Small Channel Heat Transfer for Airfoil Cooling Applications
by
Michael A. Palumbo
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF SCIENCE Mechanical Engineering
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Thesis Adviser
Rensselaer Polytechnic Institute
Troy, New York
August, 2008
i
CONTENTS
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
ACKNOWLEDGMENT.................................................................................................... v
ABSTRACT ...................................................................................................................... vi
NOMENCLATURE ........................................................................................................ vii
1. INTRODUCTION ....................................................................................................... 1
2. BACKGROUND ......................................................................................................... 3
3. METHODOLOGY ...................................................................................................... 6
3.1
CFD Results and Discussion .............................................................................. 9
3.2
Thermal FEA Results and Discussion .............................................................. 14
4. CONCLUSION .......................................................................................................... 24
5. REFERENCES .......................................................................................................... 25
6. APPENDIX ................................................................................................................ 26
ii
LIST OF TABLES
Table 1 - CFD Solution Initial Conditions......................................................................... 7
Table 2 - Material Properties of Air ................................................................................... 7
Table 3 - Thermal Material Properties From ANSYS - MAR-M-509 ............................ 16
iii
LIST OF FIGURES
Figure 1 - Typical Airfoil Cross Section............................................................................. 4
Figure 2 - Wall Cooling Feature Relative Scale to Airfoil Wall ........................................ 5
Figure 3 - Study Geometry, Baseline (L) and Proposed (R).............................................. 5
Figure 4 - Dimensioned View of Baseline Geometry (L) and Proposed Geometry (R)..... 6
Figure 5 - Cooling Air Velocity Vectors, Baseline Geometry.......................................... 10
Figure 6 - Freestream Gaspath Film Temperature, Baseline Geometry ........................... 10
Figure 7 - Proposed Geometry, Top View ........................................................................ 11
Figure 8 - Contours of Total Pressure, Baseline Geometry (L) and Proposed Geometry
(R) ..................................................................................................................................... 12
Figure 9 - Proposed Geometry, Coolant Exit Velocity ..................................................... 13
Figure 10 - Film Temperature, Proposed Geometry ......................................................... 13
Figure 11 - ANSYS Model, Baseline Geometry .............................................................. 14
Figure 12 - ANSYS Model, Proposed Geometry ............................................................. 15
Figure 13 - Core Side Heat Transfer Coefficient Map, Baseline Geometry (Unscaled) .. 17
Figure 14 - Core Side Heat Transfer Coefficient Map, Proposed Geometry (Unscaled) . 17
Figure 15 - Gaspath Heat Transfer Coefficient Map, Baseline Geometry (Unscaled) ..... 18
Figure 16 - Gaspath Heat Transfer Coefficient Map, Proposed Geometry (Unscaled) .... 18
Figure 17 - Gaspath Convective Temperature Map, Baseline Geometry (Unscaled) ...... 19
Figure 18 - Gaspath Convective Temperature Map, Proposed Geometry (Unscaled) ..... 19
Figure 19 - Thermal Analysis Results, Scaled FLUENT Boundary Conditions .............. 20
Figure 20 – Thermal Analysis Results, Constant Hgas and Tgas ..................................... 21
Figure 21 - Baseline Thermal Results Along Midline Nodes, Gaspath Surface .............. 22
Figure 22 – Thermal Results Along Midline Nodes, Constant Hgas and Tgas ................ 23
iv
ACKNOWLEDGMENT
Thanks to all who have supported me throughout my lengthy journey to completing my
graduate studies.
Thanks as well to Dr. Gutierrez-Miravate for the guidance and
encouragement throughout the Seminar process.
v
ABSTRACT
The application of small channel heat transfer for airfoil cooling applications has been
investigated. The small cooling passages that may be placed in the wall of the airfoil
during the casting process are approximately 0.015 inch in thickness, and are intended to
be formed to meet the airfoil wall contour in both the axial and radial directions. The
challenge with such cooling mechanisms is the balance of internal heat transfer
augmentation with the external film cooling effectiveness provided by cooing air exiting
the passages into the gaspath. By selectively placing the internal features of these small
passages to achieve peak heat transfer augmentation by tailoring internal coolant pressure
drop, the external film effectiveness can be enhanced.
