**3.2.1 Numerical simulation**

The computational part of the method consists in sequentially solving the following problems: the electromagnetic problem based on the Maxwell equations, the transient heat problem based on the solution of the heat conduction equation, and the problem of determination of the thermostressed state. The first problem was solved with due regard for the recommendations proposed in (Kuvaldin & Lepeshkin, 2006). By solving this problem (taking into account the gap between the inductor and the part and the electric current frequency of 440 kHz), we determined the distribution of internal heat sources (specific heat power) over the thickness of the base metal (the refractory nickel alloy of the flame tube) with an intermediate refractory metal coating NiCoCrAlY, as well as in the ceramic coating due to the induction heating (as a result of the change in the electrical resistivity ofzirconium oxide with an increase in temperature) and dielectric heating (as a result of the change in the permittivity and the dielectric loss tangent with an increase in temperature). The obtained distributions of internal heat sources are nonstationary; i.e., they depend on the heating time. During the solution of the coupled electromagnetic and heat problems at each computational step, the value of the current temperature was transferred from the module of the solution of the heat problem to the module of the solution of the electromagnetic problem in order to correct the electrophysical properties of the materials. The computational investigations allow one to refine the thermal and thermostressed states of thermal barrier ceramic coatings on cooled blades and models during high-frequency induction heating with the inclusion of dielectric heating. The initial data used in the performed calculations were electrophysical, thermophysical, and strength properties of the ceramic coatings and the material of cooled parts, the characteristics of bench conditions for heating and cooling, and the parameters of the test thermal cycle. The electrophysical and dielectric properties of the ceramic (zirconia) coating were taken from (Rubashev at al., 1980), and the electrophysical, thermophysical, and strength properties of the ceramic coatings were taken from (Tamarin & Kachanov, 2008). The parameters of the permittivity and dielectric loss tangent *tg* of a zirconium oxide depending on temperature are shown in Fig. 9. Electrical resistivity of a zirconium oxide makes at the temperatures: 100 C - 1011 Ohmcm,1000 C - 10 Ohmcm.

The calculations performed by author using the finite element method implemented in the ANSYS program and the distribution of the heat flux from the inductor between the zirconia coating and the metal of the cooled part at an induction current frequency of 440 kHz made it possible to investigate the nonstationary thermal state of the coating and the cooled part with the inclusion of the parameters of the test thermal cycle. The boundary conditions for the solution to the heat problem were as follows: the temperature of the ambient air was 20 °C, the heat-transfer coefficients of the ambient air were equal to 20-30W/(m2 K), the heattransfer coefficients of the cooled air inside the model of a flame tube were equal to 1800- 2000 W/(m2 K) (according to the experimental data), the specific heating power on the surface of the refractory metal coating was 9 x 105 W/cm2, and the specific heating power

peratures in a metal-ceramic part are set in computational and experimental studies. By using multivariant calculations, it is necessary to obtain a generalized dependence of the temperature gradient across the ceramic coating thickness on the frequency of the electric

The computational part of the method consists in sequentially solving the following problems: the electromagnetic problem based on the Maxwell equations, the transient heat problem based on the solution of the heat conduction equation, and the problem of determination of the thermostressed state. The first problem was solved with due regard for the recommendations proposed in (Kuvaldin & Lepeshkin, 2006). By solving this problem (taking into account the gap between the inductor and the part and the electric current frequency of 440 kHz), we determined the distribution of internal heat sources (specific heat power) over the thickness of the base metal (the refractory nickel alloy of the flame tube) with an intermediate refractory metal coating NiCoCrAlY, as well as in the ceramic coating due to the induction heating (as a result of the change in the electrical resistivity ofzirconium oxide with an increase in temperature) and dielectric heating (as a result of the change in the permittivity and the dielectric loss tangent with an increase in temperature). The obtained distributions of internal heat sources are nonstationary; i.e., they depend on the heating time. During the solution of the coupled electromagnetic and heat problems at each computational step, the value of the current temperature was transferred from the module of the solution of the heat problem to the module of the solution of the electromagnetic problem in order to correct the electrophysical properties of the materials. The computational investigations allow one to refine the thermal and thermostressed states of thermal barrier ceramic coatings on cooled blades and models during high-frequency induction heating with the inclusion of dielectric heating. The initial data used in the performed calculations were electrophysical, thermophysical, and strength properties of the ceramic coatings and the material of cooled parts, the characteristics of bench conditions for heating and cooling, and the parameters of the test thermal cycle. The electrophysical and dielectric properties of the ceramic (zirconia) coating were taken from (Rubashev at al., 1980), and the electrophysical, thermophysical, and strength properties of the ceramic coatings were taken from (Tamarin & Kachanov, 2008). The parameters of the

current.

