optimized cooling passage design

HyperWorks is a division of1

Optimizing Cooling Passages In Turbine Blades

Optimizing Cooling Passages in Turbine Blades

AbstractTurbine blades have internal passages that provide cooling during operation in a high

temperature engine. The design of the cooling passages is critical to achieve near uniform

temperature of the blade during operation. The temperature of the blade is dependent on the

thermal properties of the blade material as well as the fluid dynamics of the air circulating in

the cooling passages. Computational optimization methods have successfully been applied

to design lighter and more efficient structures for many aerospace structures. An extension of

these techniques is now applied to guiding the thermal design of a turbine blade by designing

the optimal cooling passage layout. Optimization methods will be applied to determine the

optimum pattern of the cooling passages and then to optimize the size of the individual

cooling passages. The goal is to produce a more thermally efficient turbine blade design that

will produce blades with longer lives and better performance.

IntroductionIndividual turbine blades make up the turbine section of a gas turbine engine. The blades

purpose is to extract energy from the high temperature, high pressure gas produced by the

combustor. Cooling of the blade is very important and one of the cooling methods is to include

internal air channels in the blade. These internal cooling passages rely on convection cooling

and work by passing cooling air through passages internal to the blade. Heat is transferred by

conduction through the blade, and then by convection into the air flowing inside of the blade.

A large internal surface area is desirable for this method, so the cooling paths tend to be

serpentine and full of small fins.[1][2 Optimizing the cooling passages will lead to more efficient

cooling and hence more efficient operation. Also, if the weight of the blades can be reduced,

this leads to overall weight reduction and fuel efficiency improvements.

Optimization MethodsThe traditional design process involves an iterative trial and error approach where a design

is incrementally refined until an acceptable design is achieved. A design is produced, next it

is modeled and analyzed mathematically and then based on the analysis results, the design

is modified and reanalyzed. This process is repeated until all design requirements are met.

Once the design requirements are achieved analytically, a prototype is built and tested. If the

prototype testing indicates a problem, the product is redesigned and the design process repeats.

by Robert Yancey, Michael Dambach, J.S. Rao, Marc Ratzel and David Corson Altair Engineering, Inc.



The traditional design approach can be time-consuming and may fall short of an optimum

solution. By contrast, an optimization-driven solution can provide better conceptual designs,

moves the trial and error process to the computer, and ensures all design constraints

are achieved in an optimum manner. The end result is shorter design times and more

robust designs.

Finite element based optimization methods have been widely used for the optimization of

metallic structures [3-5] including many aerospace components [6-8] such as turbine blades [9,10] and has now added capabilities for optimizing composite structures [11,12]. Components

engineered with these tools have shown lower weight, increased performance, and the ability

to operate in more robust environments.

Optimizing Cooling PassagesThe goal of this study was to apply optimization methods to the design of cooling passages

in a turbine blade. A representative turbine blade geometry was used as shown in Figure 1

along with the coordinate system used for the study. The Y-axis runs from the root to the

blade tip. The portion of the blade for study was extracted and shown in Figure 2.

The extracted geometry just includes the airfoil shape that would include the cooling

passages. Cylindrical cooling passages were modeled into the blade shape and the entire

model was meshed in HyperMesh. An example with four cooling passages is shown in Figure

3 with the corresponding finite element mesh Since computational fluid dynamics (CFD)

software will be used to generate the temperature and pressure boundary conditions on the

blade, HyperMesh was used to generate the CFD mesh on the outside of the blade as shown

in Figure 4.

Figure 1. Turbine Blade Geometry



Figure 2. Extracted Geometry for Optimization

Figure 3. FEA Mesh of Blade with Cooling Passages

Figure 4. CFD Mesh on Outside of Blade



A HyperWorks script was written to allow for variation of the size and number of cooling

passages. The script takes as input the number of cooling passages and the diameter of the

cooling passages and distributes these uniformly across the blade shape, taking into account

the change in pitch by using a camber line at the root and tip of the blade. The meshing of

the blade for the thermal mesh is carried out automatically in HyperMesh[13]. Constraints are

built into the script that prevents cooling passages from extending beyond the blade profile or

into an adjacent cooling passage. The script also submits the analysis run to a Radioss and

returns the results[14].

