A
`
`structural Materlals1 Properties,
`Mlcrostructure and Processing
`
`·tors:
`• Koiwa
`• Kostorz
`.C. Koch
`
`Including selected papers from the
`1997 Thermal Barrier Coatings Workshop
`19-21 May, 1997, Cincinnati, OH, USA
`
`Guest Editor: W .J. Brindley
`
`ENGINEERING LIBRARY
`DISPLAY PERIODICAL
`Non-circulating until:
`-.1:.JL O 1 1998
`
`ELSEVIER
`
`•
`
`..
`
`•
`
`UNIVERSITY
`
`OF WASHINGTON
`MAY 2 8 1998
`
`LIBRARIES
`
`•
`
`1
`
`UTC 2025
`General Electric v. United Technologies
`IPR2016-01289
`
`

`

`ELSEVIER
`
`Materials Science and Engineering A245 ( 1998) 150- 159
`
`MATERIAIS
`SCIENCE&
`ENGINEERING
`
`A
`
`Analysis of thermal radiation effects on temperatures 1n turbine
`engine thermal barrier coatings
`
`Robert Siegel *, Charles. M. Spuckler
`NASA L ewis Research Center, Cleveland OH 44135, USA
`
`Abstract
`
`Thermal barrier coatings on combustor liners and on turbine vanes and rotating blades are important for reducing metal
`temperatures in current and advanced turbine engines. Some coating materials such as zirconia are partially transparent to
`thermal radiation , and radiation within a coating will increase as temperatures are raised for higher efficiency engines. Hence, it
`is necessary to determine if radiation effects in a coating are a design consideration. For this purpose, the engine thermal
`environment is first summarized with regard to factors affecting radiative heat transfer. Radiative and thermal properties of
`zirconia are then considered, and methods of radiative analysis are briefly discussed . Typical temperature distributions and heat
`fluxes are given from the analysis of zirconia thermal barrier coatings on vanes and rotating blades, and on a combustor liner
`where the coating surface is expected to be covered with soot. The effects of various thermal conditions and heat transfer
`parameters are examined to indicate when radiation effects might be significant within a coating in a turbine engine. The largest
`effects were found in the combustor where coatings are subjected to large incident radiation . For coatings on turbine blades away
`from the combustor, and hence without large incident radiation, effects of radiation were found to be very small. © 1998 Elsevier
`Science S.A. All rights reserved.
`
`Keywords: Thermal barrier coatings; Thermal radiation effects; Zirconia
`
`1. Introduction
`
`Thermal barrier coatings are important, and in some
`instances a necessity, for protecting metal parts in high
`temperature applications such as combustor liners, and
`turbine vanes and rotating blades for current and ad(cid:173)
`vanced turbine engines. Ceramic components being de(cid:173)
`veloped for these applications may also require an
`environmental or thermal protective coating. Some
`coating materials, such as zirconia which is in wide(cid:173)
`spread use, are partially transparent to thermal radia(cid:173)
`tion [1 - 4]. A translucent coating permits energy to be
`transported internally by radiation, thereby increasing
`the energy transfer above that by conduction alone.
`This degrades the insulating ability of the coating.
`Because of the strong dependence of radiant emission
`on temperature, internal radiative transfer effects are
`increased as temperatures are raised . Hence the possible
`significance of internal radiative transfer must be evalu(cid:173)
`ated as temperatures are increased in advanced engines.
`
`* Corresponding author. Tel.: + I 216 4335831; fax: + I 216
`4338864.
`
`092 l-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved .
`Pl/ S092 I -5093(97)00845-9
`
`transfer partially depends on the
`The radiative
`amount of external radiative energy incident on a ther(cid:173)
`mal barrier coating, and this depends on the coating
`location in the engine. In a combustor there is radiation
`from the flame, soot, and hot gases to the combustor
`liner, first stage turbine vanes, and partially to the first
`stage blades. Within a hot coating there is local internal
`radiant emission, absorption, and scattering, that act in
`combination with heat conduction. Further back in the
`engine away from the combustor, a turbine blade is
`surrounded by similar cooled blades so external radia(cid:173)
`tive exchange is negligible; however, radiation inside the
`hot coating needs to be quantified relative to heat
`conduction.