permittivity

C - 1011 Ohmcm,1000 C - 10 Ohmcm.

and dielectric loss tangent *tg*

are shown in Fig. 9. Electrical resistivity of a zirconium oxide makes at the temperatures: 100

The calculations performed by author using the finite element method implemented in the ANSYS program and the distribution of the heat flux from the inductor between the zirconia coating and the metal of the cooled part at an induction current frequency of 440 kHz made it possible to investigate the nonstationary thermal state of the coating and the cooled part with the inclusion of the parameters of the test thermal cycle. The boundary conditions for the solution to the heat problem were as follows: the temperature of the ambient air was 20 °C, the heat-transfer coefficients of the ambient air were equal to 20-30W/(m2 K), the heattransfer coefficients of the cooled air inside the model of a flame tube were equal to 1800- 2000 W/(m2 K) (according to the experimental data), the specific heating power on the surface of the refractory metal coating was 9 x 105 W/cm2, and the specific heating power

of a zirconium oxide depending on temperature

**3.2.1 Numerical simulation** 

in the ceramic coating was 1.8 x 105 W/cm2 (these specific heating powers were obtained from the solution of the electromagnetic problem). The minimum and maximum heating temperatures of the metal surface of the part in the thermal cycle were equal to 350 and 900 °C, respectively. The mathematical simulation of the thermal state of the ceramic coatings takes into account the specific features of the electrophysical properties of zirconia. In particular, an increase in the temperature results in an increase in the permittivity, the dielectric loss tangent, and the electrical conductivity (Kuvaldin & Lepeshkin, 2006). On the whole, the ceramic coating in the course of the test thermal cycle was heated by means of both the heat transfer from the metal of the part and the dielectric heating. The computational scheme for a fragment of the cooled part with the thermal barrier coating is shown in Fig. 10.

Fig. 9. Parameters and *tg*depending on temperature

Fig. 10. Schematic diagram of a fragment of the cooled part with the thermal barrier ceramic coating: *(1)* ceramic coating, *(2)* metal of the workpiece, *(3)* refractory metal layer, and *(4)*  direction of the flow of cooling air in the hole. Designation: *d* is the hole diameter

Investigations of Thermal Barrier Coatings for Turbine Parts 143

zirconia thermal barrier coating approximately corresponds to 80 % for the metal (the high-frequency energy is released in the metal of the sample) and 20 % for the coating (the high-frequency energy is released in the zirconia ceramic coating due to the induction heating (10 %) and the dielectric losses (10 %)). According to the results of the numerical calculations under the aforementioned conditions at a heating rate of 100 K/s, the temperature on the outer surface of the model of the part with the thermal barrier coating in contact with the environment is approximately 60-80 °C higher than that at the "metalthermal barrier coating" interface; i.e., the temperature state of the part is simulated in operation. In this case, compressive thermal stresses of 100 MPa on the metal surface and tensile thermal stresses of 30-35 MPa on the side of the thermal barrier ceramic coating are

coating thickness on the frequency of the electric current was obtained using multivariant

Fig. 13. Dependence of the temperature gradient across the ceramic coating thickness on the

The experimental part of the method provides simulation of high-frequency induction heating and the performance of thermophysical measurements in the course of thermal cyclic tests of blades and other cooled parts and takes into account the electrophysical and thermophysical properties of their materials. In the developed method, the contactless thermophysical measurements are carried out using a thermal vision system for the performance of investigations and for the confirmation of the calculated results for the nonstationary thermal state of the part with the thermal barrier ceramic coating (with the

*t(f)* with variations in the frequency of the electric current

*t(f)* across the ceramic

observed. A generalized dependence of the temperature gradient

calculations. This dependence

frequency of the electric current

**3.2.2 Experimental investigations** 

from 200 to 2000 kHz is plotted in Fig. 13.

The performed calculations of the nonstationary thermal and thermostressed states of the models of cooled parts with thermal barrier ceramic coatings (Fig. 11 and Fig. 12) have demonstrated that, at the maximum temperature of the thermal cycle, the temperature of the outer surface of the ceramic coating at the end of heating is higher than the temperature of the metal and, consequently, there arise temperature gradients across the ceramic coating thickness.