A CFD simulation using AcuSolve was performed on a mesh with boundary layers on the

non slip walls and tetra elements in the core of the fluid domain as shown in Fig. 4. Special

care has been taken to generate a smooth transition between the last boundary layer

elements and the adjacent tetra elements. The complete mesh contained around 700.000

cells. To consider turbulence effect, the Spalart-Allmaras turbulence model with standard

wall functions has been applied. For the underlying mesh, the maximum y+ value was 240.

Assuming rotational symmetry, periodicity was prescribed for the two boundaries aligned with

the inflow direction. A fixed mass flow rate was used as an inflow condition and zero pressure

was prescribed at the outlet. The rotation of the impeller was modeled by using a rotating

reference frame with a constant angular velocity. An advective-diffusive equation governing

the transport of enthalpy has been used for heat transfer modeling. The enthalpy equation

was solved in a coupled manner with the flow equations.

HyperStudy was used to set up an optimization analysis of the turbine blade [15]. An adaptive

response surface (ASR) optimization method was used since it allows for a discrete variable

number of cooling passage holes. The size and number of cooling passages were the

variables used in the study. The script described previously was produced to automate the

model set-up for each run in the optimization. The script produces the turbine blade mesh

based on cooling passage geometry parameters (position and diameter of passages).

The thermal boundary conditions and pressure on the outside of the blade are provided from

the AcuSolve CFD analysis performed prior to the study. The CFD analysis is only carried out

once and is not repeated for each optimization run. The material properties are also fixed.

Therefore, the size, position, and number of cooling passages are the only variables for

each analysis run. The internal passages were assigned a constant temperature

assuming a constant coolant temperature. Variations in the temperature due to flow were

not considered. A flowchart of the process is shown in Figure 5. The gray area designates the

optimization loop.



For the HyperStudy optimization analysis, an objective function was set to minimize the

displacement of the blade in the y-direction (root to tip). Thermal expansion in this direction

can cause the blade to contact the casing. The optimum configuration of the model is shown

in Figure 6. The optimized blade tip displacement showed a 4% reduction over the baseline

model shown in Figure 3. The mass of the optimized blade was 6.6% less than the baseline

providing an added benefit. The optimized blade shows a total of 8 cooling passages of

variable size. As shown, the optimization produced larger and more cooling passages towards

the trailing edge indicating that the sensitivity of the tip displacement was mostly influenced

by the cooling passages on the trailing edge. The analysis run performed 25 iterations to

achieve the optimal result for the set of conditions considered. The entire optimization

process was automated as shown in Figure 5.

Figure 5. Flowchart of Analysis Process

Figure 6. Optimal Cooling Passage Design for Given Set of Boundary Conditions (4 Holes with diameters

of 5.8, 7.2, 9.0, and 10.8 mm respectively)



DiscussionSeveral simplifying assumptions were made in this study. The main flow path is between the

combustor flame, diaphragms and blades. We assumed it to be cyclically symmetric with one

rotating blade of the rotor. We did not include radiation effects. Though the flow is not steady,

we assumed this to be mean flow for the purpose of illustrating structural optimization. For

simplicity, we used a Spalart-Allmaras turbulence model although a K-epsilon or K-omega

model is more appropriate for this type of analysis. We assumed that there is no secondary

(cooling) flow from the compressor. We did not include centrifugal loads. Steady state

conditions were assumed acknowledging that maximum thermal strains are generating during

the transient conditions of start-up.

The main objective of the study was to determine if the cooling passages of a turbine blade

could be optimized using finite element analysis and computational fluid dynamics working

together with a numerical optimization code. Future work should consider modeling the

coolant flow within the cooling passages, looking at arbitrary shapes for the cooling passages,

considering start-up transient conditions, and performing stochastic studies on the material

properties for heat transfer and thermal expansion. The study should also consider additional

constraints and/or different objective functions. Generally with numerical optimization, one

can consider multiple constraints and a single objective function. For example, one could set

a constraint on blade tip displacement and set the objective function to minimize the thermal

strains globally or at a particular point.

