A Suleiman

A Trombe
email: trombe@insa-tlse.fr

Y Le Maoult

S Monteix

Dr A Trombe

EXPERIMENTAL AND NUMERICAL ANALYSIS OF BUILDING BOUNDARY CONDITIONS

One of the conditions for the determination of conductive heat transfer through building walls is a knowledge of the heat exchanges at their boundaries and particularly the ra-diative and the convective heat transfer occuring at their surfaces. To study the influence of these two types of heat transfer, the authors have performed a combined experimental and numerical study.

The experimental work consisted of building an experimental setup to satisfy a great variety of boundary conditions that may be encountered on building walls. It was composed mainly of an enclosure, a vertical, heated plate in which natural convection heat flow was generated, and a light source that imposed a known radiative flux condition on the solid surface.

An inverse heat transfer method has also been developed. This numerical method gives the total heat flux leaving the vertical flat plate by conduction, together with surface temperatures. Then it is possible to use a simple thermal balance to determine the radiative and the convective heat flux variations with time. The results of the study are presented together with the corresponding uncertainty calculations. They show that the method could be useful for following heat exchange variations at the solid surfaces of walls.

Several thermal balance models have been developed over recent years, particularly for building applications concerning dwellings equipped with ordinary-sized windows. These thermal balance applications are generally calculated assuming that surface temperatures are uniform. This is not the case if we consider the absorption of the incoming solar direct beam at the solid surface. For this case, boundary conditions can vary with time and intensity if a dynamic process such as a sun patch occurs, even in dwellings filled with obstacles (Figure 1).

Furthermore, this problem is increased in highly glazed enclosures such as verandas or atria, which have become a common feature in building architecture. This type of enclosure, with large volumes that are generally not heated, are subject to large convective and radiative heat exchanges. So these enclosures are difficult to simulate and to design (risks of overheating and comfort problems) if we do not take the incoming solar direct beam into account precisely. That is the reason why our laboratory has developed simulation programs which are now able to give an accurate distribution over time of the different radiative heat fluxes inside these enclosures [START_REF] Mavroulakis | Dynamic Processing of Direct Solar Gains in T.R.N.S.Y.S Building Simulation Environment, ISES Solar Congress[END_REF][START_REF] Kraus | Investigation of the Energy Flows for Transparent Building Façade[END_REF][START_REF] Pfrommer | Thermal Modelling of Highly Glazed Spaces[END_REF][START_REF] Mavroulakis | Développements d'outils destinés à la modélisation des échanges radiatifs dans des enceintes de géométrie complexe[END_REF][START_REF] Serres | Etude de l'impact d'une perturbation thermique locale de type tache solaire, Influence sur le confort thermique[END_REF]. But we now need to know the impact of the radiative flux on the convective heat exchanges, and this is the main goal of the present research work, based on an original experimental setup.

NOMENCLATURE

EXPERIMENTAL SETUP

Description

The experimental setup was composed mainly of an enclosure, a uniformly heated vertical flat plate, and a light source (Figure 2).

The active plate was located inside an enclosure to avoid the influence of external turbulence on the development of the boundary layer. Its dimensions were 1 m height, 0.40 m width, and 0.008 m thickness (resin only). It was composed, from the back face to the front face, of the following components (Figure 3): An insulating material on all sides except the front face of the plate, to provide adiabatic conditions. A heat exchanger with hot water circulating at a defined temperature. A copper plate to ensure uniform temperatures. On it were fixed several thermocouples so that the temperature imposed at the back face of the resin could be known. A synthetic material (resin) in which K-type thermocouples with a 0.08-mm mean diameter and a thermal accuracy of ±0.15 • C were buried.

The back face was in contact with a heat exchanger (in addition to the copper plate), which imposed a fixed boundary temperature at the back of the resin material. Radiative and convective heat transfer occurred at the front face.

The light source was also built for this experiment. It was composed of an insulated box made of aluminum, in which several short infrared lamps were located (Figure 4).

The surface temperature of the protection enclosure was also measured so that radiative exchanges could be calculated. It should be noted that surfaces having high emissivity coefficients (ε > 0.9) were chosen in order to correspond to those classically encountered in building enclosures.

Optimization

Front face material of the plate. Preliminary numerical studies were necessary to optimize both the choice of the front face material and the location of the thermocouples inside it. To do this, we used a method developed by Blanc [START_REF] Blanc | Problèmes inverses multidimensionnels de conduction de la chaleur. Optimisation du positionnement des capteurs et utilisation des mesures de thermo-déformations[END_REF]. It is based on a quantity called the normalized ratio of representation, which is defined as

τ = τ j τ max (1)
where

τ j = m i=1 X i,j for j = 1 -n τ max = Max(τ j ) for 1 ≤ j ≤ n
This ratio allows the sensitivity of the sensor to a flux density to be determined according to the location where it is used. The sensor location method consists of successive trials to find the locations that satisfy relationship (2):

∀j 0.75 ≤ τ ≤ 1 (2)
It is important to obtain a uniform value of the normalized representation ratio. We studied several types of building materials for the surfaces, namely, plaster, wood, and insulation materials. We finally chose a synthetic resin having thermophysical properties suitable for the planned studies (Table 1). This material presents two advantages. First, it has a good insulation coefficient that keeps its sensitivity coefficient values high. Second, its heat capacity is sufficient and very similar to the heat capacity of plaster. Therefore, the thermocouples were located inside that material in order to reach high values of the normalized representation ratio (Figure 5). Radiative source. The location of the lamps inside the box was optimized in order to obtain a uniformly lighted area. This work, which is not presented here, was done in collaboration with the Ecole des Mines of Albi [START_REF] Monteix | Modélisation du chauffage convecto-radiatif de préformes en P.E.E.T. pour la réalisation de corps creux[END_REF]. Here we present only the process of calibration and its final result.

