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Active laser pyrometry and lock-in thermography for characterisation of deposited layer on TEXTOR graphite tile
Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Active laser pyrometry and lock-in thermography for characterisation of deposited layer on TEXTOR graphite tile A. Semerok a,n, S.V. Fomichev a,b, F. Jaubert a, C. Grisolia c a
CEA, DEN, F-91191 Gif-sur-Yvette, France NRC Kurchatov Institute, 123182 Moscow, Russia c CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France b
art ic l e i nf o
a b s t r a c t
Article history: Received 19 July 2013 Received in revised form 22 November 2013 Accepted 26 November 2013 Available online 7 December 2013
Active laser pyrometry and lock-in thermography were applied for non-destructive characterisation of a deposited carbon-layer (5–40 mm thickness, different thermal contact quality) on TEXTOR graphite tile. The experimental installation comprised a pulse repetition rate laser (Nd-YAG, 1064 nm, 0.5–250 ms pulse duration, 2 Hz to 1 kHz repetition rate, 10–100 W amplitude power) and a home-made active laser pyrometry system. Active laser pyrometry was used to obtain some unknown layer properties (thermal capacity, conductivity, optical absorptivity, layer/surface thermal contact coefficient). With the developed 3D theoretical model, it was possible to calculate the heated layer temperatures with a good temporal and spatial resolution. The layer characterisation was based on the comparison of the modelling and the measured temperatures. To complete active laser pyrometry, lock-in thermography measurements of the layer/surface thermal contact coefficient were made with a new model for rapid phase shifts calculations. The obtained coefficients in both methods were comparable. Though there was no gain in the measurements accuracy, lock-in thermography has demonstrated its advantage as being much more rapid for characterisation of deposited layers of micrometric thickness. & 2013 Elsevier B.V. All rights reserved.
Keywords: Tokamak graphite Plasma facing components Deposited carbon layer Layer characterization Active laser pyrometry Lock-in thermography
1. Introduction In modern fusion thermonuclear installations (tokamaks), plasma is heated up to extremely high temperatures ( 10 keV). Though magnetic field is applied to confine plasma, it may, however, come in contact with tokamak walls. Being affected by plasma, the plasma facing components (PFC) of the tokamak walls are eroded and deposited on the “cold” parts of the reactor, thus forming the deposited layer with a high tritium concentration [1–3]. The deposited layer is a source of dust, which may cause undesirable plasma losses and affect plasma properties [4,5]. To ensure regular cleaning maintenance and efficient rapid cleaning and detritiation of the deposited layers, it is necessary to provide in situ nondestructive characterisation of the deposited layers without disassembly of the reactor components. To avoid tile damage during cleaning, an accurate characterisation of some thermo-physical properties (thickness, thermal conductivity, layer/substrate thermal conductance or contact) of the deposited layer is required. In search for appropriate methods for deposited layer characterisation, active laser pyrometry and lock-in thermography were considered in our study.
n
Corresponding author. Tel.: þ 33 1 69 08 65 57; fax: þ33 1 69 08 77 38. E-mail address: [email protected] (A. Semerok).
0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.11.100
Active laser pyrometry was developed and applied for layer characterisation in [6]. The method is based on the measurement of the heating temperature resulting from the surface heating by repetition rate laser beam. With the developed 3D theoretical model of the laser heating of the layer, it was possible to calculate the temperatures of the heated layer with a good temporal and spatial resolution [7–11]. Based on the comparison of the experimental and theoretical results on thermal response of the surface under laser heating, it was possible to determine optical and thermal properties of the deposited layer – reflectivity, thickness, density, thermal capacity, conductivity and layer/surface thermal contact coefficient. However, as active laser pyrometer measurements are sensitive to the applied laser power and surface reflectivity, the question is whether the temperature changes are attributed to different surface reflectivity or to layer/substrate thermal contact. This consideration implies certain ambiguity of the method for in situ deposited layer characterisation. Lock-in thermography to determine some properties of PFC deposited layer (thickness, layer/surface thermal contact) was introduced in Refs. [12–14]. The method is based on phase shift measurements between the laser power and surface temperature modulations. The phase shift depends on the layer properties and is sensitive to the under-surface defects. Lock-in thermography measurements have the advantage of being independent of optical features (absorptivity, emissivity) of a sample surface. Lock-in
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thermography for thermal contact characterisation of the deposited layers was under study in Refs. [15–18]. In these investigations, the heating of the samples (of millimetre thickness) was provided by the light lamps (0.7 Hz and 1.8 Hz modulation frequencies). The surface temperature was measured by the infrared camera [15]. However, as the measurement sensitivity depends on modulation frequency, a low (1–2 Hz) modulation frequency of the applied lamps was not high enough to provide quantitative characterisation of thin (below 100 μm) layers [18]. To determine thermal contact of micrometric layers, heating sources of a higher modulation frequency (above 10 Hz) are required. In this study, both the methods were used in tandem to check whether the methods “coupling” would result in a more rapid characterisation of the carbon deposited layer (10–40 mm thickness, different thermal contact quality) on TEXTOR graphite tile, which had already been under characterisation by active laser pyrometry [6] and lock-in thermography [18]. The modified experimental installation comprised a Nd:YAG laser (1064 nm, acousto-optical intercavity modulation, pulse repetition rate νL ¼2 Hz to 1 kHz, pulse duration τL ffi 0.5/νL, 10–100 W amplitude power) and a home-made pyrometry system. Active laser pyrometry was applied to determine some unknown properties of the deposited layer (thermal capacity, conductivity, layer/surface thermal contact, optical absorptivity). With the developed 3D theoretical model, it was possible to calculate the heated layer temperatures with a good temporal and spatial resolution. The multi-parametric characterisation of the layer was based on the comparison of the modelling and the measured temperatures. To complete active laser pyrometry characterisation of the deposited layer, lock-in thermography was used for phase shifts measurements to determine the layer/surface thermal contact coefficient. A new model for rapid calculations of the phase shifts was applied for comparison with the experimental results. The investigations of this paper should be regarded as a continuation of our studies on deposited layer characterisation [6–11,18] and layer detritiation [19–22]. Section 2 presents theoretical fundamentals of graphite layer heating and rapid phase shift calculations for lock-in thermography. Multi-parametric modelling for phase shifts is also presented. 1D- and 3D-modelling of laser heating are compared. Section 3 describes the experimental installation and the sample. Section 3.3 presents the experimental results obtained by active laser pyrometry and lock-in thermography used as a combined complementary approach. The experimental and simulation results are compared and discussed. Section 4 presents the conclusions.