Fig. 11. Calculated temperature distribution of the fragment of the cooled part with the thermal barrier ceramic coating in the region of the cooling hole

Fig. 12. Calculated thermostress distribution of the fragment of the cooled part with the thermal barrier ceramic coating in the region of the cooling hole

The temperature gradients depend on the thermal conductivity coefficient, the coating thickness, and the heat loss due to the environment on the surface of the coating. The heat losses were calculated taking into account the convective heat exchange, the radiative heat exchange, and the maximum experimental temperature of uncooled plates of the inductor (300 °C) at the end of heating in the first stage of the thermal cycle. At an induction current frequency of 440 kHz and taking into account the ratios between the heated masses of the base material from the refractory alloy and the coating, as well as their electrophysical and thermophysical properties and cooling conditions, the calculated distribution of the highfrequency electromagnetic energy over the sample from the nickel-based alloy with the

The performed calculations of the nonstationary thermal and thermostressed states of the models of cooled parts with thermal barrier ceramic coatings (Fig. 11 and Fig. 12) have demonstrated that, at the maximum temperature of the thermal cycle, the temperature of the outer surface of the ceramic coating at the end of heating is higher than the temperature of the metal and, consequently, there arise temperature gradients across the ceramic coating

Fig. 11. Calculated temperature distribution of the fragment of the cooled part with the

Fig. 12. Calculated thermostress distribution of the fragment of the cooled part with the

The temperature gradients depend on the thermal conductivity coefficient, the coating thickness, and the heat loss due to the environment on the surface of the coating. The heat losses were calculated taking into account the convective heat exchange, the radiative heat exchange, and the maximum experimental temperature of uncooled plates of the inductor (300 °C) at the end of heating in the first stage of the thermal cycle. At an induction current frequency of 440 kHz and taking into account the ratios between the heated masses of the base material from the refractory alloy and the coating, as well as their electrophysical and thermophysical properties and cooling conditions, the calculated distribution of the highfrequency electromagnetic energy over the sample from the nickel-based alloy with the

thermal barrier ceramic coating in the region of the cooling hole

thermal barrier ceramic coating in the region of the cooling hole

thickness.

zirconia thermal barrier coating approximately corresponds to 80 % for the metal (the high-frequency energy is released in the metal of the sample) and 20 % for the coating (the high-frequency energy is released in the zirconia ceramic coating due to the induction heating (10 %) and the dielectric losses (10 %)). According to the results of the numerical calculations under the aforementioned conditions at a heating rate of 100 K/s, the temperature on the outer surface of the model of the part with the thermal barrier coating in contact with the environment is approximately 60-80 °C higher than that at the "metalthermal barrier coating" interface; i.e., the temperature state of the part is simulated in operation. In this case, compressive thermal stresses of 100 MPa on the metal surface and tensile thermal stresses of 30-35 MPa on the side of the thermal barrier ceramic coating are observed. A generalized dependence of the temperature gradient *t(f)* across the ceramic coating thickness on the frequency of the electric current was obtained using multivariant calculations. This dependence *t(f)* with variations in the frequency of the electric current from 200 to 2000 kHz is plotted in Fig. 13.

Fig. 13. Dependence of the temperature gradient across the ceramic coating thickness on the frequency of the electric current

### **3.2.2 Experimental investigations**

The experimental part of the method provides simulation of high-frequency induction heating and the performance of thermophysical measurements in the course of thermal cyclic tests of blades and other cooled parts and takes into account the electrophysical and thermophysical properties of their materials. In the developed method, the contactless thermophysical measurements are carried out using a thermal vision system for the performance of investigations and for the confirmation of the calculated results for the nonstationary thermal state of the part with the thermal barrier ceramic coating (with the

Investigations of Thermal Barrier Coatings for Turbine Parts 145

operating in the spectral range from 3.0 to 5.6 m. The specific features of the technique used for measuring temperatures with thermal vision systems are described in (Bychkov, 2008). The model of the cooled part (the flame tube with holes) is shown in Fig. 15. The diameter of two rows of holes is equal to 1 mm. The diameters of holes of the other rows are

The cooling air was fed into a box-like hollow model (with a rectangular cross section) of the flame tube. The model had a wall thickness of 1 mm and a cross section of 10 x 25 mm. In the examination of the temperature state of the part with the ceramic coating, the optical accessibility of the object during the thermal cycle was provided by a small hole (5 mm in diameter), which was drilled in the inductor and through which the surface region was scanned (Fig. 16). Thermal images in the course of thermal cyclic tests were recorded in a personal computer with a frequency of three to five frames per second. The analog signal of the thermal imager was digitized using an L-783 analog-to-digital converter board fabricated by the L-CARD Corporation. The complete cycle (from the beginning of heating

smaller than 1 mm. The refractory joining layer (coating) has a thickness of 0.06 mm.