`Internal radiative behavior depends on the properties
`of the coating material. Zirconia is somewhat translu(cid:173)
`cent for a considerable portion of the radiant energy
`spectrum at turbine engine temperatures. Heat transfer
`analyses for translucent zirconia coatings on a cooled
`metal wall in an turbine engine environment have been
`made in [5] and [6], and a detailed study was made in
`[l] for translucent coatings in diesel engine cylinders.
`
`2
`
`

`

`R. Siegel, C.M. Spuck/er / Materials Science and Engineering A245 (/998) 150- /59
`
`151
`
`This paper will briefly summarize the radiative heat
`transfer conditions in an engine environment needed for
`computing
`temperature distributions
`in
`translucent
`thermal barrier coatings, and will briefly review the
`thermal properties of zirconia. Typical results for tem(cid:173)
`perature distributions and heat flows within zirconia
`coatings are given for a combustor liner, a turbine vane
`and a rotating blade. Results including internal radia(cid:173)
`tion in a coating are compared with heat conduction
`calculations omitting internal radiation. For this limit(cid:173)
`ing condition radiant absorption and emission occur
`only at the external surface. The results provide insight
`on when internal radiation may be of concern in zirco(cid:173)
`nia coatings for turbine engine applications.
`
`2. Heat transfer environment in an engine
`
`Radiative behavior is a strong function of tempera(cid:173)
`ture level. In a combustor the gas temperature can be in
`the approximate range of 1700- 2000 K . Radiant fluxes
`from the gas and soot are given in [7] as up to 230000
`W m - 2
`; this corresponds to a blackbody temperature
`of 1419 K. Higher radiative fluxes are expected in
`advanced engines. With radiative and convective heat(cid:173)
`ing, mostly convective for turbine vanes and rotating
`blades, the surface temperature at the hot side of the
`thermal barrier coating can be in the range of 1400-
`1800 K. Since the metal walls are cooled, the tempera(cid:173)
`ture decreases through the coating so the metal wall
`temperature on the hot side might be in the vicinity of
`1300 K . Hence the temperature range throughout the
`coating is approximately 1300- 1800 K. The tempera(cid:173)
`ture at the hot side of the coating must not be too high
`to avoid sintering the zirconia and increasing its ther(cid:173)
`mal
`conductivity
`during
`continued
`operational
`exposure.
`The local distribution of the internal radiation with
`wavelength, and hence the applicable radiative proper(cid:173)
`ties that depend on wavelength, are related to these
`temperatures. The radiation absorption properties of
`zirconia show that it is somewhat transparent for radia(cid:173)
`tion in the wavelength range up to at least 5 µm (the
`'cutoff wavelength'), and its transparency decreases
`rapidly for larger wavelengths. For zirconia crystals a
`translucent range from about 0.35 - 7 µm was obtained
`in [8]. The radiative behavior of zirconia depends on
`the amount of radiative energy within its translucent
`region. For energy with a blackbody spectrum, Fig. 1
`shows the fraction of blackbody energy in the wave(cid:173)
`length range up to cutoff wavelengths of Ac = 5 and 6
`µm . For the typical range of temperatures in a thermal
`barrier coating, a considerable fraction of the radiant
`energy is in the partially transparent spectral region. In
`[7] it was found that 95% of the radiation in a combus(cid:173)
`tor was in the range A= 0.5 - 9.5 µm , and that the
`
`largest radiation from the soot was in the range from
`A= 0.5- 4 µm . This indicates that at its hot side, a
`zirconia coating will be translucent for close to 90% of
`blackbody radiation emitted at the hot-side tempera(cid:173)
`ture. At the cooler side this decreases to perhaps 70%
`depending on the temperatures involved. Hence, inter(cid:173)
`nal radiation effects diminish somewhat as energy is
`transferred through the coating. Fig. 1 demonstrates in
`a qualitative way that radiative effects may be present
`in zirconia in an engine environment.
`There are two sources for radiative transport within a
`coating. One is the transmission through the exposed
`coating surface of external radiation from hot combus(cid:173)
`tion gases and soot. This penetrates into the coating
`and provides an internal heat source. The other is
`internal emission from within the hot coating itself, and
`the transport of radiation between volume elements of
`the hot coating by successive processes of emission,
`absorption and reemission, and by scattering. On the
`external surface of a coating in a combustor there is
`likely to be a soot deposit. Since soot is highly inter(cid:173)
`nally absorbing, a thin layer can eliminate direct trans(cid:173)
`mission of external radiation into the zirconia coating.