The internal heat transfer
augmentation and film effectiveness can both be tailored simultaneously to provide for
enhanced metal temperature reduction for a selected configuration of this cooling
geometry.
Thermal predictions by Finite Element Analysis (FEA) have been completed for a
baseline application of this cooling methodology as well as for a configuration that has
been tailored to provide enhanced cooling flow distribution on the simulated airfoil
surface.
The comparison of the baseline geometry results to those of the tailored
geometry show reduced metal temperature for the tailored geometry.
This study has direct applicability to airfoil cooling, where metal temperatures must be
reduced to maintain component survivability in the elevated gaspath temperatures of
modern gas turbine engines. Reduced metal temperatures lead to improved component
life, and reduced cooling flows improve turbine efficiency.
vi
NOMENCLATURE
vii
1. INTRODUCTION
As the combustor exit temperature of modern gas turbines has increased, the goal of the
turbine airfoil designer has become ever more challenging. Airfoil materials are being
used in applications where the thermal environment is above the temperature at which
the alloys have any useful strength or oxidation resistance. In an effort to study potential
advancements in the area of turbine airfoil cooling, the use of small channel heat transfer
augmentation has been proposed. This methodology employs both internal features
within the wall of the airfoil as additional coolant side augmentation as well as the
external discharge of the cooling air as a film of air to protect the surface of the airfoil
from the hot gaspath air. Both methodologies have been employed on their own and in
conjunction for many years to decrease the metal temperature of turbine airfoils to
increase the service life of these components.
The use of internal features as a method of coolant side heat transfer augmentation has
been used for many years. Roughened internal coolant passages, pin-fins, dimples and
the like have been employed as ways to augment coolant heat transfer. One of the
challenges with internal coolant side augmentation has been the management of pressure
loss in roughened channels. As an additional challenge, the compressor bleed air that is
used as the source for turbine airfoil cooling is usually only available in small amounts,
with very closely regulated pressures. The best use of the available pressure requires
that pressure loss and the associated heat transfer augmentation be used where best
needed.
The other method of protecting the airfoil walls from the combustion chamber exit
temperatures has been to bleed the internal channel cooing air out of the airfoil through
discreet cooling holes drilled in the wall of the airfoil in an effort to lay down a film of
cooler air on the external surface of the airfoil. A more effective way to bleed the
cooling flow out over the external surface is to use longer slots to provide additional
spanwise film coverage. Athough the fabrication of these cooling slots is generally
difficult, the benefits should be weighed against the cooling air flow reduction, metal
temperature benefit and overall life improvement potential.
1
The proposed methodology seeks to use the most beneficial parts of both coolant side
heat transfer augmentation and film cooling in close conjunction.
By maximizing
internal augmentation at the axial location where the film cooling benefit has begun to
be minimized, overall heat transfer augmentation will provide the maximum benefit and
maintain the airfoil wall at temperatures that most closely match requirements.
2
2. BACKGROUND
The thermal efficiency and power output of turbine engines both increase as turbine inlet
temperatures continue to rise, and for this reason, advanced cooling techniques are
becoming increasingly necessary to ensure turbine hardware is able to operate as
designed for safety and high performance.
The cooling methodology investigated here involves the combination of small scale
convective augmentation within the wall of the airfoil as well as advanced, long slot film
cooling of the external surface of the airfoil, a baseline configuration as well as a
modified geometry were investigated.
Based on a comparison of several key
parameters, the results show that the modified configuration offers a good balance
between internal convective augmentation and enhanced cooling film effectiveness.
The general arrangement of turbine airfoil cooling requires the use of air extracted from
the compressor section of the engine to be used as coolant. Due to the loss of thermal
efficiency associated with this flow, the use of this air as coolant must be done
judiciously. By optimizing the cooling scheme, the maximum thermal benefit can be
achieved using the minimum amount of cooling air. To operate the airfoils at the correct
temperature for maximum component life and engine time-on-wing, the airline,
powerplant operator or industrial application can operate the engine for the desired cost.