Fig. 14. Blackness degree *b* depending on temperature

Fig. 15. Model of the cooled part with holes

inclusion of the temperature gradient across the ceramic coating thickness) in thermal cyclic tests of rotating blades and models of flame tubes with thermal barrier ceramic coatings. The temperatures of the surfaces of the ceramic coating and the metal under the coating were measured simultaneously with a thermal imager lens through a hole in the inductor. In this method, we also proposed the design of a split uncooled plate inductor (Bychkov, 2008) with a hole for the examination of thermal and thermostressed states of the cooled and uncooled blades, including parts of gas turbine engines with coatings. The specific features of this method are as follows: the possibility of performing thermal cyclic tests of parts of gas turbine engines with retaining a guaranteed minimum constant gap between the inductor and the blade surface, which decreases the probability of distortion of the temperature field after the replacement of the parts and favors an increase in the efficiency of high-frequency induction heating; the fulfillment of the relationship < 0.1*h*, where is the depth of penetration of the electric current (the electromagnetic wave) and *h* is the minimum thickness of the metal wall of the part (the cooled blade) for the choice of the frequency of the electric current; etc. Two cooling circuits are used to create the required nonstationary thermal state of the cooled part and to provide the optimum parameters of the thermal cycle. The first cooling circuit ensures air supply into the inner cavity of the part, and the second circuit is responsible for supply of air passing between the inductor plates and the part for blowing the surface of the part and its cooling at the end of each thermal cycle. Preliminary, while heating the model in electric furnace there were obtained empirical data about degree of blackness for specimen with and without the thermal-protective coating which were used for thermal-imaging measurements. The values of blackness degree *<sup>b</sup>* for specimen with the coating under temperatures, approximately, of 850900 С close to peak ones in the cycle were equal to about 0.55 and for blade specimen in hightemperature-resistant alloy without the coating their value was about 0.80 (Fig. 14). The thermal cyclic tests of the blades with a thermal barrier coating and the models of cooled parts were carried out in the course of high-frequency induction heating of the object at a frequency of 440 kHz according to the developed technique on a setup (Lepeshkin, 2005) equipped with a VChG-10/0.44 high-frequency valve generator. In order to perform comparative thermal cyclic tests, the working surface of the models of flame tubes produced from a refractory alloy sheet 1.0 mm thick with preliminarily perforated holes (Fig. 15) was subjected to sand blasting with synthetic corundum, followed by the deposition of two variants of the thermal barrier ceramic coating with the intermediate refractory joining NiCoCrAlY layer and without it. Figure 10 shows a fragment of the model of a cooled part (the model of a flame tube with a thermal barrier coating) mounted inside the inductor connected to electric buses of the VChG-10/0.44 generator. Air with a controlled flow rate and a controlled pressure was fed inside the sample. This scheme provided the possibility of reproducing the operating fields of temperatures and thermal stresses for the model and the possibility of experimentally determining the thermal cyclic fatigue life of the models of a section of the flame tube with different variants of thermal barrier coatings and without them.

The temperature was controlled by a chromel-alumel thermocouple. The temperature state of the surface of the thermal barrier coating in the working region was controlled using an Agema thermal imager. For the experimental verification of this thermal state, we carried out contactless measurements of the temperature of the surface of the model with the thermal barrier coating based on zirconia with the use of an Agema 782 SW thermal imager

inclusion of the temperature gradient across the ceramic coating thickness) in thermal cyclic tests of rotating blades and models of flame tubes with thermal barrier ceramic coatings. The temperatures of the surfaces of the ceramic coating and the metal under the coating were measured simultaneously with a thermal imager lens through a hole in the inductor. In this method, we also proposed the design of a split uncooled plate inductor (Bychkov, 2008) with a hole for the examination of thermal and thermostressed states of the cooled and uncooled blades, including parts of gas turbine engines with coatings. The specific features of this method are as follows: the possibility of performing thermal cyclic tests of parts of gas turbine engines with retaining a guaranteed minimum constant gap between the inductor and the blade surface, which decreases the probability of distortion of the temperature field after the replacement of the parts and favors an increase in the efficiency