`Incident radiation is absorbed by the soot, and there is
`reradiation into the coating and back into the combus(cid:173)
`tor. In the coating, energy transfer continues by com(cid:173)
`bined radiation and conduction.
`For the exposed portions of a first stage vane, the
`conditions may be somewhat the same as for a combus(cid:173)
`tor liner, as the vane would become somewhat coated
`with soot. Further into the blade rows away from the
`combustor, each cooled blade is surrounded by other
`
`1.0
`
`0.9
`
`0.8
`
`0.7
`
`0.6
`
`0.5
`
`0.4
`
`0 «
`~
`Q)
`.0
`ti)
`,r;
`C)
`C
`(1)
`Q)
`> CII
`~
`<ii
`C
`0
`u
`~ 0.3
`>,
`"O
`0
`.0
`.:.:.
`0
`CII
`ai
`
`0.2
`
`0.1
`
`0.0 L._...___,__..___._~__J'---'---'-~-'-~---'-~..__~ .....
`500
`750
`1000 1250 1500 1750 2000 2250 2500
`
`Blackbody emission temperature, K
`
`Fig. I. Fraction of blackbody rad iation in the wavelength range from
`,l = O to the cutoff wavelength ,le as a function of blackbody temper(cid:173)
`ature.
`
`3
`
`

`

`152
`
`R. Siegel, C.M. Spuck/er / Materials Science and Engineering A245 (/998) 150- 159
`
`- 300
`
`E
`....
`~
`cu
`C:
`Q)
`·c3
`E
`Q)
`0
`(.)
`C:
`.Q
`a.
`....
`0
`1/)
`.0
`<(
`
`200
`
`100
`
`0
`0
`
`-
`
`30000
`
`E
`....
`~
`"' b
`C:
`Q)
`·c3
`20000 E
`Q)
`0
`(.)
`C)
`C:
`·;::
`Q)
`
`10000
`
`~
`en
`
`Absorption
`
`1
`
`2
`3
`Wavelength, A, µm
`
`4
`
`0
`5
`
`Fig. 2. Example of spectral absorption and scattering coefficients for zirconia.
`
`similar cooled blades. There is very little radiative
`exchange between the blades, and radiative effects are
`produced only internally since the coating is hot and its
`volume is emitting. In the blade rows, this will be
`shown to have a small effect on temperature distribu(cid:173)
`tions for the engine conditions considered here; heat
`conduction is dominating for these conditions.
`
`3. Heat transfer properties for a zirconia thermal
`barrier coating
`
`For thermal barrier coatings in an engine, heat con(cid:173)
`duction is generally more dominant than radiation;
`hence, the thermal conductivity of zirconia is very
`important for estimating temperature distributions and
`heat flows. Unfortunately it is difficult to select a
`precise value because conductivity can vary with poros(cid:173)
`ity, temperature, and with the time that the coating is in
`high temperature operation because of sintering its
`porous structure. The thermal conductivity for plasma
`sprayed zirconia is given in [9 - 14], and values range
`from 0.2 to 3.5 W m - 1 K - 1 (values as low as 0.2 W
`m - 1 K - 1 are unusual in practice); this range will yield
`large differences in predicted heat transfer performance.
`For consideration in turbine engines it is common to
`use values of kc = 0.8 - 1 W m - 1 K - 1 for plasma spray
`coatings; in [l] kc= 0.8 W m - I K - 1 was selected for
`diesel engine cylinder coating studies. In the present
`study most of the calculations are for kc= 0.8 W m - 1
`K - I, and the effect of conductivity is demonstrated by
`comparing with some results for kc = 2 W m - 1 K - 1
`•
`
`To predict thermal performance, radiative absorption
`and scattering properties of zirconia are required. Ab(cid:173)
`sorption and scattering coefficients define how rapidly
`radiation traveling along a path decays in an exponen(cid:173)
`tial manner. Both coefficients depend on the radiation
`wavelength. Some results from [l ] are in Fig. 2. As
`evident from the left and right ordinates, at wave(cid:173)
`lengths between approximately O and 5 µm , scattering is
`much larger than absorption. Absorption is the means
`of direct interaction of radiation with the energy equa(cid:173)
`tion, and the local radiant emission from a volume
`element also depends on the absorption coefficient. The
`results in Fig. 2 are for one type of zirconia, and there
`is no assurance that these properties are characteristic
`of zirconia deposited in different ways or that has been
`sintered by being at high temperatures for extended
`periods of time. The results show that absorption is
`relatively low for small wavelengths up to about 5 µm ,
`and becomes large for greater wavelengths.
