ones. Such result, as also described by other authors
[23, 24], is mainly due to the different wake behavior of the two
devices: while circular pin fins produce a wake with two large counter-rotating
vortexes, for the elliptic pin fin configurations, such vortexes usually are
not present. Hence, streamwise elliptic pin fins produce less turbulence and
then lower HTC values. On the contrary, in the spanwise-oriented configuration,
the wakes cover a large part of the endwall surface (see Figure 5), and then
the heat transfer is highly enhanced.In order to have a general overview about the cooling
performance of the two elliptic geometries, Figure8 shows the experimental
data of the whole L1 region, together with L0 and L2 values. As expected, the entrance region (L0) is not affected by the pin
fin orientation, while in the L1 region, the higher Nusselt number
values of the spanwise configuration are evident.As already highlighted in the row by row data
reduction (Figure7), in the constant height region (L2) with circular filleted pin fins, the
elliptic pin orientation does not have a large effect on the heat transfer
behavior.


## 4.2. Staggered and Pentagonal Scheme Configurations

For each configuration, five
tests were performed at different Reynolds
numbers (9000<Red7<27000), once again keeping the Mach number at 0.3.
Both Ma and Red evaluated in the minimum passage
are between two pins of the seventh row (i.e., in the throat section). Figure 9
depicts a detailed map of the heat transfer coefficient of the standard
staggered configuration and of the innovative configuration with pentagonal
arrangement at Red7=18000.
The colors inside the pins correspond to the average HTC measured over the pin
fin surface with the inverse data reduction, in the G2.6 geometry, such
measurement was performed in only 8 of the 29 pins that make up a repeatable
array.G2.5 and G2.6 endwall HTC [W/m2K] map—Red7=18000.
(a)(b)The two HTC maps in Figure9 clearly show the
different flowfield induced by the different pin fin
arrangements. As expected, the HTC distribution is symmetric in the staggered configuration (G2.5), a stagnation region is present in
front of each pin fin and the spanwise averaged HTC increases row by row. The pentagonal configuration shows a
nonuniform development of the HTC map, actually there are noticeable
differences in the spanwise direction. Due to pin fin distribution, in some
areas they work as an inline array, while in other areas as staggered. For
instance, for y/Sy=0.9−1,
there are no pin fins over the endwall and
then the HTC are lower. On the contrary, for −1<y/Sy<0,
pin fins arrangement is similar to a staggered configuration and then heat
transfer in that area is higher.The surface flow visualization in Figure10 confirms
the nonuniform flowfield. Anyway, the stagnation point and the recirculation
ahead and behind each pin are almost always in line with the mainstream
direction, while when two pin are in line, they are
not clearly distinguishable. In this visualization, the low HTC area present at y/Sy=0.9−1 is depicted by a single streamline that runs
along the streamwise direction.Figure 10
Surface flow
visualization ofG2.6.The spanwise-averaged endwall HTC values presented in
Figure11 show the heat transfer enhancement in the streamwise direction of
both configurations. In the staggered array (G2.5),
the stagnation ahead each pin fin row is visible, while for the pentagonal
arrangement, it is noticeable only for x/Sx=0.4 where there are three aligned pin fins.
Finally, looking at the spanwise-averaged endwall values, the G2.6 configuration always shows higher HTC values, especially for x/Sx>5.
On the other hand, the pin fin HTC values are always slightly higher in the
staggered configuration (G2.5), with the consequence that the overall
heat transfer performance of both geometries is the same (Figure 12).Figure 11
G2.5 and G2.6 endwall spanwise averaged and pin fin HTC—Red7=18000.Figure 12
G2.5 and G2.6 data—NuL0 versus ReL0.As for the elliptic configurations, in Figure12, the
overall Nusselt number of the L1 region of both configurations is
compared to the L0 values. The entrance region values are, as expected,
the same for both configurations, while it is
surprising that the two pin fin arrangements generate an equal heat transfer
enhancement too.Some interesting considerations can be drawn looking at the
row by row Nusselt values of the staggered configuration reported in Figure13
(having a nonuniform arrangement, the definition of row by row values is not
possible for the pentagonal array). Due to the higher number of rows, the
aforesaid behavior for the spanwise elliptic geometry G2.2 is now more
evident. The heat transfer capability of each row increases quickly up to the
third row, then it is quite constant up to the fifth, increasing once again in
the last two rows. Finally, the comparison with the correlation proposed by
[4] for a constant
height duct shows a general good agreement even if the flow acceleration due to
the wedge-shaped duct leads to a lower dependence on the Reynold number, as was
already reported once again by [4].Figure 13
G2.5 row by row heat transfer data.Figure 14
Pressure losses.


## 4.3. Pressure Losses

In order to complete the experimental investigation,
pressure losses of the four configurations were calculated using the definition
of (4).Due to the non-aerodynamic shape and to the very high
flow velocity between the pin fins, the elliptic spanwise configurationG2.2 generates pressure losses up to seven times higher than the streamwise one.
Such difference, also compared to the heat transfer enhancement capability that
is only twice, demonstrates that the spanwise-oriented pin fins are not the
optimal arrangement to be implemented in a trailing edge cooling system. Anyway,
they can be employed in all the situations where low pressure losses are not
required, while very high heat transfer coefficients are necessary.Regarding the two circular configurations, the
pentagonal arrangementG2.6 generates lower pressure losses than the
standard staggered one. This result, considering that the two configurations
showed the same heat transfer capabilities as well, proves the good
capabilities of such innovative arrangement.


## 5. Concluding Remarks

The present
study reports an experimental investigation of four different pin fin-based
trailing edge cooling geometries. The heat transfer measurement were carried
out employing a combined transient technique that allows to evaluate the
separate contribution to heat transfer of pin fins and endwall surfaces.
Results show that the pin fin surface heat transfer values are always higher
than the surrounding endwall ones.The comparison between streamwise- and
spanwise-oriented pin fins with elliptic cross-section highlighted the very
high capability in enhancing heat transfer of the spanwise array that is twice
the streamwise one. On the other hand, pressure losses are seven times higher,
making such array suitable when pressure losses are not a mandatory requirement
of the cooling system. An oil and dye surface flow visualization allowed to
depict the flowfield around each pin. Such investigation shows that pin fins of
the first row have wider stagnation and recirculation areas compared to the
following pins which exhibit a repeatable behavior.An innovative array based on a pentagonal pin fin
distribution has been then compared to a standard staggered configuration,
keeping constant the overall pin fin density. Such pentagonal array shows a
nonuniform heat transfer distribution over the endwall surface, anyway it seems
to be very promising because it has the same performance of the standard
staggered array in terms of heat transfer, while it generates lower pressure
losses.About the effects of the flow acceleration caused by
the wedge-shaped duct, a general remark for all the four configuration can be
done: the Nusselt number is less dependent on Reynolds number than in constant
height ducts. Such behavior should be addressed to the turbulence intensity
weakening typical of accelerating flows.



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*Source: 109120-2008-12-30.xml*