the depth of penetration of the electric current (the electromagnetic wave) and *h* is the minimum thickness of the metal wall of the part (the cooled blade) for the choice of the frequency of the electric current; etc. Two cooling circuits are used to create the required nonstationary thermal state of the cooled part and to provide the optimum parameters of the thermal cycle. The first cooling circuit ensures air supply into the inner cavity of the part, and the second circuit is responsible for supply of air passing between the inductor plates and the part for blowing the surface of the part and its cooling at the end of each thermal cycle. Preliminary, while heating the model in electric furnace there were obtained empirical data about degree of blackness for specimen with and without the thermal-protective coating which were used for thermal-imaging measurements. The values of blackness

*<sup>b</sup>* for specimen with the coating under temperatures, approximately, of 850900 С

close to peak ones in the cycle were equal to about 0.55 and for blade specimen in hightemperature-resistant alloy without the coating their value was about 0.80 (Fig. 14). The thermal cyclic tests of the blades with a thermal barrier coating and the models of cooled parts were carried out in the course of high-frequency induction heating of the object at a frequency of 440 kHz according to the developed technique on a setup (Lepeshkin, 2005) equipped with a VChG-10/0.44 high-frequency valve generator. In order to perform comparative thermal cyclic tests, the working surface of the models of flame tubes produced from a refractory alloy sheet 1.0 mm thick with preliminarily perforated holes (Fig. 15) was subjected to sand blasting with synthetic corundum, followed by the deposition of two variants of the thermal barrier ceramic coating with the intermediate refractory joining NiCoCrAlY layer and without it. Figure 10 shows a fragment of the model of a cooled part (the model of a flame tube with a thermal barrier coating) mounted inside the inductor connected to electric buses of the VChG-10/0.44 generator. Air with a controlled flow rate and a controlled pressure was fed inside the sample. This scheme provided the possibility of reproducing the operating fields of temperatures and thermal stresses for the model and the possibility of experimentally determining the thermal cyclic fatigue life of the models of a section of the flame tube with different variants of thermal barrier coatings and without

The temperature was controlled by a chromel-alumel thermocouple. The temperature state of the surface of the thermal barrier coating in the working region was controlled using an Agema thermal imager. For the experimental verification of this thermal state, we carried out contactless measurements of the temperature of the surface of the model with the thermal barrier coating based on zirconia with the use of an Agema 782 SW thermal imager

< 0.1*h*, where

is

of high-frequency induction heating; the fulfillment of the relationship

degree 

them.

operating in the spectral range from 3.0 to 5.6 m. The specific features of the technique used for measuring temperatures with thermal vision systems are described in (Bychkov, 2008). The model of the cooled part (the flame tube with holes) is shown in Fig. 15. The diameter of two rows of holes is equal to 1 mm. The diameters of holes of the other rows are smaller than 1 mm. The refractory joining layer (coating) has a thickness of 0.06 mm.

Fig. 14. Blackness degree *b* depending on temperature

Fig. 15. Model of the cooled part with holes

The cooling air was fed into a box-like hollow model (with a rectangular cross section) of the flame tube. The model had a wall thickness of 1 mm and a cross section of 10 x 25 mm. In the examination of the temperature state of the part with the ceramic coating, the optical accessibility of the object during the thermal cycle was provided by a small hole (5 mm in diameter), which was drilled in the inductor and through which the surface region was scanned (Fig. 16). Thermal images in the course of thermal cyclic tests were recorded in a personal computer with a frequency of three to five frames per second. The analog signal of the thermal imager was digitized using an L-783 analog-to-digital converter board fabricated by the L-CARD Corporation. The complete cycle (from the beginning of heating

Investigations of Thermal Barrier Coatings for Turbine Parts 147

As an example, Fig. 18-20 displays three thermal images of the model with the thermal barrier coating during induction heating. The temperatures at the surfaces of the ceramic coatings shown in the thermal images in Figs. 18-20 are equal to 946.6 °C (Fig. 17, point *1),*  969.4 °C (Fig. 17, point *2),* and 953.9 °C (Fig. 17, point *3),* respectively. At the peak temperature, the indication of the control thermocouple on the sample (which corresponds to the lower edge of the thermal image) is approximately 60—70°C below the temperature of the outer layer of the coating (in the vicinity of the thermocouple), which is recorded by the

Fig. 18. Thermal image of the sample with the thermal ceramic barrier coating (0.2 s before

thermal imager (Fig. 18-20).

the heating is switched off)

of the sample to cooling) was recorded; however, only the frames in the vicinity of the peak value of the temperature were used in the processing. The parameters of the thermal cycle are presented in Fig. 17.