`Another important radiative property is the coating
`refractive index; this is because internal radiant emis(cid:173)
`sion depends on the refractive index squared. A larger
`refractive index also increases external and internal
`reflections from boundaries that are not covered with
`soot. Increased internal reflections lead to trapping of
`radiation within the material by multiple internal reflec(cid:173)
`tions. The refractive index of zirconia has been reported
`to have a range of values. In [l] values were from
`n = 1.2 ton= 2.5, and n = 1.58 was selected for calcula(cid:173)
`tions of zirconia coatings in a diesel engine cylinder.
`The values in [15 - 17] are within the range of n = 2.0-
`2.3, and in [8] n = 2.11 - 2.17 for zirconia crystals. For
`
`•
`
`4
`
`

`

`R. Siegel, C.M. Spuckler / Materials Science and Engineering A245 (1998) 150- 159
`
`153
`
`the calculations in [2], n = 1.6 was used. To show the
`effect of n, results are given here for n = 1.58 and
`n = 2.1, which are typical of values in the references.
`The refractive index is a factor in the optical relations
`that can be used to estimate the reflectivity at an
`interface with another material. The nature of the
`reflection at the surface of a clean coating, such as
`being diffuse or partly directional, is difficult to define
`accurately. There is also uncertainty in the amount of
`reflection at the zirconia- metal interface where there is
`a thin bond coat. This contributes to internal reflections
`that are included in the radiative boundary conditions.
`Note that the emissivity from the metal wall into the
`zirconia differs from that for the same metal into air
`because the zirconia refractive index is larger than one.
`Tabulated emissivities such as in textbooks [18] are for
`emission into air or vacuum that have a refractive index
`of one.
`
`4. Heat transfer equations and simplifying assumptions
`
`A brief outline of heat transfer relations is given here
`with the nomenclature in Appendix A. The relations
`consist of the energy equation that has conduction and
`radiation terms, and boundary relations with convec(cid:173)
`tion, conduction, and radiation. The two-flux method
`that has been found very useful to provide the radiative
`flux term in the energy equation, is briefly described in
`Appendix B, and additional relations are in [l], [5], [6],
`[19], and [20]. The relations are given in terms of
`frequency, which is convenient for analysis because
`frequency does not change when radiation travels into a
`material with a different refractive index.
`A translucent thermal barrier coating is considered
`on a metal wall, Fig. 3. The zirconia and metal layers
`
`Clean or
`soot covered
`
`Incident
`.__
`radiation
`qr2
`Em
`
`Ts2
`
`Emission, Ebe
`absorption,
`& scattering
`-+---.,....--=-----1~~',4<:,.<,..<,444--- qtot
`Pi or 1-E50
`Po or 1-E80
`Radiation and
`
`Convection
`h1, Tg1
`
`conduction -x=O
`
`I
`
`Fig. 3. Geometry and nomenclature for a thermal barrier coating on
`a metal wall with and without soot on the exposed surface of the
`coating, and with external radiation and convection at both outer
`boundaries.
`
`have thicknesses ,\ and Jm. The gas temperatures on
`the two sides of the wall are Tg1 and Tg2, and there is
`external convection on each side with heat transfer
`coefficients h, and h2• Depending on the location in the
`engine, the external surface of the coating can be clean
`or have a thin opaque layer of soot. For an advanced
`engine the combustion chamber pressure is high enough
`that the combined gas and soot radiation is approxi(cid:173)
`mated as providing a black environment at a tempera(cid:173)
`ture Ts1• When the coating is soot covered, the outer
`surface of the soot has a total heat flux through it that
`consists of the external convection combined with the
`net radiation equal to absorption from the surround(cid:173)
`ings minus reemission:
`
`(la)
`
`where the soot emissivity, Eso, can be assumed indepen(cid:173)
`dent of frequency.