both the time-dependent and radial-dependent laser intensity on the surface (at z¼ 0). In Eq. (1), the layer thickness d is assumed to be larger than the layer photon absorption length αl 1 (dαl ⪢ 1), and the laser heating source term is included only in the layer heating Eq. (1a). Generally, it requires the layer thickness d Z1 μm. For typical experimental conditions without convection cooling and radiation losses, the initial and boundary conditions to these equations can be taken as ΔTðt ¼ 0; z; rÞ ¼ 0;
ð2aÞ
∂ΔT ∂ΔT ∂ΔT ¼ 0; k ¼ k s l ∂z z ¼ 0 ∂z z ¼ d 0 ∂z z ¼ d þ 0 ¼ qd ; ΔTjz ¼ d 0 ΔTjz ¼ d þ 0 ¼ qd =h;
ð2bÞ
where qd is the heat flux through the layer/substrate interface, and h is the coefficient of the heat contact (thermal conductance) which is inverse to the thermal resistance of the layer/substrate interface. The time t¼0 is set as the time for the laser turning on. Laser beams with intensity I L ðt; rÞ ¼ IðtÞf L ðrÞ are considered. For the Gaussian laser beam, fL(r) ¼expð r 2 =r 20 Þ, while for the flat-top laser beam, fL(r)¼1 at r rr0 and fL(r)¼0 at r 4r0. Here, r0 is the laser spot radius. As thermal and optical properties depend on temperature, the direct numerical solution of Eq. (1a) and (1b) in 3D space and time for high repetition rate laser heating is seen as a problem even for moderate computers. For graphite, the exact and approximate analytical solutions were verified and proved to be the same within accuracy of 10% [7]. The simplified version of the analytical solution for ΔT (t, z, r) can be obtained in the cylindrical geometry with circular symmetry of the laser spot and immobile laser beam [9]. This solution was applied for heating temperature calculation in these studies. Thus, the optical and thermal properties of the layer and substrate are assumed to be temperature-independent in our studies. 2.1.1. Basic equations of lock-in thermography The thermal response of the sample can also be expressed as the Fourier series: 1
ΔTðt; z; rÞ ¼ ΔT 0 ðz; rÞ þ ∑ ðAn ðz; rÞ sin 2π nυL t þ Bn ðz; rÞ cos 2π nυL tÞ n¼1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðnÞ A2n þ B2n sin ð2π nυL t þ ϕLH Þ ¼ ΔT 0 ðz; rÞ þ ∑ n¼1 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðnÞ A2n þB2n e ið2π nνL t þ ϕLH Þ ¼ Re ΔT 0 ðz; rÞ þi ∑ n¼1
1
Re ∑ ΔT n ðz; rÞe i2π nνL t ;
2. Theoretical studies 2.1. Basic equations for the stationary periodical laser heating In cylindrical coordinates z and r, the equations for circularsymmetric time-dependent heating temperature ΔT (t, z, r) T (t, z, r) – Ta of a complex surface with a layer deposited on the substrate can be written as ρl C l
2 ∂ΔT ∂ ΔT ∂2 ΔT 1∂ΔT þ þ ¼ kl þ αl ð1 Rl ÞI L ðt; rÞexpð αl zÞ; ∂t r ∂r ∂z2 ∂r 2
ð0 o z o dÞ
ð1aÞ 2 ∂ΔT ∂ ΔT ∂2 ΔT 1∂ΔT ¼ ks : ρs C s þ þ 2 2 ∂t r ∂r ∂z ∂r
ð3Þ
n¼0
heating temperature, and where ΔT0(z, r) is the mean steady-state qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 iϕðnÞ 1 LH ϕðnÞ ðz; rÞ ¼ tan ðB =A Þ and ΔT ¼i A are, respecn n n n þ Bn e LH tively, the temperature phase and complex amplitude of the nthharmonic. If the temperature trace is known either from the experiments or calculations, the heating temperature phase can be found from the expression: Z tn þ 1=υL . Bn ðz; rÞ ðnÞ tan ϕLH ¼ ðz; rÞ ¼ ΔTðt; z; rÞ cos ð2π nυL tÞdt n An ðz; rÞ t Z t n þ 1=υL ΔTðt; z; rÞ sin ð2π nυL tÞdt; ð4Þ tn
ðz ZdÞ
ð1bÞ
Here, Ta is the ambient temperature, ρl, Cl, kl and ρs, Cs, ks are, respectively, density, mass specific heat, and thermal conductivity of the layer and the substrate; d is the layer thickness; αl and Rl are the laser beam absorption and matter reflectivity coefficients. IL(t, r) is
n
where t is an arbitrary time moment of the stationary regime for a mean heating temperature. Both expressions (3) and (4) can be used for the phase shift calculations with respect to the laser pulse phase. The mean heating temperature increasing rate (mean temperature derivative) should be removed if the measurements are made before the stationary regime of laser heating. Thus, the
A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
theoretical phase shifts can be derived from the temperatures obtained with the developed numerical model of laser heating [6–9]. But this approach is very time-consuming, especially in a 3D-regime. Laser intensity I(t) can be also expressed as the Fourier series: 1
IðtÞ ¼ I 0 þ ∑ ðan sin 2π nυL t þ bn cos 2π nυL tÞ n¼1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 a2n þ bn ∑ n¼1
¼ I0 þ
sin ð2π nυL t þ ϕðnÞ LP Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ¼ Re I 0 þ i ∑ a2n þ bn e ið2π nνL
t þ ϕðnÞ LP Þ
n¼1
1
Re ∑ I n e i2π nνL t ; n¼0
ð5Þ ðnÞ where I0 is the ffi mean laser intensity, and ϕLP ¼ tan 1 ðbn =an Þ and qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 iϕðnÞ 2 In ¼i an þ bn e LP are, respectively, the laser pulse phase and the laser complex intensity corresponding to the nth Fourier harmonic of the pulse repetition rate frequency νL. The mean laser intensity R tn þ 1=νL should be normalised by the mean laser power P as I 0 ¼ υL t n IðtÞ dt ¼ P=ðπ r 20 Þ, and the coefficients an and bn (n 40) can be determined either from the experimental or from the simulated time-dependent laser intensity from the relations:
Z bn ¼ 2νL
Z
t n þ 1=νL
IðtÞ cos ð2π nνL tÞdt; an ¼ 2νL
tn
t n þ 1=νL
tn
IðtÞ sin ð2π nνL tÞdt;
ð6Þ so that tan ϕðnÞ LP ¼
bn ¼ an
Z
t n þ 1=υL
tn
IðtÞ cos ð2π nνL tÞdt
.Z
t n þ 1=υL
tn
IðtÞ sin ð2π nνL tÞdt:
ð7Þ For example, for the rectangular laser pulses starting at t¼0 with the duration of 0.5νL 1 , that is half of the laser repetition period, bn ¼0 and an ¼(2I0/(π n))(1 cos(π n)), ϕðnÞ LP ¼ 0. 2.1.2. Method of the direct phase shift calculations The rapid method of phase shift calculations for the heating temperature Fourier amplitudes was developed in Ref. [23]. For the temperature Fourier amplitudes ΔTn (z,r), the following equations can be applied 2 ∂ ΔT n ∂2 ΔT n 1∂ΔT n þ þ i2π nνL ρl C l ΔT n ¼ kl 2 2 r ∂r ∂z ∂r ð8aÞ þ αl ð1 Rl ÞI n expð αl zÞf L ðrÞ ; ð0 o z o dÞ i2π nνL ρs C s ΔT n ¼ ks
2 ∂ ΔT n ∂2 ΔT n 1∂ΔT n : ðz Z dÞ þ þ 2 2 r ∂r ∂z ∂r
ð8bÞ
The heating temperature corresponding to the one measured by the pyrometer can be found from the expression [23]: R þ1 ~ ~ ξÞ Φð ΔT n ðz ¼ 0; r ¼ 0Þ ¼ αl ð1 k Rl ÞIn 0 2 ~2 2 ξ =r 0 αl 2π inνL ρl C l =kl