A general arrangement typical of turbine airfoil cooling is shown in Figure 1. As can be
noted, this geometry relies on the combination of convective augmentation on the
internal surface of the airfoil, as well as film cooling benefits on the external, gaspath
surface. The careful application of these two methodologies leads the cooling designer
to the best configuration. One of the major limitations to the combination of internal
augmentation and external film cooling is that internal augmentation relies heavily on
pressure drop in the cooling circuit to elevate skin friction, turbulence and the like at the
inner wall surface. However, film cooling often requires that the internal cavity pressure
feeding the cooling holes be significantly greater than the freestream gaspath pressure to
3
prevent the ingestion of the hot gaspath air into the airfoil. This dilemma plagues
cooling designers throughout the industry.
Figure 1 - Typical Airfoil Cross Section
A typical application of the geometry studied is shown in Figure 2. The general cross
section of the airfoil wall shows the basic scale of the cooling passage in relation to the
airfoil wall thickness. The study geometry was then idealized as a flat plate for the
analysis.
For typical airfoil wall thicknesses of 0.045”, the cooling passage is
approximately 1/3 of this thickness, leaving metal walls of 0.015” on either side, one
adjacent to the gaspath and one next to the coolant supply passage. As shown in Figure
3, two configurations of internal features within the wall cooling passage were studied.
The baseline configuration is a uniform distribution of constant size pedestals arranged
perpendicular to the direction of cooling flow within the passage.
The modified
geometry has pedestals of various size arranged within the same axial distance, but with
non-uniform spacing radially. The intent of the analysis was to show that the nonuniform geometry managed internal pressure loss and heat transfer augmentation as well
as improved film coverage on the gaspath surface to reduce metal temperature as
compared to the baseline, uniformly distributed features.
The baseline geometry
produces an extremely non-uniform flow distribution at the exit to the gaspath, leading
to reduced film coverage. This geometry also displays high pressure loss near the inlet
side of the cooling passage. By modifying the distribution and size of the features in the
4
proposed geometry, the internal pressure loss can be tailored to augment the internal heat
transfer farther upstream in the passage. In the counter-flow arrangement of this cooling
scheme, the film coverage on the gaspath side and the internal augmentation within the
wall cooling passage can be selectively maximized for overall cooling improvement.
Figure 2 - Wall Cooling Feature Relative Scale to Airfoil Wall
Figure 3 - Study Geometry, Baseline (L) and Proposed (R)
5
3. METHODOLOGY
To investigate the thermal improvements of the modified geometry, first a solution for
the flow field within both cooling passages was completed. Once the thermal boundary
conditions were able to be obtained from the Computational Fluid Dynamics (CFD)
solution, these were mapped onto a thermal Finite Element Model (FEM) to obtain the
resulting metal temperatures that would be representative of airfoils running in today’s
gas turbine aircraft engines.
.050
.050
.492
.050
TYP
.025
TYP
.025
.350
.025
.200
.200
Figure 4 - Dimensioned View of Baseline Geometry (L) and Proposed Geometry (R)
The solid models of the geometry were constructed using Unigraphics CAD/CAE
software. A dimensioned view is shown in Figure 4. The geometry was then transferred
to and meshed using the HEXA routine in ICEM CFD. The ICEM CFD mesh was built
entirely of hexahedral elements, and consisted of 435710 elements with 364356 nodes.
The quality of this mesh was very high, indicated by a mean value for the determinant of
0.992. The determinant is a calculation which checks the deformation of the elements in
the mesh using a test that computes the Jacobian of each hexahedron and then scales the
determinant of the matrix in such a way that 100 is a perfectly regular mesh element, 0 is
6
degenerate in one or more edges, and negative values indicate inverted elements. In
general, values above 0.25 are acceptable for most solvers (1).
After meshing in ICEM CFD, the resulting mesh was transferred into FLUENT to obtain
the flow field solution and to visualize the differences between the results of the two
versions of the geometry. Table 1 shows the initial conditions specified for the CFD
analysis. Although the initial conditions were not directly representative of engine
conditions, the comparison between the results of the 2 geometries is valid.
The
pressure ratio between the inlet and exit was 1.5 which is fairly representative of engine
operating conditions.
Table 2 shows the material properties of air as used in the
solution.