`The soot is very thin so the very small temperature
`variation through its thickness is neglected. At the
`interface of the soot and the translucent coating, the
`radiative flux within the coating in the positive x direc(cid:173)
`tion consists of emission by the soot into the coating,
`and the small reflection by the soot of radiation inci(cid:173)
`dent at the coating- soot interface from the negative x
`direction. Then, for a frequency interval d v:
`q ! (0) d V = E"s0 n 2evb(O) d V + (I -
`If the coating surface is clean, as expected for vanes
`and rotating blades after the first few rows away from
`the combustor, the radiation in the positive x direction
`at the surface (x = 0) inside the coating is composed of
`incident external radiation, q vr I dv, transmitted through
`the surface, and the reflection of radiation from the
`negative x direction inside the thermal barrier coating:
`q ! (O) dv = (1 - p 0 )qvr l dv + Piq;(O) d v
`Within the translucent coating the energy equation
`states that the total heat flux consists of the sum of
`conduction and radiation, and is constant (not a func(cid:173)
`tion of x ):
`
`E"s0 )q ;,: (0) d V
`
`(I b)
`
`(le)
`
`(2)
`
`qvlx ) d v = constant
`
`f oo
`dTc(x )
`qtot = - kc -d--+
`X
`v = O
`The integral for radiative flux is evaluated only in the
`translucent spectral regions. The radiative flux qv,(x ) is
`obtained from the approximate two-flux method in
`Appendix B. The qv,(x ) in the coating depends on the
`local blackbody emission that depends on the local
`temperature. Since the temperature distribution is un(cid:173)
`known, an iterative procedure is usually required to
`simultaneously obtain the spectral radiative flux qvc(x)
`and the temperature distribution Tc(x) in the coating.
`At the interface x = Jc between the translucent coat(cid:173)
`ing and the metal, the temperature distribution is con(cid:173)
`that, Tc(Jc) = Tm(JJ. The
`tinuous so
`temperature
`
`5
`
`

`

`154
`
`R. Siegel, C.M. Spuck/er / Materials Science and Engineering A245 (/998) 150- 159
`
`1850 \ ~,.
`
`1800
`
`'
`
`'\'.\_
`
`Uncoated metal wall
`Opaque coating
`Translucent coating
`
`With soot
`
`Metal wall
`
`1-...;N~o;.;s;;.;:oo;,:t::_ __ ..J
`2
`Qtot, W/m
`/f_280,000
`
`difference across the zirconia- metal bond coat is small
`and has been neglected. The radiative flux relation at
`this interface depends on the emissivity of the metal or
`bond coat. The relation between positive and negative
`radiative fluxes at x = be is similar to that at the soot
`interface in Eq. (I b ):
`q;,(Jc) dv = €bcn 2evb(Jc) dv + (I - Ebc)q ;;,: (Je) dv
`In the opaque metal wall, heat is transferred only by
`conduction so that:
`
`(3)
`
`(4)
`
`At the cooled side of the metal wall, heat flow is by
`convection to the cooling gas, and by radiation to the
`surrounding structure. Radiative transfer may be ap(cid:173)
`preciable depending on the surrounding temperature
`and geometry. For the results given here, large sur(cid:173)
`roundings at T52 are assumed, and the metal emissivity
`is assumed independent of frequency so that:
`qtot = h2[Tc(Je + JnJ - Tg2] + Emcr[T~((\ + Jm) - T!2J
`(5)
`
`Eqs. (la), (lb) and (lc) - (5) are solved along with
`radiative flux relations, as in Appendix B, to determine
`the temperature distribution and heat flow in the coated
`wall; solution procedures are in [5], [6], [19], and [20].
`
`5. Results and discussion
`
`5.1. Combustor liner
`
`A zirconia thermal barrier coating is now considered
`on a metal combustor liner. Illustrative temperatures
`are in Fig. 4 for one set of typical conditions in a
`turbine engine combustor. A Ni-based superalloy liner
`0.794 mm thick is protected by a zirconia coating 1.0
`mm thick. For an advanced engine with high combus(cid:173)
`tor pressure, the combined gas and soot radiation are
`assumed to provide a black environment at T51 = Tg1,
`and this specifies the distribution with frequency of the
`radiation incident on the coating. When the exposed
`surface of the zirconia is covered with soot, this pro(cid:173)
`vides a thin opaque outer layer with an emissivity
`assumed as E50 = 0.97 (P so = 0.03). The results with a
`soot coating are contrasted with those for a clean
`coating that can reflect away part of the incident radia(cid:173)
`tion. The zirconia spectral radiation properties were
`approximated from results such as in Fig. 2 as having a
`translucent region at wavelengths ,l. = 0- 5 µm, with
`absorption and scattering coefficients, a;. = 30 m - 1 and
`0-5;. = 10000 m - 1
`; the zirconia is assumed opaque for
`,l. > 5 µm. The effective blackbody surroundings tem(cid:173)
`peratures, and the convection parameters are in the
`caption of Fig. 4. At the cooled side of the metal wall,
`
`,~.