l
2αl e κ1n d ks κ 2n ðe αl d e κ1n d Þ 1 þ κ 1n D h κ 1n αl d ks κ 2n α κ 1n d ~ þ e þ 1 l dξ: e αl kl κ 1n κ1n
27
where I~ 1 is proportional to I1 with some inessential real normalizing coefficient, while ΔT0(z¼ 0, r¼0) and |ΔT1(z¼ 0, r¼ 0)| can give the mean heating temperature and the temperature oscillations amplitude on the fundamental repetition rate frequency νL, respectively. The phase shift does not depend on the temporal shape of the laser intensity if the optical and thermal properties of the layer and substrate do not depend on the temperature. Thus, if only phase shifts are required, it is not necessary to introduce the experimental temporal laser pulse shape in the simulations. The phase shift is determined for the Fourier component on the laser repetition rate frequency. In this case, the phase shifts calculations even for 3D laser heating may be performed much faster than with the very complex and time consuming method with the calculations involving the full temperature traces [6–9]. 2.2. Modelling of phase shift sensitivity The developed method of fast calculations (see Section 2.1.2) was applied to determine phase shift sensitivity. It was possible to calculate a phase shift as a function of νL and h in a wide range of their values. Fig. 1 presents the results for d ¼ 100 μm and r0 ¼100, 1000, and 10,000 μm. The phase shift dependences on νL at different h (Fig. 2(a)) and on h at different νL (Fig. 2(b)) for d¼ 100 μm are also presented. From these results, it was concluded that the dependence of the phase shift on the laser repetition rate frequency is different for different heat contact coefficients in the range of (1 oh[kW/ (m2 K)) o 1000) for d ¼100 μm. The phase shift sensitivity on h is strongly decreasing if the heat contact coefficient is beyond both the high (1000 kW/(m2 K)) and low (1 kW/(m2 K)) range limits. The phase shift sensitivity is also decreasing with the important increase in the laser repetition rate frequency. In this case, the moderate repetition rate frequencies (νL o200 Hz) are preferable. Generally, the phase shift is a non-monotonous function of both νL and h (see Figs. 1 and 2). The phase shift depends on r0 (see Fig. 1). In Fig. 1, r0 ¼10,000 μm is given as a limiting case of 1D-regime of laser heating. For lower r0, the 3D-laser heating regime with r0dependent phase shift is applied. 2.3. 1D- and 3D-modelling comparison The difference between 1D- and 3D-regime of laser heating was verified for the phase shift calculations. The surface plots of the phase shift as a function of νL and h for r0 ¼1000 μm and for (r0-1) to satisfy the limits of 1D approximation are presented in Fig. 3(a) and (b), respectively. For the highest and lowest values of νL and h, the phase shifts were different. For νL ¼10–1000 Hz, however, 1D approximation was still good to describe quantitatively the phase shifts for r0 ¼1000 μm for the carbon layer with d¼ 40 μm. From the point of view of the maximal phase shift sensitivity, this laser repetition rate frequency range should be considered for lock-in thermography.
ð9Þ 3. Experiment
~ ¼ ~ ¼ 0:5ξexpð ~ ~ ξÞ ~ ξÞ Here, Φð ξ~ =4Þ for the Gaussian laser beam and Φð qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ~ for the flat-top laser beam, κ1n ¼ ξ~ =r 2π i nνL ρl C l =kl , J 1 ðξÞ 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ~ κ 2n ¼ ξ =r 0 2π i nνL ρs C s =ks (Reκ1n 40 and Reκ 2n 40), D ¼ ð1 þ
2n þ ð1 e 2κ1n d Þ 1 þ ks hκ2n . For the phase shift calculations, e 2κ1n d Þkksκκ1n 2
l
it is sufficient to consider only the particular Fourier contribution ΔT1 corresponding to n¼1, that is, to the laser fundamental repetition rate frequency νL. The phase shift can be found from the expression: ð1Þ ~ Δφð1Þ φð1Þ LH φLP ¼ Refi lnðΔT 1 ðz ¼ 0; r ¼ 0Þ=I 1 Þg
ð10Þ
3.1. Experimental installation Active laser pyrometry and lock-in thermography were applied in tandem as a combined complementary approach for in situ non-destructive characterisation of micrometric carbon layer deposited on TEXTOR graphite tile to cross-check the deposited layer characterisation determined by active laser pyrometry and lock-in thermography. Fig. 4 presents the general scheme of the modified experimental installation based on a Nd:YAG laser, a home-made
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pulses (number, pulse duration, repetition rate). The laser acoustooptical modulator adjustments provided the laser pulses of nearly rectangular shape for the applied repetition rates νL ¼2 Hz to 1 kHz. Laser pulse duration was τL ffi 0.5/νL. The pyrometer system comprised two Kleiber pyrometers: KGAF 274C-LWL (pyro-1) and KGAF 740-HS (pyro-2) of (600– 2600 K) and (500–1300 K) temperature range, respectively. Both the pyrometers (1.58–2.2 mm spectral range, time constant t98% ¼ 15 ms) were applied in consecutive order for temperature measurements. An optical lens system was used to image the heated zone ( ffi 500 mm diameter) onto the entrance of the pyrometer fibre (1.5 m length, 200 mm diameter). The pyrometers were with “direct” outputs to provide the exit signal (Volts) proportional to the photon flux. The pyrometers were calibrated with the black body etalon source. All the data were recorded by a computer system and processed by MATLAB software. 3.2. Sample Fig. 5 presents the sample with a carbon deposited layer on TEXTOR graphite tile with different zones under study. The sample has already been under deposited layer characterisation [6,18]. From these studies, the sample may be described as follows. Zones A1 and A2 are without the deposited carbon layer which has suffered overheating and was destroyed by laser ablation. In (B, C, D) zones, the carbon deposited layer is not homogeneous and of a different thermal contact with a substrate. The layer thickness is 33713 mm, 47 2 mm, E 10 mm for zones B, C, and D respectively. In zone D, the deposited layer is visibly detached from the graphite tile. 3.3. Experimental results and simulations
Fig. 1. TEXTOR graphite layer on the TEXTOR graphite substrate, d¼ 100 μm. The surface plots of the phase shift dependence on νL and h. r0 ¼ 100 μm (d), 1000 μm (e), 10,000 μm (f).