Model Zone
Initial Pressure (psi)
Gaspath Inlet
Initial Temperature
(deg R)
540
Gaspath Exit
540
14.70
Coolant Inlet
0
22.05
Coolant Exit
0
22.05
22.05
Table 1 - CFD Solution Initial Conditions
Property
Units
Value
Density
lbm/ft3
0.07647169
Specific Heat (Cp)
BTU/lb-R
0.24038799
Thermal Conductivity
BTU/hr-ft-R
0.013986014
Molecular Weight
lb/lbmol
28.966
Viscosity
Lbm/ft-sec
1.2024212E-05
Table 2 - Material Properties of Air
The CFD solution was run using a single equation turbulence model as defined by
Spalart and Allmaras (2). For this analysis no wall grid was specified, although if
further investigation were to be undertaken on the benefits of the proposed geometry,
both a wall grid spacing to fully capture the wall function as well as a more appropriate
turbulence model would likely be employed to more fully characterize the modified
cooling configuration. In its original form, the Spalart-Allmaras model is effectively a
low-Reynolds-number model, requiring the viscous-affected region of the boundary
layer to be properly resolved. In FLUENT, however, the Spalart-Allmaras model has
been implemented to use wall functions when the mesh resolution is not sufficiently
7
fine. This might make it the best choice for relatively crude simulations on coarse
meshes where accurate turbulent flow computations are not critical. Furthermore, the
near-wall gradients of the transported variable in the model are much smaller than the
gradients of the transported variables in the
-
or
-
models. This might make the
model less sensitive to numerical error when non-layered meshes are used near walls (3).
8
3.1 CFD Results and Discussion
An interrogation of the CFD results for the baseline geometry shows several important
trends. First, due to the close spacing of the internal features, the base geometry shows
the greatest pressure loss very close to the inlet of the cooling passage. While this may
be desirable from the standpoint that the resulting lower velocity of the cooling flow will
keep the air in the passage longer, this may also lead to increased heat-up of the cooling
air as it slowly flows through the passage towards the exit. Also, all of the internal heat
transfer augmentation that is driven by pressure drop occurs at an axial location far
downstream of where the external film cooling benefit has degraded.
In such a
counterflow arrangement as shown, it is widely believed that the forward flowing
cooling air in the channel should provide the peak augmentation at the same axial
location where the aft-flowing film cooling is loosing effectiveness at the greatest rate.
For this reason, by providing peak cooling air augmentation at the inlet to the cooling
passage, the maximum benefit cannot be achieved. Furthermore, the velocity vectors of
the flow out of the cooling slot at the exit of the channel in Figure 5 show a great deal of
dispersion in the radial direction, with localized jets present. This radial ‘spray’ of the
film exiting the slot degrades the momentum mixing of the coolant injection into the free
stream, diminishing the overall, slot-length averaged level of film effectiveness. In
general, as the exit momentum of the coolant is reduced, the cooling effectiveness is
increased (4).
By having the cooling flow exiting non-uniformly, the cooling
effectiveness is also quite non-uniform. Figure 6 shows a large radial variation in the
freestream gaspath temperature for the baseline configuration that can be attributed to
the non-uniformity in exit coolant velocity.
9
Figure 5 - Cooling Air Velocity Vectors, Baseline Geometry
Figure 6 - Freestream Gaspath Film Temperature, Baseline Geometry
The modified geometry is again show in Figure 7.
The main objectives of the
modifications were to show reduced pressure drop at the inlet to the cooling passage and
10
to reduce the radial variation of the cooling flow exit velocity. Both of these goals have
been accomplished in the modified cooling passage configuration. Figure 8 shows the
resulting distribution of total pressure within the cooling passage for both geometries.
Note that the coolant pressure drop for the modified geometry occurs much farther
downstream in the passage, away from the inlet, at an axial location more corresponding
to the location where film effectiveness would tend to decrease at the greatest rate away
from the film injection into the freestream. .
Figure 7 - Proposed Geometry, Top View
11
Figure 8 - Contours of Total Pressure, Baseline Geometry (L) and Proposed Geometry (R)
The exit velocity vectors for the modified geometry are shown in Figure 9. The more
uniform flow field of the coolant at the exit of the modified geometry can be directly
related to the uniform film temperature as seen in Figure 10. The much more uniform
velocity of the film exiting the slot of the baseline geometry, will lead to improved film
cooling coverage and effectiveness.