A very thin copper plate, covered by a defined black paint, was used to calibrate the power of the infrared lamp system (Table 2). This copper plate was placed between the lamp system and an infrared camera. We considered that the plate temperature variation was uniform as the copper plate satisfied a Biot number condition (Bi < 0.1). To determine the radiation power of this system, we recorded with the infrared camera, the time variation T (t) of the copper plate temperature field. We did this for several supply voltages of the lamps (Figure 6). The plate temperature variation (internal energy) may be represented by the following thermal balance:

ρV C p dT dt = conv (t) + abs (t) (3)
Replacing the convective and the radiative terms by their values, we obtain

ρV C p dT dt = -2h g S(T -T air ) + aES (4)
This first-order differential equation admits a solution of the type

T = T air + abs 2h g S (1 -e t/Tau ) (5)
where Tau = mC p /(2h g S) is the time constant. By derivation of Eq. ( 5) with the respect to time, we can reach the value of the flux absorbed by the copper plate: abs = mC p dT dt 0 (6) The factor (dT /dt) 0 in Eq. ( 6) represents the slope of the copper plate temperature with variation time when the lamp system is lighted. It corresponds to the linear part of the T (t) curve at the first moments of lighting; see Figure 6. The knowledge of that slope finally led to the value of the light flux density of the radiative source, Eq. ( 7):

E = mC p (dT /dt) 0 aS (7)
The results of calibration are given in Figure 7 for each supply voltage of the lamps. The uncertainty bars are calculated as described in Appendix A.

The light flux density was limited by one factor, which corresponded to the distance between the front side of the aluminum box and the lighted area represented by the resin. In fact, it was necessary to keep a sufficient distance between these two elements to avoid perturbations of the convective heat flow generated by the uniformly heated vertical flat plate. Consequently, the possibilities of the radiative system were reduced to a variable power within the range 0-170 W/m 2 .

NUMERICAL METHOD

The numerical method developed for this work was based on the inverse identification method presented in [START_REF] Cuniasse-Langhans | Evaluation par méthode inverse de la distribution de flux de chaleur pariétaux le long d'une plaque plane verticale en convection naturelle[END_REF][START_REF] Cuniasse-Langhans | Efficiency of an Inverse Method to Determine Natural Convection Heat Transfer[END_REF]. We give a brief review of the main steps of this method below.

1. The numerical solution of the direct problem was based on a finite-difference technique [START_REF] Jaluria | Computational Heat Transfer[END_REF]. This was a three-dimensional model because, for the sun patch study, we needed to know the temperature distribution inside the plate in all directions. Therefore, we stated the boundary conditions of our plate in a three-dimensional Cartesian system of coordinates. The mathematical representation is

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ α ∂ 2 T ∂x 2 + ∂ 2 T ∂y 2 + ∂ 2 T ∂z 2 =
∂T ∂t

for z = 0, -λ ∂T ∂z z=0 = q cond i for z = (
2. The heat transfer flux at the solid surface was the sum of the radiative and the convective effects, so the inverse problem was nonlinear. Furthermore, the heat transfer was also a function of the local surface temperature distribution. To take these phenomena into account, a linear inverse method elaborated by Taler [START_REF] Taler | Nonlinear Steady-State Inverse Heat Conduction Problem with Space-Variable Boundary Conditions[END_REF] was chosen, and we used the following hypotheses.

The global heat flux q cond i leaving the front face was divided into n components q 1 , q 2 , . . . , q n along the Y coordinate (Figure 8). Consequently the radiative q rad i and the convective q cv i heat fluxes were also divided into n components. 3. The numerical solution of this problem was found by a minimization process between the experimental temperatures given by the thermocouples buried inside the resin and the numerical temperatures calculated by the model. As it was an iterative process, it was solved again for new flux values until the variation between two calculation steps reached a low value, i.e., Eq. ( 9):

q k+1 j -q k j q k j < ε for j = 1, . . . , n (9)
4. The use of the inverse method also led to the knowledge of the average surface temperature of each component of the active plate. Therefore, before determining the convective heat flux, it was first necessary to calculate the radiative heat flux for each component of the plate. This was done using the classical radiosity method [START_REF] Siegel | Thermal Radiation Heat Transfer[END_REF][START_REF] Sparrow | On the Calculation of Radiant Interchange between Surfaces[END_REF].

5. Finally, to determine the radiative and the convective fluxes of each component, on the front face of the plate, we applied the following two thermal balances.