pyrometer system, optical systems for laser beam transportation and optical focusing, and a generator to trigger laser pulses. The pulse repetition rate laser (Nd:YAG, 1064 nm, 10–100 W amplitude power) was used for sample surface heating. A fusion quartz optical fibre (32 m length, 1 mm diameter) was used for laser beam transportation and to provide homogeneous intensity distribution (flat-top) of the laser beam spot. An optical system was used for laser beam focusing on the sample surface (2 mm diameter spot). A photodiode was used to register the laser power reflected from the surface to provide laser beam control. A pulse generator (Princeton, DG535) was used to control the applied laser
Zones B, C, and D with a carbon deposited layers were under laser heating with the laser repetition rate frequencies νL ¼2– 1000 Hz. The laser power was carefully adjusted to avoid the layer overheating which may affect the initial layer properties and results in undesirable modification in surface features. The applied laser power was P ¼12 W for zone B (33713 mm layer thickness), P¼ 12 W or 16 W for zone C (4 72 mm layer thickness), while for zone D (E10 mm layer thickness, detached), the laser power was P ¼8 W to provide the condition (ΔT o1000 K) for any zone under heating, regardless of the layer thickness, thermal contact quality and applied repetition rate frequency. The experimental heating temperatures evolutions were determined for all the zones under study. For zone B, the evolutions of experimental heating temperature are given in Fig. 6. The maximal temperature and modulation amplitude decrease with the increasing of laser repetition rate frequency. For zone C and zone D, the heating temperature evolutions are quite similar to those obtained for zone B. With the 3D modelling (see Section 2), it was possible to calculate the heating temperature with a good temporal and spatial resolution. In our simulations, the graphite properties for the TEXTOR tile (substrate) were taken as in Ref. [9]: density ρs ¼ 1680 kg/m3, porosity ps ¼25%, mass specific heat Cs ¼ 1500 J/ (kg K), thermal conductivity ks ¼60 W/(m K). The fitting for the experimental/calculated temperatures for zones (B, C, and D) was made. For zones B, C, and D, respectively, Figs. 7–9 present the best temperature fitting obtained with the adjusted carbon layer properties. The set of the layer parameters corresponding to the best fit of the experimental/simulation results was considered as the layer properties. Table 1 presents the adjusted mean carbon layer properties and thermal contact coefficient determined by active laser pyrometry with E 10% accuracy (for a given layer thickness d) for TEXTOR tile as a substrate.
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Fig. 2. TEXTOR graphite layer on the TEXTOR graphite substrate, d ¼100 μm. The phase shift dependence on νL at different h (panel a) and on h at different νL (panel b). r0 ¼1000 μm.
Fig. 4. The general scheme of the experimental installation.
Fig. 5. TEXTOR graphite tile with different zones under study.
Fig. 3. The phase shift dependences on νL and on h. r0 ¼1000 μm (panel a), r0-1 (panel b). Sample is TEXTOR graphite substrate with a layer (d ¼40 μm).
To complete the above layer characterisation made by active laser pyrometry, lock-in thermography was applied to determine thermal contact coefficient (hph) by phase shifts measurements on different laser repetition rate frequencies. To determine the experimental phase shifts, the temperature evolution traces obtained by pyrometer measurements (Fig. 6) were used. Theoretical phase shifts were simulated with a new model for rapid calculations (see Section 2). Both the experimental and theoretical phase shifts versus laser repetition rate frequency for zones B, C, and D are presented in Figs. 10–12, respectively. The phase shifts in these figures correspond to the Fourier component with n ¼1, that is, to the Fourier component on laser repetition rate frequency νL.
The phase shift modelling was made with the adjusted layer properties obtained by laser active pyrometry (see Table 1) and layer/surface thermal contact coefficient hph was a given parameter. From the above Figures, for zones B, C, and D, respectively, the thermal contact coefficients are hph E10 kW/(m2 K), hph E10– 100 kW/(m2 K), and hph E 1 kW/(m2 K). Table 2 presents the thermal contact coefficients determined by active laser pyrometry (halp) along with the coefficients determined by lock-in thermography (hph). From Table 2, one may conclude that the results obtained by both methods are quite comparable. Though there was no gain in the measurements accuracy, lock-in measurements have demonstrated their advantage as being much more rapid. For zones (A1) and (A2) without the deposited carbon layer, the obtained phase shifts were almost the same and equal to zero for all the applied νL ¼ (20–1000) Hz (Fig. 13).
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Fig. 6. Temperature evolutions for zone B (337 13 mm layer thickness). P¼ 12 W, νL ¼ (2–1000) Hz.
4. Conclusions Active laser pyrometry and lock-in thermography were applied for in situ non-destructive characterisation of micrometric carbon
layer (10–40 mm thickness, different thermal contact quality) deposited on TEXTOR graphite tile. The study was aimed to crosscheck the layer thermal contact coefficients obtained by active laser pyrometry and lock-in thermography. The modified experimental
A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
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Fig. 7. Theoretical fit of the heating temperatures for zone B (337 13 mm layer thickness). P¼ 12 W, νL ¼100 Hz. Panel (a) presents the results for the 45th laser pulse in the saturation regime for mean temperature. Panel (b) presents the profiles of the minimal and maximal heating temperatures for 50 laser pulses on the whole temperature trace.
Fig. 8. Theoretical fit of the heating temperatures for zone C (4 7 2 mm layer thickness). P ¼16 W, νL ¼100 Hz. Panel (a) presents the results for the 45th laser pulse in the saturation regime for mean temperature. Panel (b) presents the profiles of the minimal and maximal heating temperatures for 50 laser pulses on the whole temperature trace.
Fig. 9. Theoretical fit of the heating temperatures for zone D ( E10 mm layer thickness, detached). P¼ 8 W, νL ¼ 100 Hz. Panel (a) presents the results for the 95th laser pulse in the saturation regime for mean temperature. Panel (b) presents the minimal and maximal heating temperatures for 100 laser pulses on the whole temperature trace.