`~--, t, ~--. ~~·, .
`Soot f 252,700
`(.f 255,700
`~~ ·-.,
`........
`1550 Zirconia coati~:·, ... ;~~ -~.i~; ·· ;;;;·-
`·, - --~~ ~:'f...1 ---:- ..
`
`1750
`
`1700
`
`1650
`
`1600
`
`' ·, .,.,
`·,
`·,,
`......
`
`\~ '·,
`~~ ·,.
`~~ '·
`~~ ' ·,
`
`·,., ~\ -..
`
`n = 1.58
`1500'---'---'-~....l................JL..........--L~...L__~~!.....t....~..L......_J
`0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
`
`Position within coating and metal, x, mm
`
`Fig. 4. Temperature distributions in a zirconia thermal barrier coat(cid:173)
`ing on the wall of a combustor, compa red with an opaque thermal
`barrier coating. Temperature distributions for oxidized metal without
`a coating, with an opaque thermal ba rrier coating, and with a
`translucent thermal barrier coating with and without soot on its
`exposed surface. Parameters (units are in Appendix A): h1 = 250,
`h2= 110, kc =0. 8, km=33 , ,\ = I0 - 3, bm =0.794 x 10 - 3, n = 1.58,
`a= 30 and <T, = 104 for 2 < 5 µm , T, 1 = Tg1 = 2000, T,2 = Ts2 = 800,
`Ebe = 0.3 , <'m = 0.6, <',0 = 0.97.
`
`the metal surface is assumed radiating in large black(cid:173)
`body surroundings at T52 = Tg2 in addition to being
`convectively cooled. The cooled surface of the metal
`wall is assumed oxidized with an emissivity of Em= 0.6
`obtained from textbook tabulations [18] ([7] gives Em
`for oxidized inconel as ~ 0. 7 5). The other surface of
`the metal wall, that is in contact with the coating, is
`assumed to be clean with an emissivity of Ebe= 0.3 (in
`[7] the emissivity for clean inconel is given as 0.25 - 0.5).
`Some results are also given for a turbine blade with a
`bond coating emissivity of Ebe = 0.8. For a coating with
`a clean surface, the zirconia exterior was assumed to
`have a diffuse reflectivity computed by using the zirco(cid:173)
`nia refractive index in the Fresnel optical relations [ 18];
`the value n = 1.58 was used for Fig. 4. Results for
`n = 2. l will also be given since n values this large are
`indicated in some of the references.
`The two solid lines that are only in the metal in Fig.
`4 are for an uncoated metal wall. The lower solid line is
`for metal oxidized on both sides with the emissivity on
`both sides, Em= 0.6. For the upper solid line the metal
`is also covered with an opaque soot layer on the
`combustion side with E50 = 0.97. For the assumed cool(cid:173)
`ing conditions, the metal temperatures are excessive.
`With a zirconia coating, a limiting calculation for com(cid:173)
`parison is for the zirconia assumed to be opaque and
`with a constant thermal conductivity (dashed lines).
`For a coating 1 mm thick the metal temperature is
`
`6
`
`

`

`R. Siegel, C.M. Spuck/er / Materials Science and Engineering A245 (1998) 150- 159
`
`155
`
`K. This would be the extreme amount of radiant energy
`that could be received by a part of the vane or blade
`exposed to the combustion chamber. In Fig. 6a the
`exposed zirconia surface is assumed to be clean, and
`results are given for two refractive indices, n = 1.58 and
`n = 2.1. Comparisons are made with heat conduction
`solutions with the coating assumed opaque so radiative
`exchange is only at the exposed surface. For each n
`value the semitransparency of the coating is predicted
`to yield higher metal temperatures than for an opaque
`coating. The convective heat transfer coefficients are
`much higher for a turbine blade than for a combustor
`liner so radiative effects diminish in importance com(cid:173)
`pared with convection. The effect of scattering becomes
`
`substantially reduced as compared to bare metal. Soot
`on the coating surface has only a small effect in increas(cid:173)
`ing the temperatures (dashed lines). The dot- dashed
`Jines are for a translucent zirconia coating. If the coat(cid:173)
`ing surface can be kept clean the calculations for the
`parameters in Fig. 4 show that the high scattering of
`zirconia reflects away significant incident radiation, re(cid:173)
`ducing temperatures in the zirconia and achieving a 20
`K reduction in metal temperature. If, however, the
`zirconia is covered with soot, the temperatures in the
`metal wall are increased compared with those for an
`opaque coating. In this case the incident radiation is
`absorbed by the soot on the zirconia surface and is
`partially reradiated into the coating, and the semitrans(cid:173)
`parency of the zirconia increases the metal temperature.