Fig. 16. Tests of the cooled part with the heat resistant ceramic coating: (*1*) inductor and (*2*) cooled part.

Fig. 17. Heating thermogram.

of the sample to cooling) was recorded; however, only the frames in the vicinity of the peak value of the temperature were used in the processing. The parameters of the thermal cycle

Fig. 16. Tests of the cooled part with the heat resistant ceramic coating: (*1*) inductor and (*2*)

are presented in Fig. 17.

cooled part.

Fig. 17. Heating thermogram.

As an example, Fig. 18-20 displays three thermal images of the model with the thermal barrier coating during induction heating. The temperatures at the surfaces of the ceramic coatings shown in the thermal images in Figs. 18-20 are equal to 946.6 °C (Fig. 17, point *1),*  969.4 °C (Fig. 17, point *2),* and 953.9 °C (Fig. 17, point *3),* respectively. At the peak temperature, the indication of the control thermocouple on the sample (which corresponds to the lower edge of the thermal image) is approximately 60—70°C below the temperature of the outer layer of the coating (in the vicinity of the thermocouple), which is recorded by the thermal imager (Fig. 18-20).

Fig. 18. Thermal image of the sample with the thermal ceramic barrier coating (0.2 s before the heating is switched off)

Investigations of Thermal Barrier Coatings for Turbine Parts 149

Fig. 20. Thermal image of the sample with the thermal ceramic barrier coating (0.2 s after the

The control thermocouple is fixed on the metal surface (locally protected against the ceramic coating) of the refractory layer. The temperatures of the thermal barrier coating and the refractory layer were recorded on the thermal imager simultaneously. The performed experimental investigations and measurements of the temperature of the part with the thermal barrier coating with the use of the thermal imager in the course of thermal cycling confirmed the calculated value of the temperature gradient across the ceramic coating thickness. Thus, the analysis of the results obtained has demonstrated that the thermostressed state observed for parts of the hot gas section of gas turbine engines (combustion chambers, turbine blades, etc.) during blowing them by a high-temperature gas flow under operating conditions can be simulated under laboratory conditions on a setup with high-frequency heating. The temperature gradient across the ceramic coating thickness can be varied over a wide range by varying the flow rate of air supplied for cooling, the power of the high-frequency generator, and the wall thickness. Thus, the analysis of the results of thermal fatigue tests of blades (Fig. 21, Fig. 22) of gas turbine engines during thermal cycling according to the regime *t*min ↔ *t*max (350 °C ↔ 900–1000 °C have shown that the thermal cyclic fatigue life of blades with a thermal-barrier ceramic coating deposited by the electron-beam method increases, on average, by a factor of 3.4 compared to the blades

heating is switched off)

Fig. 19. Thermal image of the sample with the thermal ceramic barrier coating at the instant of switching off

Fig. 19. Thermal image of the sample with the thermal ceramic barrier coating at the instant

of switching off

Fig. 20. Thermal image of the sample with the thermal ceramic barrier coating (0.2 s after the heating is switched off)

The control thermocouple is fixed on the metal surface (locally protected against the ceramic coating) of the refractory layer. The temperatures of the thermal barrier coating and the refractory layer were recorded on the thermal imager simultaneously. The performed experimental investigations and measurements of the temperature of the part with the thermal barrier coating with the use of the thermal imager in the course of thermal cycling confirmed the calculated value of the temperature gradient across the ceramic coating thickness. Thus, the analysis of the results obtained has demonstrated that the thermostressed state observed for parts of the hot gas section of gas turbine engines (combustion chambers, turbine blades, etc.) during blowing them by a high-temperature gas flow under operating conditions can be simulated under laboratory conditions on a setup with high-frequency heating. The temperature gradient across the ceramic coating thickness can be varied over a wide range by varying the flow rate of air supplied for cooling, the power of the high-frequency generator, and the wall thickness. Thus, the analysis of the results of thermal fatigue tests of blades (Fig. 21, Fig. 22) of gas turbine engines during thermal cycling according to the regime *t*min ↔ *t*max (350 °C ↔ 900–1000 °C have shown that the thermal cyclic fatigue life of blades with a thermal-barrier ceramic coating deposited by the electron-beam method increases, on average, by a factor of 3.4 compared to the blades