Table 1 The adjusted mean properties of the carbon layer deposited on the TEXTOR tile determined by active laser pyrometry. The accuracy of the results is mainly determined by the accuracy of the layer thickness d. Carbon layer parameters
Zone B
Zone C
Zone D (detached)
d [mm] ρ l [kg/m3] C l [J/(kg K)] k l [W/(m K)] α l [1 μm 1] Rl h alp [kW/(m2 K)]
33 713 650 1500 0.1 1 0.7 3.925
4 72 1792 1500 10 2.13 0.23 14
10 450 1500 0.1 1 0.9 0.325
installation comprised a Nd:YAG pulsed repetition rate laser (1 Hz to 1 kHz repetition rate frequency, homogeneous spot) and a homemade pyrometer system based on two pyrometers for the temperature consecutive measurements in (500–2600)K range. Both for active laser pyrometry and lock-in thermography, the layer characterisation was provided by the best fit of the experimental results and simulations. The experimental results obtained by active laser pyrometry were simulated by 3D model for heating temperatures. The experimental phase shifts determined by lockin thermography were simulated by the developed model for rapid phase shift calculations. The layer thermal contact coefficients determined by active laser pyrometry (halp) and those by the
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Fig. 10. Zone B. Simulated phase shifts (a-f) versus νL for different h (kW/(m2 K)). For (a) h r 0.001, (b) h ¼ 0.01, (c) h ¼ 0.1, (d) h ¼ 1, (e) h ¼ 10, (f) h Z 100. The layer thickness in the simulations is d ¼ 33 μm, and the laser beam radius r0 ¼ 1000 μm. The experimental results are given by points with errors bars.
Fig. 11. Zone C. The simulated phase shifts (a–f) versus the applied νL for different h (kW/(m2 K)). For (a) h r 0.001, (b) h ¼ 0.01, (c) h ¼ 0.1, (d) h ¼1, (e) h ¼ 10, (f) h Z 100. The experimental results for zone C given by points with errors bars. P ¼12 W and 16 W.
Fig. 12. Zone D. Simulated phase shifts (a-f) versus the νL for given h (kW/(m2 K)). For (a) h r0.001, (b) h ¼0.01, (c) h ¼ 0.1, (d) h ¼ 1, (e) h ¼ 10, (f) h Z 100. The experimental results are given by points with errors bars. P¼ 8 W.
Table 2 Thermal contact coefficients determined by solely active laser pyrometry (hfit ) and those by lock-in thermography (hph) used complementary. Carbon layer zones B, C, and D on the TEXTOR tile under study. Thermal contact coefficient
Zone B
Zone C
Zone D (detached)
halp [kW/(m2 K)] hph [kW/(m2 K)]
4 70.5 h 10
147 2 h 10–100
0.3 7 0.05 0.1o h o1.0
lock-in thermography (hph ) were quite comparable (see Table 2). Though there was no gain in the measurements accuracy, lock-in measurements have proved their advantage as being much more rapid for determination of thermal contact coefficient for deposited layers of micrometric thickness. Based on the comparison of
Fig. 13. Zones (A1 – A2) ablated by laser. The experimental phase shifts versus applied νL. For. zone A1, P¼ 12 W. For zone A2, P ¼40 W.
the obtained results, it was concluded that lock-in thermography may provide a more rapid determination of thermal contact coefficient for deposited layers of micrometric thickness. To improve lock-in thermography measurements of the phase shifts, the following considerations should be taken into account. Careful adjustment of the laser repetition rate is required. The laser pulse energy should not be too high to avoid any modifications in the layer properties resulting from the excessive heating of the surface layer. For the zones with a poor thermal contact, the rapid increase in the surface temperature may result in the layer surface modifications. In this case, it is not evident whether the measured phase shifts are attributed to different thermal contact quality or to the resulted layer modifications. For surface properties characterisation by lock-in thermography or active laser pyrometry, it may be advised to use a pyrometer of (330–1300 K) temperature measurements range which may provide measurements of a rather low temperature modulation of the surface under heating. At the low temperature modulation, the layer properties may be regarded as constant, and the phase shifts measurements are not sensitive to the layer properties dependence on a heating temperature. In addition, the undesirable surface oxidation may be avoided. To decrease laser heating fluence, it may be advised to increase the laser spot diameter on the layer surface. For the temperature measurements in this case, the infrared camera rather than the pyrometer should be used. The infrared camera may offer the advantage of making the sample surface thermography and phase measurements simultaneously for each pixel of the camera. For in situ measurements by active laser pyrometry and lock-in thermography in fusion installations (tokamaks), an optical scheme for laser beam transportation and thermal signal collection should be adjusted to the optical windows of the vacuum chamber. With optical windows of 100 mm diameter and adequately chosen optical system inside the vacuum chamber, a large surface of the inner walls of the vacuum chamber may be tested. For example, an optical scheme which was used for LIBS in situ measurements on JET [24,25] can be also applied for active laser thermography. In general, with additional plasma-facing mirrors, no special problems may be expected with the zone accessibility. In this case, to ensure the required optical mirror transmission and dust-free quality, a regular laser cleaning of the mirrors should be provided [26,27].
Acknowledgements The authors would like to express their gratitude to Mr. D. Farcage (DPC/SEARS/LISL, CEA Saclay) for the assistance in the development of the experimental setup scheme.
A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
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[5] [6]
[7] [8]
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R.A. Causey, Journal of Nuclear Materials 300 (2002) 91. I. Youle, A.A. Haasz, Journal of Nuclear Materials 248 (1997) 64. G. Federici, et al., Journal of Nuclear Materials 266–269 (1999) 14. M. Friedrich, et al., in: Proc. 14th Int. Conference on Ion Beam Analysis, 26–30 July 1999, Nuclear Instruments and Methods in Physics Research B 161–163 (2000) 216. C.H. Skinner, et al., Physica Scripta T111 (2004) 92. A. Semerok, S.V. Fomichev, F. Brygo, P.-Y. Thro, Laser Heating of Complex Graphite Surfaces by High Repetition Rate Nanosecond Pulses (Comparative Modelling and Experimental Studies), report CEA, NT DPC/SCP/06-170-A, March 2006, 36 pp. S. Fomichev, et al., Modelling of Complex Surface Heating by Continuous and Pulsed Lasers, report CEA, NT DPC/SCP 05-109-A, January 2005, 76 pp. A. Semerok, et al., Surface heating by pulsed repetition rate nanosecond lasers, 4th International Symposium "Laser Technologies and Lasers", 2005, Plovdiv, Bulgaria, LTL Symposium Proceedings, April 2006, pp.76–83, ISSN 1312-0638. A. Semerok, et al., Journal of Applied Physics 101 (2007) 084916. A. Semerok, et al., Journal of Nuclear Materials 420 (2012) 198. A. Semerok, et al., Fusion Engineering and Design 87 (2012) 267. G. Busse, et al., Journal of Applied Physics 71 (1992) 3962. G. Busse, D. Wu, Lock-in thermography for non-destructive evaluation of materials, Revue Generale de Thermique 37 (1998) 693–703. H. Traxler, et al., Physica Scripta T111 (2004) 203. A. Durocher, et al., Fusion Engineering and Design 75–79 (2005) 401.