As has been shown in film cooling research,
___________, uniformly flowing cooling films tend to provide more complete coverage
and the film effectiveness is also increased over the axial distance of the film cooling
flow. By tailoring the axial location and arrangement of the internal features, rows of
additional wall cooling passages can be added to the airfoil, whereby increasing the film
effectiveness by the method of non-linear superposition.
12
Figure 9 - Proposed Geometry, Coolant Exit Velocity
Figure 10 - Film Temperature, Proposed Geometry
13
3.2 Thermal FEA Results and Discussion
The FLUENT results from the flow analysis have been interrogated and applied to a
section of each of the geometries. The baseline solid is shown in Figure 11. Note that
the midline nodes as shown by blue line will provide a plotting path for the thermal
results in subsequent discussion. The proposed geometry, with a similar representation
of the mid-line nodes is shown in Figure 12.
Figure 11 - ANSYS Model, Baseline Geometry
14
Figure 12 - ANSYS Model, Proposed Geometry
Due to the initial conditions specified for the FLUENT analysis, the resulting heat
transfer coefficients were scaled by a factor of 5 to bring them up to realistic running
conditions for turbine airfoils. Also, the temperatures specified during the FLUENT
analysis were scaled to a peak value of 2500 deg F, to bring the fluid temperatures up to
a more realistic level as well.. These scaled heat transfer coefficients and convective
film temperatures were then applied to the ANSYS model.
The material specified for the ANSYS analysis was MAR-M-509. This cast cobaltbased alloy is commonly used in static turbine airfoils due to the high chrome content
which is beneficial from an oxidation resistance stand point. The thermal material
properties used in the analysis are shown in Table 3. The ANSYS analysis also used
SOLID70 (8-noded brick thermal solid) elements for meshing. ANSYS version 10 was
used for this analysis.
15
Temperature
Thermal Conductivity
Temperature
Specific Heat
deg F
BTU-in/sec in2 F
deg F
BTU-in/sec2 lbf F
200
2.04E-04
200
3.92E+01
400
2.42E-04
404
4.16E+01
600
2.80E-04
605
4.44E+01
800
3.15E-04
809
4.71E+01
1000
3.49E-04
1010
5.00E+01
1205
3.82E-04
1203
5.22E+01
1400
4.11E-04
1415
5.51E+01
1594
4.40E-04
1604
5.83E+01
1805
4.71E-04
1803
6.19E+01
2000
5.00E-04
2000
6.53E+01
2150
5.22E-04
2150
6.82E+01
2300
5.44E-04
2300
7.10E+01
Table 3 - Thermal Material Properties From ANSYS - MAR-M-509
The core-side heat transfer coefficient maps for both the baseline geometry and the
proposed configuration are shown in Figure 13 and Figure 14, respectively. The coreside fluid temperature was held constant at 1000 deg F for both geometries, at all
locations within the core. The coolant feed cavity side for both geometries were also
held constant, with a heat transfer coefficient of 50 BTU/hr ft2 F and a coolant
temperature of 1000 deg F. These values are consistent with airfoils currently operating
in high temperature high pressure turbine (HPT) applications. The freestream gaspath
heat transfer coefficient map for the baseline geometry is shown in Figure 15 and for the
proposed geometry in Figure 16. The freestream convective temperature maps are
shown for the baseline geometry in Figure 17 and for the proposed geometry in Figure
18. Note that the maps all show the unscaled results from FLUENT. The scaled values
for each map are shown in Appendix A.
16
Figure 13 - Core Side Heat Transfer Coefficient Map, Baseline Geometry (Unscaled)
Figure 14 - Core Side Heat Transfer Coefficient Map, Proposed Geometry (Unscaled)
17
Direction of Freestream Flow
Figure 15 - Gaspath Heat Transfer Coefficient Map, Baseline Geometry (Unscaled)
Figure 16 - Gaspath Heat Transfer Coefficient Map, Proposed Geometry (Unscaled)
18
Figure 17 - Gaspath Convective Temperature Map, Baseline Geometry (Unscaled)
Figure 18 - Gaspath Convective Temperature Map, Proposed Geometry (Unscaled)
Thermal analysis results for both the baseline geometry and proposed configuration are
shown in Figure 19.