The first corresponds to locations outside the lighted area,

q cond i = q cv i + q rad i (10)
The second corresponds to locations inside the lighted area,

q cond i + a × q light = q cv i + q rad i (11)

RESULTS

Presentation of the Results

The results presented here concern unsteady-state variations of experimental parameters (buried thermocouples) or values calculated by the model. For this study the active plate was divided into 12 components, of which four were located inside the lighted area (Figure 9). Various boundary conditions were tested. They corresponded to:

A light flux density of 166 W/m 2 applied to the front face of the resin for 220 s Different temperatures imposed at the back face of the resin, allowing temperature differences T = T surf -T air within the range 2.7-14.7 • C.

Experimental Analysis of Thermocouple Behavior

We first present an experimental analysis corresponding to the temperature variations of the thermocouples numbered 29, 32, 34, and 49, located inside the lighted area (Figure 10).

Figure 10 shows the temperature variations of the thermocouples with the duration of illumination. During the illumination, the temperature varied in the range 28.5-32.5 • C for all the sensors. However, two types of thermocouple thermal behavior may be distinguished. The first corresponds to thermocouples 49 and 32, located in the central part of the lighted area. These thermocouples presented the greatest amplitude of variation. The second is relative to the two thermocouples located at the limits of the lighted area (bottom or top). In this case the variation amplitudes of the two thermocouples (29 and 34) were lower. The reason is that the energy emitted by the radiative source and absorbed by the resin is diffused toward the nonlighted area. Note that this thermal behavior was confirmed for all other experimental conditions used during this experimental work.

T air ( • C) T surf ( • C) T = T surf -T ∞ ( • C) Gr = βg T H 3 v 2 23

Conductive, Convective, and Radiative Variations

We chose experimental conditions that were representative of the general thermal behavior of the conductive, radiative, and convective fluxes. They were a light flux density of 166 W/m 2 and other conditions as indicated in Table 3.

The variations with time of six components are drawn in Figures 11,12, and 13. Four were located inside the lighted area (components 4, 5, 6, and 7), the two others (components 1 and 12) being outside that area at the bottom and at the top of the active plate, respectively.

Concerning the variation of conductive heat fluxes of the lighted components (4-7) we see (Figure 11) that they decrease from the first moments of lighting. This phenomenon corresponds to flux inversions which depend on the component locations. Then, just after the extinction of the radiative source, the conductive flux increases rapidly and reaches higher values during the heat restitution because the material had stored heat in the previous periods. Note that components 1 and 12, not located in the lighted area, do not exibit significant variation during the lighting period.

Figures 12 and13, for the radiative and convective heat exchanges, show that the variations of components 4, 5, 6, and 7, located inside the lighted area, are significant. Nevertheless, if we compare these two heat exchanges occurring at the solid surface, the followings observations can be made.

The order of variations between the different components of the lighted area

is respected. The central components (5 and 6) of the lighted area present the greatest temperature variations. For the other two, located at extreme positions (components 4 and 7), the variations are lower. We note again here, as mentioned earlier, that the energy emitted by the radiative source and absorbed by the resin is diffused toward the nonlighted area. 2. The amplitudes of variations are different between the two types of exchanges.

Due to the illumination, the convective heat exchange varies by more than twice its initial value before lighting. This is the case for the three upper components located in the lighted area, except for component q cv4 . This may be explained, on the one hand, by the heat restitution of the energy stored in the resin during lighting, and, on the other hand, by the increase in air temperature due to convection effects from the bottom to the top of the plate.

Finally, if we consider now the two components (1 and 12) not located in the lighted area, we see that the illumination does not affect their variation in a significant manner. Nevertheless, a very slight variation may be observed, certainly due to the reflections of beam from the radiative source inside the enclosure.

Convective Heat Exchange Variations

Figure 14 shows the variations of convective heat exchange coefficients with time. These coefficients were calculated using the convective fluxes given by the inverse method and in terms of the average temperature difference T = T surf -T air for each component of the lighted area. Of course, we see again the flux variations corresponding to the variations of thermocouples already recorded in Figure 10. If we consider now the highest variation, represented by the component H cv6 (component 6, Th 32), we see that this variation can reach more than 50% of its initial value before illumination (Figure 15). Figure 15 indicates, as was foreseeable, that uncertainties (calculated in Appendix B) are high for weak values of convective heat exchanges. This fact points out the weakness of the thermal balance method for such values.

Heat Exchange Convective Law

The observation of two facts allowed us to propose a global convective heat exchange law for the lighted area.

1. The temperature variations observed, Figure 10, for all the components are very similar. 2. The convective heat exchange variation is also similar to that observed (Fig-

ure 15) for all the other components located in the lighted area.

Consequently, this law was determined in terms of the average temperature difference T = T surf -T air for all the components of the lighted area, Eq. ( 12):

h cv = 1.83 × (T surf -T air ) 0.33 (12)
Note that this law has a power coefficient of 0.33. According to the literature, e.g., [START_REF] Bejan | Convective Heat Transfer[END_REF][START_REF] Bejan | Heat Transfer[END_REF], this indicates a situation of turbulent flow. However, we cannot conclude this with certainty because, during the lighting period, the Grashof number varies with the increase of surface temperature and we may encounter several flow regimes.