33
[16] X. Courtois, et al., In Situ Monitoring of Actively Cooled Plasma Facing Components Using Acoustic and Thermal Methods, 2006, PFMC 11th (Garching). [17] F. Escourbiac, et al., Journal of Nuclear Materials 367–370 (2007) 1492–1496. [18] A. Semerok, et al., Infrared Active Thermography for Surface Layer Characterization, report CEA, NT DPC/SCP 07-225-A, May 2007, 29 pp. [19] A. Semerok, et al., Studies on Graphite Surfaces Detritiation by Pulsed Repetition Rate Nanosecond Lasers, report CEA, NT DPC/SCP 04-076-A, January 2004, 39 pp. [20] A. Semerok, et al., Studies on TOKAMAK Wall Surfaces Decontamination by Pulsed Repetition Rate Lasers, report CEA, NT DPC/SCP 05-111-A, January 2005, 50 pp. [21] A. Semerok, et al., Design and Construction of the System for Laser Detritiation of JET co-Deposited Layers, report CEA, NT DPC/SCP 06-171-A, February 2006, 35 pp. [22] A. Semerok, et al., Laser Detritiation System Tests in the Beryllium Handling Facility and JET Environment, report CEA, NT DPC/SCP 08-292-A, December 2008, 45 pp. [23] A. Semerok, et al., Nuclear Instruments and Methods in Physics Research A 693 (2012) 98. [24] J.-M. Weulersse, et al., In situ Laser Breakdown Spectroscopy of JET Deposited Layers, CEA Report NT DPC/SCP 08-293-A, December 2008, 72 p. [25] A. Semerok, C. Grisolia, Nuclear Instruments and Methods in Physics Research A 720 (2013) 31. [26] A. Widdowson, et al., Journal of Nuclear Materials 415 (2011) S1199. [27] A. Leontyev, et al., Fusion Engineering and Design 86 (2011) 1728.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Active laser pyrometry and lock-in thermography for characterisation of deposited layer on TEXTOR graphite tile A. Semerok a,n, S.V. Fomichev a,b, F. Jaubert a, C. Grisolia c a
CEA, DEN, F-91191 Gif-sur-Yvette, France NRC Kurchatov Institute, 123182 Moscow, Russia c CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France b
art ic l e i nf o
a b s t r a c t
Article history: Received 19 July 2013 Received in revised form 22 November 2013 Accepted 26 November 2013 Available online 7 December 2013
Active laser pyrometry and lock-in thermography were applied for non-destructive characterisation of a deposited carbon-layer (5–40 mm thickness, different thermal contact quality) on TEXTOR graphite tile. The experimental installation comprised a pulse repetition rate laser (Nd-YAG, 1064 nm, 0.5–250 ms pulse duration, 2 Hz to 1 kHz repetition rate, 10–100 W amplitude power) and a home-made active laser pyrometry system. Active laser pyrometry was used to obtain some unknown layer properties (thermal capacity, conductivity, optical absorptivity, layer/surface thermal contact coefficient). With the developed 3D theoretical model, it was possible to calculate the heated layer temperatures with a good temporal and spatial resolution. The layer characterisation was based on the comparison of the modelling and the measured temperatures. To complete active laser pyrometry, lock-in thermography measurements of the layer/surface thermal contact coefficient were made with a new model for rapid phase shifts calculations. The obtained coefficients in both methods were comparable. Though there was no gain in the measurements accuracy, lock-in thermography has demonstrated its advantage as being much more rapid for characterisation of deposited layers of micrometric thickness. & 2013 Elsevier B.V. All rights reserved.
Keywords: Tokamak graphite Plasma facing components Deposited carbon layer Layer characterization Active laser pyrometry Lock-in thermography
1. Introduction In modern fusion thermonuclear installations (tokamaks), plasma is heated up to extremely high temperatures ( 10 keV). Though magnetic field is applied to confine plasma, it may, however, come in contact with tokamak walls. Being affected by plasma, the plasma facing components (PFC) of the tokamak walls are eroded and deposited on the “cold” parts of the reactor, thus forming the deposited layer with a high tritium concentration [1–3]. The deposited layer is a source of dust, which may cause undesirable plasma losses and affect plasma properties [4,5]. To ensure regular cleaning maintenance and efficient rapid cleaning and detritiation of the deposited layers, it is necessary to provide in situ nondestructive characterisation of the deposited layers without disassembly of the reactor components. To avoid tile damage during cleaning, an accurate characterisation of some thermo-physical properties (thickness, thermal conductivity, layer/substrate thermal conductance or contact) of the deposited layer is required. In search for appropriate methods for deposited layer characterisation, active laser pyrometry and lock-in thermography were considered in our study.
n
Corresponding author. Tel.: þ 33 1 69 08 65 57; fax: þ33 1 69 08 77 38. E-mail address: [email protected] (A. Semerok).
0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.11.100
Active laser pyrometry was developed and applied for layer characterisation in [6]. The method is based on the measurement of the heating temperature resulting from the surface heating by repetition rate laser beam. With the developed 3D theoretical model of the laser heating of the layer, it was possible to calculate the temperatures of the heated layer with a good temporal and spatial resolution [7–11]. Based on the comparison of the experimental and theoretical results on thermal response of the surface under laser heating, it was possible to determine optical and thermal properties of the deposited layer – reflectivity, thickness, density, thermal capacity, conductivity and layer/surface thermal contact coefficient. However, as active laser pyrometer measurements are sensitive to the applied laser power and surface reflectivity, the question is whether the temperature changes are attributed to different surface reflectivity or to layer/substrate thermal contact. This consideration implies certain ambiguity of the method for in situ deposited layer characterisation. Lock-in thermography to determine some properties of PFC deposited layer (thickness, layer/surface thermal contact) was introduced in Refs. [12–14]. The method is based on phase shift measurements between the laser power and surface temperature modulations. The phase shift depends on the layer properties and is sensitive to the under-surface defects. Lock-in thermography measurements have the advantage of being independent of optical features (absorptivity, emissivity) of a sample surface. Lock-in
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A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
thermography for thermal contact characterisation of the deposited layers was under study in Refs. [15–18]. In these investigations, the heating of the samples (of millimetre thickness) was provided by the light lamps (0.7 Hz and 1.8 Hz modulation frequencies). The surface temperature was measured by the infrared camera [15]. However, as the measurement sensitivity depends on modulation frequency, a low (1–2 Hz) modulation frequency of the applied lamps was not high enough to provide quantitative characterisation of thin (below 100 μm) layers [18]. To determine thermal contact of micrometric layers, heating sources of a higher modulation frequency (above 10 Hz) are required. In this study, both the methods were used in tandem to check whether the methods “coupling” would result in a more rapid characterisation of the carbon deposited layer (10–40 mm thickness, different thermal contact quality) on TEXTOR graphite tile, which had already been under characterisation by active laser pyrometry [6] and lock-in thermography [18]. The modified experimental installation comprised a Nd:YAG laser (1064 nm, acousto-optical intercavity modulation, pulse repetition rate νL ¼2 Hz to 1 kHz, pulse duration τL ffi 0.5/νL, 10–100 W amplitude power) and a home-made pyrometry system. Active laser pyrometry was applied to determine some unknown properties of the deposited layer (thermal capacity, conductivity, layer/surface thermal contact, optical absorptivity). With the developed 3D theoretical model, it was possible to calculate the heated layer temperatures with a good temporal and spatial resolution. The multi-parametric characterisation of the layer was based on the comparison of the modelling and the measured temperatures. To complete active laser pyrometry characterisation of the deposited layer, lock-in thermography was used for phase shifts measurements to determine the layer/surface thermal contact coefficient. A new model for rapid calculations of the phase shifts was applied for comparison with the experimental results. The investigations of this paper should be regarded as a continuation of our studies on deposited layer characterisation [6–11,18] and layer detritiation [19–22]. Section 2 presents theoretical fundamentals of graphite layer heating and rapid phase shift calculations for lock-in thermography. Multi-parametric modelling for phase shifts is also presented. 1D- and 3D-modelling of laser heating are compared. Section 3 describes the experimental installation and the sample. Section 3.3 presents the experimental results obtained by active laser pyrometry and lock-in thermography used as a combined complementary approach. The experimental and simulation results are compared and discussed. Section 4 presents the conclusions.