ConclusionsIt has been difficult in the past to perform numerical optimization for structures that operate

in an environment where multiple physical conditions affect the performance. For example,

structural optimizations are straight forward when just load or temperature effects or

included. When pressure, temperature, and flow are all considered, it has been a challenge

to manage all of the variables and develop a process flow that can be completely automated.

In general, some human intervention is required at each step of the process.

This study provides a demonstration of how the process can be automated and optimization

can be performed for a turbine application that includes pressure, temperature, and flow

considerations. To be truly useful, a more in depth study would be required to determine

sensitivities and validate the modeling assumptions with test data. The intent of this study

was to provide a proof of concept of the approach. Given the success of this effort, we plan

to continue this effort to refine the approach and produce studies that can have a definite

impact on improving the performance of turbine engines.



References1. Flack, Ronald D. (2005). Chapter 8: Axial Flow Turbines. Fundamentals of Jet

Propulsion with Applications. Cambridge Aerospace Series. New York, NY: Cambridge

University Press. ISBN 9780521819831, p. 428.

2. Boyce, Meherwan P. (2006). Chapter 9: Axial Flow Turbines and Chapter 11: Materials. Gas

Turbine Engineering Handbook (3rd ed.). Oxford: Elsevier. ISBN 9780750678469. Pg. 370

3. Schramm, U., Designing with Structural Optimization A Practical Point of View, AIAA-

2002-5191, Proceedings of the 9th AIAA MDO Conference, Atlanta, GA, 2002.

4. Schramm, U., How Topology Optimization Changed the Design Process. In: C.A. Mota

Soares et. al., eds., Proceedings of the 3rd European Conference on Computational

Mechanics, Lisbon, POR, 2006.

5. Schramm, U., and Zhou, M., Recent Developments in the Commercial Implementation

of Topology Optimization. In: M. Bendsoe et al., eds., IUTAM Symposium on Topological

Design Optimization of Structures, Machines and Materials: Status and Perspectives

(Springer, 2006) 239-248.

6. Schumacher, G., Stettner, M., Zotemantel, R., OLeary, O., and Wagner, M., Optimization

Assisted Structural Design of a New Military Transport Aircraft, AIAA-2004-4641,

Proceedings of the 10th AIAA MDO Conference, Albany, NY, 2004.

7. Gruber, H., Schumacher, G., Fortsch, C., Rieder, E., Optimization Assisted Structural

design of the rear Fuselage of the A400M, A New Military Aircraft, NAFEMS Seminar:

Optimization in Structural Mechanics, Wiesbaden, GER, 2005

8. Taylor, R.M., Thomas, J.E., Mackaron, N.G., Riley, S., and Lajczok, M.R., Detail Part

Optimization on the F-35 Joint Strike Fighter, AIAA-2006-1886, Proceedings of the 47th

AIAA Structures, Structural Dynamics, and Materials Conference, Newport, RI, 2006.

9. Rao, J.S., Recent Advances in the Optimization of Aerospace Structures and Engines,

8th Intl Conf on Vibration Problems, 2007.

10. Rao, J.S., Kishore, C.B., and Mahadevappa, V., Weight Optimization of Turbine Blades,

ISROMAC12-2008-20020, 12th Intl Symp on Transport Phenomena and Dynamics of Rotating

11. Funnell, M., Targeting Composite Wing Performance Optimum Location of Laminate

Boundaries. Altair UK CAE Technology Conference 2007.

12. Yancey, R. and Stefanovic, M., Optimizing Composite Structures for Weight Reduction,

SAMPE 2009, Baltimore, MD, May 2009.

13. HyperMesh, part of HyperWorks, Altair Engineering, Troy, MI, 2010.

14. Radioss, part of HyperWorks, Altair Engineering, Troy, MI, 2010.

15. HyperStudy, part of HyperWorks, Altair Engineering, Troy, MI, 2010.

Altair Engineering, Inc., World Headquarters: 1820 E. Big Beaver Rd., Troy, MI 48083-2031 USAPhone: +1.248.614.2400 Fax: +1.248.614.2411 www.altair.com [email protected]

optimized cooling passage design

Documents