`When there is a soot covering, an opaque thermal
`barrier coating provides more effective insulation than
`a translucent coating. Total heat fluxes by combined
`conduction and radiation are also included in Fig. 4.
`For the results in Fig. 4 the refractive index of the
`zirconia is n = 1.58. As noted earlier, some measure(cid:173)
`ments of the zirconia refractive index have shown val(cid:173)
`ues higher than 2. The results for a clean coating in Fig.
`4 were reevaluated in Fig. 5a with the coating refractive
`index increased ton= 2.1 . This increases internal reflec(cid:173)
`tions within the coating resulting in increased absorp(cid:173)
`tion of radiation and increased coating temperatures.
`This leads to increased temperatures in the metal wall
`so the metal temperatures are now higher than for the
`opaque solution even though the coating surface has a
`lower temperature than for an opaque coating. These
`results for a clean coating with n = 2.1 where the metal
`wall temperature is increased by translucence of the
`coating, are in contrast with those in Fig. 4 for n = 1.58
`where the metal temperature is decreased. The n value
`can be quite significant for some conditions; a difficulty
`is that the correct n value cannot be specified with
`confidence.
`The results in Fig. 5a are for a clean coating. For a
`soot-covered coating the results in Fig. 4 for n = 1.58
`are reevaluated in Fig. 5b for n = 2.10. The effect has
`the same trend as in Fig. 5a. The increased refractive
`index causes the temperatures in the coating to be more
`uniform and the metal temperatures are increased.
`
`5.2. First stage vanes
`
`For turbine vanes and rotating blades the zirconia
`coatings are much thinner, such as 0.25 mm, than for a
`combustor liner. The internal cooling passages of the
`blade are assumed isothermal, so radiative exchange is
`omitted in the passages. First stage vanes are adjacent
`to the combustor, and to demonstrate a maximum
`radiative effect, it is assumed that radiation is incident
`on the coating from blackbody surroundings at the
`combustion gas temperature so that Ts, = Tg1 = 2000
`
`1850
`
`1800
`
`1750
`
`~
`~
`~
`~
`~
`~
`~
`
`Opaque, n = 1.58
`Opaque, n = 2.10
`Translucent, n = 1.58
`Translucent, n = 2.10
`
`Metal wall
`
`qtot, W/m2
`
`249,500
`
`\
`1700 ........................ ~~
`.....
`..........
`~~
`'···
`'
`'··· ~
`\.'
`·,.
`......
`'··- ~
`~ ..
`'·,.,
`~--...
`.....
`.......
`.. .
`·,.,.,.,
`Zirconia coating
`· ........ ...
`
`1650
`
`1600
`
`1550
`
`1271,500
`{;252,700
`-... .
`. .. -...
`------
`-
`243,000
`·-·-·-·-·-·-·-·-·-
`1500 L.......,._J__.__J_~J.................i.__.__.__._....__......_,L-...,.---L.. ..............
`0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
`
`(a)
`
`Position within coating and metal, x, mm
`1900 .......... ---.-~-.--r--,--,........,---.---r--.--,---,--..---,----,~-,
`
`~
`
`8
`
`1-
`
`Opaque coating
`Translucent, n = 1.58
`Translucent, n = 2. 10
`
`1800
`
`1750
`
`1700
`
`1650
`
`1600
`
`1550
`
`Zirconia coating
`
`255 700
`
`1500L........--1._....._J.__,__.__.....__.~__._~_,__~i.......,.---1.._._...J
`0.0
`0.2
`0.4
`0.6
`0.8
`1.0
`1.2
`1.4
`1.6
`1.8
`
`(b)
`
`Position within coating and metal, x, mm
`
`Fig. 5. Effect of zirconia refractive index on temperature distributions
`in a thermal barrier coating on a combustor wall. The parameters are
`the same as for Fig. 4, except with additional results for a coating
`refractive index n = 2.1. (a) Coating surface is clean. (b) Coating
`surface is covered with soot.