both the time-dependent and radial-dependent laser intensity on the surface (at z¼ 0). In Eq. (1), the layer thickness d is assumed to be larger than the layer photon absorption length αl 1 (dαl ⪢ 1), and the laser heating source term is included only in the layer heating Eq. (1a). Generally, it requires the layer thickness d Z1 μm. For typical experimental conditions without convection cooling and radiation losses, the initial and boundary conditions to these equations can be taken as ΔTðt ¼ 0; z; rÞ ¼ 0;
ð2aÞ
∂ΔT ∂ΔT ∂ΔT ¼ 0; k ¼ k s l ∂z z ¼ 0 ∂z z ¼ d 0 ∂z z ¼ d þ 0 ¼ qd ; ΔTjz ¼ d 0 ΔTjz ¼ d þ 0 ¼ qd =h;
ð2bÞ
where qd is the heat flux through the layer/substrate interface, and h is the coefficient of the heat contact (thermal conductance) which is inverse to the thermal resistance of the layer/substrate interface. The time t¼0 is set as the time for the laser turning on. Laser beams with intensity I L ðt; rÞ ¼ IðtÞf L ðrÞ are considered. For the Gaussian laser beam, fL(r) ¼expð r 2 =r 20 Þ, while for the flat-top laser beam, fL(r)¼1 at r rr0 and fL(r)¼0 at r 4r0. Here, r0 is the laser spot radius. As thermal and optical properties depend on temperature, the direct numerical solution of Eq. (1a) and (1b) in 3D space and time for high repetition rate laser heating is seen as a problem even for moderate computers. For graphite, the exact and approximate analytical solutions were verified and proved to be the same within accuracy of 10% [7]. The simplified version of the analytical solution for ΔT (t, z, r) can be obtained in the cylindrical geometry with circular symmetry of the laser spot and immobile laser beam [9]. This solution was applied for heating temperature calculation in these studies. Thus, the optical and thermal properties of the layer and substrate are assumed to be temperature-independent in our studies. 2.1.1. Basic equations of lock-in thermography The thermal response of the sample can also be expressed as the Fourier series: 1
ΔTðt; z; rÞ ¼ ΔT 0 ðz; rÞ þ ∑ ðAn ðz; rÞ sin 2π nυL t þ Bn ðz; rÞ cos 2π nυL tÞ n¼1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðnÞ A2n þ B2n sin ð2π nυL t þ ϕLH Þ ¼ ΔT 0 ðz; rÞ þ ∑ n¼1 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðnÞ A2n þB2n e ið2π nνL t þ ϕLH Þ ¼ Re ΔT 0 ðz; rÞ þi ∑ n¼1
1
Re ∑ ΔT n ðz; rÞe i2π nνL t ;
2. Theoretical studies 2.1. Basic equations for the stationary periodical laser heating In cylindrical coordinates z and r, the equations for circularsymmetric time-dependent heating temperature ΔT (t, z, r) T (t, z, r) – Ta of a complex surface with a layer deposited on the substrate can be written as ρl C l
2 ∂ΔT ∂ ΔT ∂2 ΔT 1∂ΔT þ þ ¼ kl þ αl ð1 Rl ÞI L ðt; rÞexpð αl zÞ; ∂t r ∂r ∂z2 ∂r 2
ð0 o z o dÞ
ð1aÞ 2 ∂ΔT ∂ ΔT ∂2 ΔT 1∂ΔT ¼ ks : ρs C s þ þ 2 2 ∂t r ∂r ∂z ∂r
ð3Þ
n¼0
heating temperature, and where ΔT0(z, r) is the mean steady-state qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 iϕðnÞ 1 LH ϕðnÞ ðz; rÞ ¼ tan ðB =A Þ and ΔT ¼i A are, respecn n n n þ Bn e LH tively, the temperature phase and complex amplitude of the nthharmonic. If the temperature trace is known either from the experiments or calculations, the heating temperature phase can be found from the expression: Z tn þ 1=υL . Bn ðz; rÞ ðnÞ tan ϕLH ¼ ðz; rÞ ¼ ΔTðt; z; rÞ cos ð2π nυL tÞdt n An ðz; rÞ t Z t n þ 1=υL ΔTðt; z; rÞ sin ð2π nυL tÞdt; ð4Þ tn
ðz ZdÞ
ð1bÞ
Here, Ta is the ambient temperature, ρl, Cl, kl and ρs, Cs, ks are, respectively, density, mass specific heat, and thermal conductivity of the layer and the substrate; d is the layer thickness; αl and Rl are the laser beam absorption and matter reflectivity coefficients. IL(t, r) is
n
where t is an arbitrary time moment of the stationary regime for a mean heating temperature. Both expressions (3) and (4) can be used for the phase shift calculations with respect to the laser pulse phase. The mean heating temperature increasing rate (mean temperature derivative) should be removed if the measurements are made before the stationary regime of laser heating. Thus, the
A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
theoretical phase shifts can be derived from the temperatures obtained with the developed numerical model of laser heating [6–9]. But this approach is very time-consuming, especially in a 3D-regime. Laser intensity I(t) can be also expressed as the Fourier series: 1
IðtÞ ¼ I 0 þ ∑ ðan sin 2π nυL t þ bn cos 2π nυL tÞ n¼1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 a2n þ bn ∑ n¼1
¼ I0 þ
sin ð2π nυL t þ ϕðnÞ LP Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ¼ Re I 0 þ i ∑ a2n þ bn e ið2π nνL
t þ ϕðnÞ LP Þ
n¼1
1
Re ∑ I n e i2π nνL t ; n¼0
ð5Þ ðnÞ where I0 is the ffi mean laser intensity, and ϕLP ¼ tan 1 ðbn =an Þ and qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 iϕðnÞ 2 In ¼i an þ bn e LP are, respectively, the laser pulse phase and the laser complex intensity corresponding to the nth Fourier harmonic of the pulse repetition rate frequency νL. The mean laser intensity R tn þ 1=νL should be normalised by the mean laser power P as I 0 ¼ υL t n IðtÞ dt ¼ P=ðπ r 20 Þ, and the coefficients an and bn (n 40) can be determined either from the experimental or from the simulated time-dependent laser intensity from the relations:
Z bn ¼ 2νL
Z
t n þ 1=νL
IðtÞ cos ð2π nνL tÞdt; an ¼ 2νL
tn
t n þ 1=νL