CONCLUSION

In this study, experimental variations and results obtained by numerical works have been presented. They show the interest in developing (optimizing) and conducting these two types of works simultaneously.

The results demonstrate that the inverse method is pertinent, even if it is subject to considerable uncertainties, particularly when the convective heat exchanges take weak values. Nevertheless, this method based on a simple thermal balance is easy to develop and may be used to obtain approximate evaluations of heat exchange coefficients. It may be interesting particularly to follow unsteady-state variations of convective heat exchange coefficients in real buildings on site.

The different algorithms and models developed for the study are robust. They may be used for other types of applications. We have particularly in mind industrial processes such as the thermoforming of plastic bottles, which needs higher levels of temperature.

APPENDIX A

The power of the radiative source was determined experimentally. Consequently, it was subject to the following uncertainties.

Uncertainty in the measurement by voltmeter of the supply voltage of the lamps. The accuracy of this apparatus, at a temperature of 23 ± 5 • C and for a voltage of 7 V (the case of our experimentation), is V = ±1.6325 × 10 -4 V. As that uncertainty is very small, we neglected it. Uncertainty in the surface temperature measurement of the copper plate for calibration.

If we assume that the lighting is given by Eq. ( 7), the relative uncertainty on that value is given by

E E = ( T ) T + ( t) t
The second term can be neglected, given the high acquisition frequency of the infrared camera. Therefore, the uncertainty on the lighting is reduced to an uncertainty depending only on the measured temperature:

E E = ( T ) T
If we accept that T measured is given by the expression below, the uncertainty on the surface temperature measurement is reduced to the dynamic and calibration uncertainties.

APPENDIX B

The uncertainty calculations of the convective heat exchange coefficients, in unsteady state, were determined from Eq. ( 11):

q cond i + a × q light = q cv i + q rad i ( 11
)
Note that this expression depends on different parameters that enter into the thermal balance of the lighted area. Two literal expressions are necessary to reach this type of result.

The first gives the relative uncertainty on the convective heat flux: ϕ cv ϕ cv max ≤ ϕ total + ϕ rad + ϕ abs ϕ total + ϕ absϕ rad

The second gives the relative uncertainty on the heat exchange coefficient from the classical law heat transfer by convection:

h cv h cv max = ϕ cv ϕ cv 2 max -2 δT T 2
For these calculations, we took the following parameter uncertainties into account.

• The absolute uncertainty on thermocouple accuracy is ± 0.15 • C. Note that this type of error occurs in the calculation of the different flux components and we took this fact into account. • Concerning conductive exchanges, the location uncertainty of thermocouples inside the resin was taken as 0.1 mm. We assumed that it was equivalent to a temperature uncertainty. • Concerning radiative exchanges, the relative uncertainty on view factors = 1% (from numerical data); and the relative uncertainty on emissivity coefficient = 2% (from experimental data).

Generally speaking, these calculations were done using a Monte Carlo method [START_REF] Beck | Parameter Estimation in Engineering and Science[END_REF]. We followed the different stages.

1. With the help of a random noise generator and assuming a Gauss law probability distribution, we can draw m values of the random variable δ(T ) of temperature error. 2. These values are added to numerical temperatures given by the model to obtain noised temperatures. 3. Finally they are injected into the numerical model to obtain a first evaluation of the total flux component q cond i , for example.

Stages 2 and 3 were repeated N times (N ≥ 50) to reach a statistical evaluation of the uncertainty.

Figure 2 .

 2 Figure 2. Schematic diagram of the projected study.

Figure 3 .

 3 Figure 3. Vertical section of the active plate.

Figure 4 .

 4 Figure 4. Diagram of the radiative heat source.

Figure 5 .

 5 Figure 5. Normalized representation ratio of thermocouples buried in the resin.

Figure 6 .

 6 Figure 6. Experimental temperature variation of the copper plate used for calibration.

Figure 7 .

 7 Figure 7. Power of the radiative system.

  Thickness) T = T 1 , ∀x, y = known at x = 0 and x = Width, ∂T ∂x = 0, ∀y, z at y = 0 and y = Height, ∂T ∂y = 0, ∀x, z

Figure 8 .

 8 Figure 8. Theoretical division of the active plate.

Figure 9 .

 9 Figure 9. Division of the active plate into components, and location of the thermocouple sensors (•) inside the lighted area.

Figure 10 .

 10 Figure 10. Experimental temperature variations of thermocouples located inside the lighted area.

Figure 11 .

 11 Figure 11. Conductive heat flux variations with time for 7.4 < T < 8.3 • C.

Figure 12 .

 12 Figure 12. Radiative heat flux variations with time for 7.4 < T < 8.3 • C.

Figure 13 .

 13 Figure 13. Convective heat flux variations with time for 7.4 < T < 8.3 • C.

Figure 14 .

 14 Figure 14. Convective heat exchange variations of the lighted components for an average temperature difference 7.4 < T < 8.3 • C.

Figure 15 .