`
`7
`
`

`

`156
`
`R. Siegel, C.M. Spuck/er / Materials Science and Engineering A245 (1998) 150- 159
`
`1150...--~--.----.-----,.---~--.----,---,,
`
`Opaque, n = 1.58
`Opaque, n = 2.10
`Translucent, n = 1.58
`Translucent, n = 2.10
`
`&bond coat = Ebe = 0.3
`Metal wall
`
`Radiative surroundings
`are hot, T s1 = 2000 K
`
`2
`qtot, W/m
`
`;.
`[.1249000
`\ ::· ~-.. -..1.f.~]92.~-... -[:1202000
`-·-·-·
`...
`.
`.
`'"
`Z1rconia
`-·-·-···- ····· . • ....... - ... - .... ...
`coating
`· ···-·· ···-·······
`1194000
`
`1600
`
`1550
`
`1500
`
`1450
`
`1400
`
`1350
`
`1300
`0.0
`
`0.2
`0.4
`0.6
`0.8
`Position within coating and metal, x, mm
`
`1.0
`
`Opaque
`Translucent, 6bc: = 0.3
`Translucent, 6bc: = 0.8
`
`Metal wall
`
`Radiative surroundings
`are hot, T s1 = 2000 K
`
`2
`qtot, W/m
`
`\
`},
`~#,
`1293000
`\..
`\ - · .•.•.•. 13470001
`Zirconia • ·- ... - .... .... ....... ~~:_:~:-·············· ·- ·
`119400
`.... .... .... ... - ... - .. .
`
`" f
`~o=~~f
`
`1550
`
`1500
`
`1450
`
`1400
`
`1350
`
`0.0
`
`1300~~-~~-~~-~-~~-~~
`0.4
`0.6
`0.2
`0.8
`Position within coating and metal, x, mm
`
`1.0
`
`~ g
`I-
`c
`.Q -s .c
`·c -VJ
`
`'c
`~
`.2
`~
`Q)
`C.
`E
`Q)
`I-
`
`(a)
`
`E I-
`
`C:
`0
`
`~ .c
`·c
`cii
`'c
`~
`.2
`~
`Q)
`C.
`E
`{:!.
`
`(b)
`
`Fig. 6. Turbine blade wall temperature distributions for blade ex(cid:173)
`posed to radiation from the combustor. Temperatures for an opaque
`thermal barrier coating, and for a translucent coating, both with
`clean exposed surfaces. Parameters (units are in Appendix A): h, =
`3014, h2 = 3768, kc = 0.8, km= 33, '5c = 0.25 X 10 - 3
`'5 m = 0.762 X
`,
`10 - 3
`, a = 30 and u, =104
`for
`,l< 5 µm , T, , = Tg1 =2000,
`T,2 = Tg2 = 1000. (a) Coating refractive index, n = 1.58 and n = 2.1,
`for Ebe= 0.3. (b) Effect of bond-coat emissivity, Ebe= 0.3 and 0. 8 for
`n = 2.1.
`
`small in providing a benefit by reflecting away incident
`radiation. The translucence of the coating increases the
`heat transfer, and the temperatures are increased in the
`metal wall for the specified conditions of combined
`convective and radiative heating. Comparing the results
`for n = 2. I and n = 1.58 shows that for an opaque
`solution where the only effect of n is to change the
`
`reflectivity of the exposed surface, there is little effect
`on the temperature distribution since radiation is small
`relative to conduction and convection. For a translu(cid:173)
`cent coating, the effect of increased internal reflections
`for n = 2. I produces an increase in the metal tempera(cid:173)
`ture of about 12 K. The heat flux results in Fig. 6a
`show that radiation increases the total heat flow by
`about 8% when n = 2.1.
`The purpose of Fig. 6b is to illustrate the effect of the
`emissivity of the bond coat between the thermal barrier
`coating and the metal wall. The parameters are the
`same as for Fig. 6a with n = 2.1 , but the Ebe is changed
`from 0.3 to 0.8. This has no effect on the solution for
`an opaque coating, that is given by the solid lines. For
`a translucent coating, by reducing reflection at the
`zirconia- metal interface, the metal absorbs more