As can be seen, the proposed geometry results in reduced metal
temperatures. The combination of improved film cooling coverage (reduced gaspath
heat transfer coefficient) and lower film temperature is responsible for this temperature
reduction. As a secondary effect, the conduction portion of the solution should be
investigated separately, by running both ANSYS models with constant heat transfer
19
coefficients on all core-side surfaces and gaspath areas to investigate the conduction
contribution to the overall temperature reduction. To investigate the coolant side heat
transfer augmentation part of the solution, the ANSYS models were run with constant
heat transfer coefficients and free-stream temperatures on the gaspath surfaces. These
results are also shown in Figure XX for each of the geometries in comparison to the
solutions for the combined internal augmentation/improved film cooling results.
Hgas and Tgas from FLUENT
Combined convective and conductive benefit
Baseline Geometry
Proposed Geometry
Figure 19 - Thermal Analysis Results, Scaled FLUENT Boundary Conditions
20
Constant Hgas and Tgas
Hgas = 500 BTU/hr ft2 F
Tgas = 2000 F
Conductive benefit only
Baseline Geometry
Proposed Geometry
Figure 20 – Thermal Analysis Results, Constant Hgas and Tgas
The plot shown in Figure 21 shows the nodal results of gaspath surface temperature
along a ‘midline’ axially aft along the direction of flow for the full scaled FLUENT
boundary condition solution.
A comparable plot showing the same results for the
constant external condition results is given in Figure 22. The discontinuity near sdistance ~ 0.16 in is the location of the film exit to the gaspath. As can be shown for
both plots, the proposed internal geometry provides improved thermal performance in
the resulting lower metal temperature. From these results, it can be determined that the
film cooling performance due to better film coverage and film effectiveness is the larger
contributor to overall surface temperature reduction, although the plot showing the
internal conduction benefit (constant hgas and tgas) indicates some additional, minor
improvement. The small difference is largely due to the increased mass of the internal
features in the baseline geometry providing additional conduction paths.
21
Midline Nodes
Gaspath Surface Temperatures
2400
Nodal Temperature (deg F)
2200
2000
1800
1600
1400
Baseline_Geometry
Proposed_Geometry
1200
1000
0
0.2
0.4
0.6
0.8
S-distance (in)
Figure 21 - Baseline Thermal Results Along Midline Nodes, Gaspath Surface
22
1
1.2
Midline Nodes
Gaspath Surface Temperatures
2400
Nodal Temperature (deg F)
2200
2000
1800
1600
1400
1200
Proposed_Geometry_Constant_Hgas_Tgas
Base_Geometry_Constant_Hgas_Tgas
1000
0
0.2
0.4
0.6
0.8
S-distance (in)
Figure 22 – Thermal Results Along Midline Nodes, Constant Hgas and Tgas
23
1
1.2
4. CONCLUSION
As turbine inlet temperatures increase, reduced metal temperatures on airfoil surfaces
lead to increased life and engine time-on-wing. This is an important factor for airline
customers who depend on robust components that allow extended service life. While
both the baseline geometry and proposed modifications both offer significant benefits
over more traditional methods of cooling airfoils, the proposed geometry offers the
added benefit of reduced metal temperatures at constant flow. As cooling flow levels are
reduced, turbine efficiency improves, improving the fuel consumption of the engine. As
fuel prices are ever increasing, airline customers will seek to reduce the amount of fuel
that is required. As world airline markets continue to evolve to more regional service,
the fuel consumption benefits that can be offered by engine makers will become the
standard by which all engines are measured.
24
5. REFERENCES
(1) ICEM CFD User Guide, Quality Checking in HEXA
(2) Spalart, P. R. and Allmaras, S. R., 1992, "A One-Equation Turbulence Model for
Aerodynamic Flows" AIAA Paper 92-0439
(3) FLUENT User Guide, Section 12.3 – Spalart-Allmaras Model Theory
(4) Dittmar, J., Jung, I. S., Schulz, A., Wittig, S., and Lee, J. S., 2000, "Film Cooling
From Rows of Holes—Effect of Cooling Hole Shape and Row Arrangement on
Adjabatic Effectiveness," Ann. N.Y. Acad. Sci., 934, pp. 321–328.
25
6. APPENDIX
26