 15 Figure 15. Values of the convective heat exchange coefficient of component 6.

T

  measured = T black body ± | T dynamic | ± | T calibration | ± | T black body | Then T dynamic = 3 * DTEB (equivalent noise temperature discrepancy) T calibration = 0.25 • C (measured on the calibration total characteristic of black body) T black body = 0 because neglected

Table 1 .

 1 Thermophysical properties of the resin

		Coefficient of
		conductivity	Heat capacity	Density
	Material	(W/m • C)	(J/kg • C)	(Kg/m 3 )	Emissivity
	Resin	0.06	1,454	480	0. 95

Table 2 .

 2 Thermophysical properties of the copper plate used for calibration

			Surface	Coefficient of	Heat
		Thickness	area	conductivity	capacity	Density
	Material	(m)	(m 2 )	(W/m • C)	(J/kg • C)	(kg/m 3 )	Absorptivity
	Copper	0.0003	0.001583	380	383	8,900	0.92

Table 3 .

 3 Characteristics of the configuration studied


Julien Sniezewski
email: julien.sniezewski@enstimac.fr

Yannick Le Maoult
email: byannick.lemaoult@enstimac.fr

Philippe Lours
email: cphilippe.lours@enstimac.fr

In Situ Thermal Gradient Controlled Investigation of Spallation -Experimental Design and Preliminary Results

Keywords: cyclic oxidation, thermal gradient, in situ analysis, videometry, TBC

Based on a coupled numerical and experimental approach, the design and implementation of an in situ thermal-gradient-controlled cyclic oxidation test, dedicated to the investigation of the TGO and TBC spallation, is presented. The influence of the specimen through thickness thermal gradient as well as the benefits of the video real-time monitoring of the cooling phase of an oxidation test is discussed in the case of the spallation of an alumina scale grown on FeCrAl alloys.

Introduction

Alumina forming alloys and complex systems such as thermal barrier coatings are used in industrial applications and gaz-turbine engines where superior oxidation resistance and good thermal insulation performances are required [1,2,3]. During service cycles, at high temperature, such materials are subject to severe thermomechanical stresses. Those stresses may provoke the degradation of oxide scales or coatings through cracking or spalling and thus limit the lifetime of components. Thermal stresses result from the thermal gradient that establishes through the thickness of the multi layers systems [4,5].

Various experimental techniques are used to investigate the durability and failure mechanisms and to study the behaviour of the materials. Isothermal [6] and cyclic oxidation [7] tests, thermogravimetry analysis [8] and acoustic emission [9] are the most employed techniques. More evolved techniques are also used such as the infrared characterization [10] (thermal wave imaging) and photo-luminescence piezo-spectroscopy (PLPS) [11].

However, all those approaches suffer some limitations. Isothermal and cyclic oxidation test, thermal wave imaging and PLPS do not give insight into the dynamics of spallation events. Thermogravimetry analysis is intrinsically a global approach and acoustic emission does not permit to discriminate easily oxide scale cracking and oxide scale spallation. An additional limitation of such techniques lies in the fact that they generally omit to generate and control a thermal gradient through the thickness of the samples while tested. Previously reported studies based on an in situ approach have evidenced the strong influence of several parameters on spallation, namely the oxide layer thickness, the substrate microstructure, the characteristics of the thermal cycles. Most importantly, it was also shown that the thermal gradient through the thickness of the investigated specimens, either during heating or cooling, is of primary importance. In addition, the occurrence of such a gradient corresponds to most of the industrial situations suffered by high temperature materials. As a consequence, dedicated cyclic oxidation equipment has been designed. It is able to generate such a gradient and is instrumented in such a way to monitor in situ the spallation events. This paper aims at describing the design and implementation of such an equipment and finally gives a few examples of the real-time analysis of the surface degradation.

Design of an in situ thermal gradient controlled cyclic oxidation test General specifications. The objective of the present work is to design an automated cyclic oxidation test able to generate a thermal gradient within the investigated specimens and instrumented with video camera to monitor in situ the behaviour of the oxidised and/or coated surface during the cooling phases of cumulative cycles. The videometry in situ technique as well as its outstanding benefit for studying spallation has been reported in [12]. In this paper, it is pointed out that the cooling rate, imposed by the cooling media in which the sample holder is immersed and leading to the establishment of a thermal gradient within the specimen, has a strong impact on the extent of spallation and possibly the characteristic size of individual spalled particles. However, the influence of a thermal gradient can only be established if this parameter is fully controlled and measured over the whole thermal cycles imposed to the specimens. In order to couple those videometry and thermal approaches, the developed experimental means must satisfy a fourfold general technical specifications, namely:

i) It must be entirely automated. This is ensured by the implementation of a computer-aided shuttlefurnace whose motion on top and out of specimens results in the required programmed thermal cycling.