tn
IðtÞ sin ð2π nνL tÞdt;
ð6Þ so that tan ϕðnÞ LP ¼
bn ¼ an
Z
t n þ 1=υL
tn
IðtÞ cos ð2π nνL tÞdt
.Z
t n þ 1=υL
tn
IðtÞ sin ð2π nνL tÞdt:
ð7Þ For example, for the rectangular laser pulses starting at t¼0 with the duration of 0.5νL 1 , that is half of the laser repetition period, bn ¼0 and an ¼(2I0/(π n))(1 cos(π n)), ϕðnÞ LP ¼ 0. 2.1.2. Method of the direct phase shift calculations The rapid method of phase shift calculations for the heating temperature Fourier amplitudes was developed in Ref. [23]. For the temperature Fourier amplitudes ΔTn (z,r), the following equations can be applied 2 ∂ ΔT n ∂2 ΔT n 1∂ΔT n þ þ i2π nνL ρl C l ΔT n ¼ kl 2 2 r ∂r ∂z ∂r ð8aÞ þ αl ð1 Rl ÞI n expð αl zÞf L ðrÞ ; ð0 o z o dÞ i2π nνL ρs C s ΔT n ¼ ks
2 ∂ ΔT n ∂2 ΔT n 1∂ΔT n : ðz Z dÞ þ þ 2 2 r ∂r ∂z ∂r
ð8bÞ
The heating temperature corresponding to the one measured by the pyrometer can be found from the expression [23]: R þ1 ~ ~ ξÞ Φð ΔT n ðz ¼ 0; r ¼ 0Þ ¼ αl ð1 k Rl ÞIn 0 2 ~2 2 ξ =r 0 αl 2π inνL ρl C l =kl
l
2αl e κ1n d ks κ 2n ðe αl d e κ1n d Þ 1 þ κ 1n D h κ 1n αl d ks κ 2n α κ 1n d ~ þ e þ 1 l dξ: e αl kl κ 1n κ1n
27
where I~ 1 is proportional to I1 with some inessential real normalizing coefficient, while ΔT0(z¼ 0, r¼0) and |ΔT1(z¼ 0, r¼ 0)| can give the mean heating temperature and the temperature oscillations amplitude on the fundamental repetition rate frequency νL, respectively. The phase shift does not depend on the temporal shape of the laser intensity if the optical and thermal properties of the layer and substrate do not depend on the temperature. Thus, if only phase shifts are required, it is not necessary to introduce the experimental temporal laser pulse shape in the simulations. The phase shift is determined for the Fourier component on the laser repetition rate frequency. In this case, the phase shifts calculations even for 3D laser heating may be performed much faster than with the very complex and time consuming method with the calculations involving the full temperature traces [6–9]. 2.2. Modelling of phase shift sensitivity The developed method of fast calculations (see Section 2.1.2) was applied to determine phase shift sensitivity. It was possible to calculate a phase shift as a function of νL and h in a wide range of their values. Fig. 1 presents the results for d ¼ 100 μm and r0 ¼100, 1000, and 10,000 μm. The phase shift dependences on νL at different h (Fig. 2(a)) and on h at different νL (Fig. 2(b)) for d¼ 100 μm are also presented. From these results, it was concluded that the dependence of the phase shift on the laser repetition rate frequency is different for different heat contact coefficients in the range of (1 oh[kW/ (m2 K)) o 1000) for d ¼100 μm. The phase shift sensitivity on h is strongly decreasing if the heat contact coefficient is beyond both the high (1000 kW/(m2 K)) and low (1 kW/(m2 K)) range limits. The phase shift sensitivity is also decreasing with the important increase in the laser repetition rate frequency. In this case, the moderate repetition rate frequencies (νL o200 Hz) are preferable. Generally, the phase shift is a non-monotonous function of both νL and h (see Figs. 1 and 2). The phase shift depends on r0 (see Fig. 1). In Fig. 1, r0 ¼10,000 μm is given as a limiting case of 1D-regime of laser heating. For lower r0, the 3D-laser heating regime with r0dependent phase shift is applied. 2.3. 1D- and 3D-modelling comparison The difference between 1D- and 3D-regime of laser heating was verified for the phase shift calculations. The surface plots of the phase shift as a function of νL and h for r0 ¼1000 μm and for (r0-1) to satisfy the limits of 1D approximation are presented in Fig. 3(a) and (b), respectively. For the highest and lowest values of νL and h, the phase shifts were different. For νL ¼10–1000 Hz, however, 1D approximation was still good to describe quantitatively the phase shifts for r0 ¼1000 μm for the carbon layer with d¼ 40 μm. From the point of view of the maximal phase shift sensitivity, this laser repetition rate frequency range should be considered for lock-in thermography.
ð9Þ 3. Experiment
~ ¼ ~ ¼ 0:5ξexpð ~ ~ ξÞ ~ ξÞ Here, Φð ξ~ =4Þ for the Gaussian laser beam and Φð qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ~ for the flat-top laser beam, κ1n ¼ ξ~ =r 2π i nνL ρl C l =kl , J 1 ðξÞ 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ~ κ 2n ¼ ξ =r 0 2π i nνL ρs C s =ks (Reκ1n 40 and Reκ 2n 40), D ¼ ð1 þ
2n þ ð1 e 2κ1n d Þ 1 þ ks hκ2n . For the phase shift calculations, e 2κ1n d Þkksκκ1n 2
l
it is sufficient to consider only the particular Fourier contribution ΔT1 corresponding to n¼1, that is, to the laser fundamental repetition rate frequency νL. The phase shift can be found from the expression: ð1Þ ~ Δφð1Þ φð1Þ LH φLP ¼ Refi lnðΔT 1 ðz ¼ 0; r ¼ 0Þ=I 1 Þg
ð10Þ
3.1. Experimental installation Active laser pyrometry and lock-in thermography were applied in tandem as a combined complementary approach for in situ non-destructive characterisation of micrometric carbon layer deposited on TEXTOR graphite tile to cross-check the deposited layer characterisation determined by active laser pyrometry and lock-in thermography. Fig. 4 presents the general scheme of the modified experimental installation based on a Nd:YAG laser, a home-made
28
A. Semerok et al. / