Heat Transfer Analysis

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4.4
Heat Transfer Analysis
Frank J. Cunha, Ph.D., P.E.
Pratt & Whitney
United Technologies Corporation
5 Bruce Lane
Avon, CT 06001
Phone: (860) 565-8909
Email: frank.cunha@pw.utc.com
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4.4-1 Introduction
The thermal effi ciency and specifi c output of a gas turbine are primarily
dependent on two major cycle parameters: the pressure ratio and the turbine
inlet temperature1. In an ideal Brayton cycle, thermal effi ciency increases up
to stoichiometric temperatures and high-pressure ratios, without considering
losses, particularly, those associated with turbine cooling. Since turbine airfoil
materials melt at temperatures much lower than the stoichiometric temperatures,
hot gas-path components, such as turbine airfoils, must be cooled and attention
must be given to cycle parasitic losses.
The recognition of material temperature limitations has led to the
continuous turbine development programs for cooling technologies, material
development, and related multi-disciplinary disciplines of fl uid dynamics, heat
transfer, aerodynamic performance, and structures, all aimed at the durability
of turbine hot-gas-path components. The pursuit of improved turbine materials
began long ago when the initial temperature limitations were found to be at
about 1500°F (800°C)2. Following this initial period, an intensive development
period took place when nickel-based alloys were developed and characterized
as having high creep resistance characteristics. Material improvements relaxed
temperature limitations by about 300°F (167°C)3. Further development of turbine
airfoil manufacturing techniques, such directionally-solidifi cation castings
and single-crystal castings led to higher metal temperature capability. More
recently, numerous testing evaluations have been conducted to characterize new
hot-gas path material superalloys in terms of tensile, rupture, fatigue, creep,
toughness, corrosion and oxidation resistances, producibility, processing, and
other thermophysical properties4. Following extensive laboratory testing, actual
operating experience is gained with engine testing subject to real operational
environments culminating in mature levels of technology readiness levels for
production.
Today, many modern turbine airfoils use single crystal superalloys.
These are two-phase alloys with a large volume fraction of precipitates,
based on the intermetallic compound, Ni3 Al, interspersed in a coherent face-
centered cubic matrix comprised of nickel, Ni, with smaller weight percent
of various other elements in solid solution5. These elements include: cobalt,
Co, aluminum, Al, chromium, Cr, tungsten, W, molybdenum, Mo, tantalum,
Ta, hafnium, Hf, rhenium, Re, and ruthenium, Ru. The elements Re and Ru are
introduced in the latest generation of single crystal alloys. All these elements
have different attributes which can be summarized as follows: Cr, Al, and
Hf are used as surface protection elements, Mo, W, and Ta are used in solid
solution strengthening, and Re and Ru are used for high creep strength6
.
The strength of these single crystal alloys is mainly a function of the
size and the percentage of precipitates. Experimentally, it has been determined
that the peak creep strength is achieved with a volume fraction of of 60%-
65%7. Much of the behavior of these alloys can be explained on the basis
that high volume fraction alloys deformation occurring by shearing of the
precipitates. The high volume fraction of precipitates precludes dislocation
bypass at low and intermediate temperatures forcing precipitate shearing.
However, the energies resisting dislocation shearing of the precipitates are
those required to form a local reversal of Al-Ni order or antiphase boundary
in stacking fault of the Ni3 Al superlattice. The energies associated with the
anti-phase boundary in the superlattice stacking faults determine the strength,
fatigue, and fracture characteristics of these alloys8. This is also evident by the
increase in yield strength at moderate to high temperatures before a monotonic
decrease in yield strength. As a result, the excellent high-temperature creep and
fatigue resistance of the superalloys is a result of a combination of solid-solution
strengthening, absence of deleterious grain boundaries, and high volume fraction
of precipitates that act as barriers to dislocation motion. It should be pointed-
out, however, that fatigue crack initiation also depends on the microscopic