ii) It must be versatile enough to cover a large range of possible programmable thermal cycles. Indeed, the experimental mean must be able to cycle specimens, in particular thermal barrier coatings, according to the universal commonly used cycle including a 10 to 15 minutes heating from room temperature to 1100°C-1150°C (heating rate about 1.3°C.s -1 ), a high temperature holding time of one hour and a 20 minutes cooling (cooling rate about 1°C.s -1 ). In addition, in order to thoroughly investigate spallation mechanisms and the influence of the cycle characteristics, it must also be able to test specimens using more exotic cycles and/or thermal shocks. This may serve to limit or enhance surface degradation, by changing for instance the exposure temperature (up to 1400°C to test a wide range of materials), the exposure time, the heating and cooling rates (two times higher than the values given above).

iii) It must be instrumented with interchangeable cameras to monitor possible spallation events at each individual cycle. Here again, the versatility of the optical characterization allows the observation scale of specimens to be changed by changing the focal length of the camera, the resolution of the images to be increased or decreased by changing the data acquisition frequency of the digital camera (number of images per seconds). This also permits thermal information characteristic of surface degradation to be obtained by using infrared thermography camera.

iv) It must be able to impose a given thermal gradient within the specimens during both the phases of oxidation and cooling. This gradient, that can reach about 200°C through the thickness of thermal barriers coatings for instance, must be generated, controlled and measured precisely.

Thermal performances. The principle used to establish a thermal gradient within the material consists of absorbing the heat flux that occurs across the bottom surface of the specimen as its top surface is exposed to the radiation of the flat heating resistance of the furnace located 10 cm above the specimen. To guarantee this thermal condition, a specific sample holder composed of a metallic cylinder chilled by the circulation of a coolant has been designed. To validate this technical solution, a prototype has been manufactured and tested using a 5 mm thick FeCrAl specimen. Several thermocouples have been welded on the bottom surface of the sample and at different locations along the overall height of the specimen holder. Fig. 1 shows the temperature monitoring of all those thermocouples when the specimen on top of the sample holder is inserted in an infrared furnace at 1150°C. The various temperatures of both the specimen and the sample-holder stabilize within less than 2000 seconds and the measured gradient through the thickness of the specimen is about 100°C, provided the coolant is maintained at 40°C, which unambiguously suggests that the cooling of the specimen holder is proper to generate the required thermal gradient.

However, this first approach has to be optimized in order to design the final ready-to-use specimenholder. This specimen holder is composed of different parts, namely a superior ceramic plate with five holes in which specimens are located on top of several IN625 cylinders piled up to vary its total height. The bottom cylinder -made of stainless steel -is circulated by a coolant supplied with a large volume heat exchanger whose characteristics permit to adjust the gradient. The temperature at the bottom surface of the specimen is measured by a thermocouple that crosses the whole height of the specimen holder while the top surface temperature is controlled by a pyrometer (with wavelength in the range 8-14 µm). Fig. 2 gives the temperature measurements at the top and bottom surfaces of a specimen of AM3 superalloy (2 mm thick) coated with EB-PVD YSZ (200 µm) exposed at 1050°C within the resistance furnace together with the targeted cycle and the resulting thermal gradient within the thickness of the specimen. It is shown that the effective thermal cycle suffered by the specimen is extremely close to the targeted cycle in terms of heating and cooling rates and maximum temperature reached. Also, those measurements indicate that the cooled sample-holder is prone to generate a 180°C stationary thermal gradient across the investigated material.

To address the performance of the sample-holder, both transient and stationary numerical simulations were performed using Femlab  software. The boundary conditions and materials properties for the calculations are given in Fig. 3. The first case investigated simulates the isothermal exposure of a 2 mm thick Hastelloy X substrate coated with 200µm thick zirconia either in bulk form or deposited with EB-PVD and plasma spray techniques. In this later case, two types of zirconia are studied, namely a high-density and a low-density material. The coated material is located on top of a cylindrical 40 mm high stainless steel specimen-holder whose bottom surface is maintained at room temperature. The top surface of the material is exposed to 1273 K. The calculated temperatures are given in Fig. 4, showing that a stationary thermal gradient establishes both in the coating and the substrate. Depending on the nature of zirconia, the thermal gradient within the coating changes drastically from say, 90°C for the high conductivity bulk material to 150°C for the low-conductivity, low-density plasma sprayed material. A transient calculation, simulating the cooling phase of a 5 mm thick FeCrAl substrate covered with a 30 µm thermally grown alumina oxide and located on top of an aluminium sample-holder, is performed. The top surface of the bi-material is held at 1300K while the opposite extremity of the sample-holder is cooled at 278 K. Fig. 5 shows the evolution of the temperature on the top surface (oxide), at the interface between the oxide and the substrate and at the bottom surface of the substrate, against the cooling time. The calculation shows that no gradient occurs within the (too thin) oxide scale while some gradient establishes across the thickness of the substrate. This is particularly significant during the very first stages of cooling where the gradient reaches about 200°C -400°C. After a few seconds, namely 30 seconds, the gradient gradually vanishes and the overall specimen is almost isothermal. Note that the cooling kinetics and the time-scale for lowering the gradient down to zero are much shorter than that measured experimentally. This is due to the fact that no thermal contact resistance between the various components of the model has been considered for the calculation. Indeed, it is particularly difficult to estimate such values that strongly depend on the surface finish of the materials involved. Optical performances. A high resolution CCD camera is used to monitor spallation events.