Investigations of Thermal Barrier Coatings for Turbine Parts 151

**4.1 Investigations of thermal barrier properties of ceramic coatings with the use pulse** 

Thermal barrier coating application efficiency depends on ceramic layer thermal conductivity, which determines the cooled blade temperature drop and corresponding increase in its service life. To measure thermal conductivity of a TBC ceramic layer, a laser flash method is used (Siegwart et al., 2006) (Parker et al., 1961). The method is based on irradiating the surface of a flat sample surface with an energy pulse, followed by recording a temperature rise on its backside. Thermal diffusivity and heat capacity are determined experimentally using the pulse method of heating. Then, thermal conductivity *()* is

in W/mK, where *a* is thermal diffusivity (cm2/s); is density (g/cm3); *Cp* is heat capacity

Measuring each thermophysical characteristic is an independent task. The most developed method is that of thermal diffusivity calculation, because the main formula for thermal diffusivity includes only one experimentally measured parameter. It is a period for the

in cm2/s, where is sample thickness, and 1/2is the time required for the temperature of the sample backside to reach the level equal to one-half of the maximum temperature. Coefficient 0.1388 corresponds to an ideal case when the following conditions are met: instantaneous and uniform heat pulse, heat pulse absorption in a thin surface layer, and no heat losses. For experimental thermal diffusivity determination, one should know neither absolute temperatures nor parameters of a heat flow affecting a sample. Measuring heat capacity by the flash technique, especially for coated samples, is a much more complicated task. Analysis of thermal diffusivity - and thermal conductivitjrof cerarrricxoaflngs are discussed elsewhere (Pawlowski et al., 1984). For thermophysical studies of ceramics condensates, the TC-3000H unit manufactured by the Sinku-Riko Company was used. A ruby laser with a wave length of 6.943 m was used as an energy source, and as a temperature pickup on the backside of the sample, either a thermocouple (Pt-PtRo) or an infrared sensor was used (Maesono, 1983). The tested sample is essentially a flat disc 10 mm in diameter and 0.8 to 2 mm thick. When thermal diffusivity is studied in this unit, two types of experimental errors are possible. The first type of errors results from some lack of information on the parameter values used in the design formulas. They are due to the available accuracy of sample thickness and time of т1/2 measurements, exactness of the temperature rise assessment, and of catching the moment of the sample irradiation start. These errors are covered in detail in (Cape & Lehman, 1963). On the basis of the results reported in the literature, one can deduce that, with the modern data collection systems used, the contribution of this type error does not exceed 0.5%. The second type of errors is due to the difference between the experimental conditions and

= a Cp (1)

*a =* 0.1388 (2/1/2) (2)

**4. Investigations of thermal barrier properties of ceramic coatings with the** 

**use of heating** 

calculated from these characteristics:

temperature to reach half of its maximum level:

**of heating** 

(J/gK).

produced from the refractory nickel alloy without a coating. The photographs of turbine blades with a ceramic TBC and inductor under thermocyclic tests are presented in Fig. 22.

The results of thermal fatigue tests of the models of flame tubes during thermal cycling according to the regime *t*min ↔*t*max (350 °C ↔ 900 °C) have revealed that the service life of the models with a three-layer coating of the thickness *h =* 320-520 m increases by a factor of approximately 2,7 compared to the models without a coating.

Fig. 21. Blade feather with a thermal ceramic barrier coating before thermocyclic tests

Fig. 22. Thermocyclic tests of the turbine blades with a thermal-barrier ceramic coating

produced from the refractory nickel alloy without a coating. The photographs of turbine blades with a ceramic TBC and inductor under thermocyclic tests are presented in Fig. 22. The results of thermal fatigue tests of the models of flame tubes during thermal cycling according to the regime *t*min ↔*t*max (350 °C ↔ 900 °C) have revealed that the service life of the models with a three-layer coating of the thickness *h =* 320-520 m increases by a factor of

Fig. 21. Blade feather with a thermal ceramic barrier coating before thermocyclic tests

Fig. 22. Thermocyclic tests of the turbine blades with a thermal-barrier ceramic coating

approximately 2,7 compared to the models without a coating.