The sensor is composed of a matrix with 1600 by 1200 pixels and can take 7.5 images per second in full resolution. It is also possible to increase the number of image per second if the resolution is lowered. The focal length of the camera can be varied from 28 to 200 mm, which guarantees the possibility to view either the whole surface of a 20 mm by 20 mm specimen or to observe much smaller zones to investigate fine details of spallation events. The images taken by the camera are directly recorded on a computer and can be straightforwardly treated using image analysis software.

The mass resolution of the technique can be calculated from the specifications and the optical characteristics of the camera. Considering that the smallest detectable spall accurately corresponds to the size of an elementary pixel of the camera detector, the mass variation ∆m can be written as (Eq. 1) : 1 gives some examples of mass resolution for various coatings. These mass resolutions are extremely high and do not correspond perfectly to the effective capability of the experimental technique. Indeed, though it is theoretically possible to detect spalled zones as small as the size of a pixel, which was used for the calculation, it is nevertheless very difficult to achieve. In practise, the reasonable smallest zone that can be viewed is about 10 pixels, which increases by an order of magnitude the minimum detectable mass of spalled particles.

Preliminary results

In order to illustrate the capability of an in situ thermal gradient controlled cyclic oxidation test, two examples are presented in the following. The first one shows the possible insight on the mechanisms of spallation of an alumina scale thermally grown on a FeCrAl alloy allowed by the real time monitoring of a cooling sequence using a high-resolution/high-speed camera. The second example focuses on the impact of a thermal gradient through the thickness of the oxidised and cooled specimen on the characteristics of the overall spallation kinetics.

Mechanisms of spallation. It has been extensively reported in the literature that the so-called buckling mode might be the preferred spallation route for thermally grown oxide [3], However, investigation of extensively spalled specimens observed after surface degradation is fully completed, only provides global information and fails to prove unambiguously that spallation occurred through buckling. Indeed, buckling is a progressive mechanism that can be divided in various successive steps including the formation of the buckle itself, the possible, more or less protracted stabilisation of the buckle and finally the ejection of the spall. The thorough analysis of buckling requires investigating in situ the mechanism, preferentially using methods that shows directly the different steps of buckle formation and ejection. Fig. 6 shows three images extracted from a video recording of the surface of a FeCrAl alloy initially oxidised at 1300°C and cooled down to room temperature. Fig. 6. Buckle formation and spallation monitored by high resolution camera.

The long-term oxidation of the material results in the formation of a 25µm thick alumina scale prone to spall upon cooling. The first micrograph shows the presence of three buckles giving an undulated aspect to the surface. Those buckles were formed during cooling at a temperature higher than 500°C. Buckles labelled (B1) and (B2) remain stable as no change in their morphology and size occurred during 340 seconds, the time interval separating the first and the second image (Fig. 6 a and Fig. 6 b). In Fig. 6 b, the contrast of buckle (B1) drastically changes suggesting that it detaches from the alloy substrate. At this stage, the buckle (B1) reaches its instability threshold as the thermal induced shear stress exceeds the alumina strength. Because of geometrical and morphological reasons leading to a slight different stress state, the buckle labelled (B2) remains further stable over a longer time but finally suffers the same instability after 7 seconds more (figure 6c).

As indicated, the stability phase of buckles can be quite different from one part of the specimen to another. This is also true from one specimen to another or from one condition of cooling to another.

Namely, it can strongly depend on the microstructure of the alloy substrate, in relation for instance to the crystal orientation of the grain or to the presence of a grain boundary underneath the oxide scale. It can be also influenced by the cooling rate or by the thermal gradient imposed through the thickness of the specimen.

In Fig. 7, the formation of a buckle in an alumina scale, grown at the surface of a FeCrAl alloy following 384 hours holding at 1300°C then cooled to room temperature, is shown to occur within two successive frames of the video recording. The in situ recording is performed using a high-speed camera capable of discriminating 88000 images per second. Each frame lasts 11 µs. Unfortunately, the high-speed capability of the camera leads to an unavoidable loss in imaging resolution. Nevertheless, interesting details on spallation mechanisms can be deduced from the sequence of images. In the first micrograph (Fig. 7 a), the oxide scale within the white circle is still undamaged (grey contrast). Note the occurrence of two white spots at the top part of the circle corresponding to two zones that have already spalled off. 11µs later (Fig. 7 b), the contrast locally changes to become light grey shaded. This change in contrast results from the formation of the interfacial crack concomitant to the nucleation and growth of the buckle. The formation of such a defect is shown to occur within a very short time scale. Afterwards, the buckle remains stable over a very short time until the next video frame (11 µs) and ejects from the substrate in the shape of numerous fragments (not shown here). This results in the complete spallation of the investigated zone as shown in Fig. 7 c where the bright contrast of the investigated zone indicates the complete detachment of the oxide particle from the alloy substrate. Considering the typical dimension of the defect investigated (1000 µm), it is assumed that the interfacial crack responsible for the formation of the buckle propagates at a rate higher than 90 m.s -1 . The mechanism of oxide failure through buckling for FeCrAl alloys has been recently investigated using combined optical microscopy, photoluminescence and piezospectroscopy [13,14]. In this work, the desktop spalling of Kanthal A1 alloy oxidised at 1200°C is investigated and the time dependence of buckling is confirmed (including initiation and growth). However in this case, buckling is observed to occur at a finer scale (20 to 200 µm is the size of buckle) and over longer periods of time (about 2 hours required to spall off the oxide through buckling). The shift in luminescence frequency with strain, namely the piezzospectroscopic effect used to estimate the residual stress, shows that there is a significant stress relaxation around the edges of buckles leading to the impossibility for buckles to overlap. This last feature is not confirmed by our results showing that new spalls can form in the close vicinity of neighbouring existing spalls (Fig. 7).

Influence of a specimen through-thickness thermal gradient. Generally speaking, high temperature materials and coatings work under transient thermomechanical conditions. Unfortunately, most of dedicated cyclic oxidation tests are performed under isothermal conditions and the influence of a thermal gradient through the thickness of the tested material, either during high temperature exposure or during cooling, is rarely taken into account. However, the presence of such a gradient can significantly change the process of surface damage by modifying for instance the mechanisms and kinetics of spallation or the characteristic size and morphology of individual spalls. In Fig. 8, the thermal gradient measured through the thickness (6 mm) of a FeCrAl alloy initially oxidised 384 hours at 1300°C then cooled by contact with a metallic sample-holder respectively immersed in air and in liquid nitrogen, is plotted against the top surface temperature of the specimen. The critical temperature range for spallation is similar for the two conditions of cooling, namely spallation occurs for top surface temperature of the specimen between 200°C and 300°C. Depending on the severity of cooling, the thermal gradient through the specimen thickness notably varies within this surface temperature range. It is either positive around (+ 60°C) and negative around (-30°C) for specimens respectively cooled on an air-chilled and liquid-nitrogen-chilled sample-holder This suggests that the thermal gradient does not have much effect on the critical temperature for spallation. On the contrary it is of primary importance regarding the characteristics of the spallation kinetics. Indeed, both the overall surface fraction of spall, estimated by image analysis of micrographs extracted from the video recording of cooling sequence, and the spallation rate strongly depend on the amplitude of the thermal gradient that establishes through the specimen. Fig. 9 shows the spallation kinetics for the two specimens discussed above where the surface fraction of spall is plotted against the cooling time. Note that the slope of the increasing part of the sigmoid curves differs significantly resulting in a spallation rate roughly four times greater in the case of the specimen severely cooled on a sample-holder immersed in liquid nitrogen. Likewise, the overall surface fraction of spall as the cooling is completed is notably higher for the severely cooled specimen (80%) than for the slowly cooled specimen (50%).

Conclusion

The design and development of a new cyclic oxidation test is presented. The specificities of the test consist in, i) the thorough control of the thermal gradient that establishes through the thickness of the investigated specimens together with, ii) the automated recording of the cooling sequences using a CCD camera. The presence of a controlled thermal gradient allows the analysis of samples in conditions close to the in-service working conditions of high temperature materials. This considerably impacts the mode of surface degradation as exemplified by the thermal shock induced spallation of an oxidised FeCrAl alloy. Though the critical temperature range for spallation does not change notably, it is shown that both the spallation rate and the total amount of spall significantly depend on the amplitude of the thermal gradient. The gradient can establish either within the metal substrate only, for alloys that grow relatively thin oxide scales during high temperature exposure, or both within the substrate and the coating for alloys with TBC. The use of the videometry technique to record the sequences of cooling gives interesting insight on the mechanisms of surface degradation. In the case of an oxidised FeCrAl alloy, it is shown that such an in situ approach allows the analysis of the preferential mode for spallation, namely buckling, and the determination of the time scale required for buckle formation and ejection.

Fig. 1 .

 1 Fig. 1. Temperature monitoring during thermal cycling of the prototype sample-holder and a FeCrAl specimen.

Fig. 2 .

 2 Fig. 2. Temperature monitoring during thermal cycling of a TBC on top of the newly designed sample-holder.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Various stationary thermal gradients in different TBC.

Fig. 7 .

 7 Fig. 7. Buckle formation and spallation monitored by a high-speed camera.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Thermal gradient through the thickness of an oxidised FeCrAl alloy versus surface temperature

Table . 1

 . Mass resolutions for various coatings

					Type of coatings	Density	Mass
	∆m=	   	d specimen d focal  2   	δx δy ξ o ρ o	and thickness (1) YSZ TBC, ξ o = 200µm YSZ TBC, ξ o = 100µm	ρ o [g.cm -3 ] 3 3	resolutions 0.0468µg 0.0234µg
					Alumina TGO, ξ o = 30µm	3.9	0.0112µg
					Alumina TGO, ξ o = 15µm	3.9	0.0056µg
	where d specimen = 400 mm is the distance from the camera to the specimen, d focal = 200 mm is the
	focal length of the camera, δ x (4.4 µm) and δ y (4,4 µm) are the sizes of a pixel for the camera used
	in the experiments, ξ

o and ρ o are respectively the coating thickness and density. Table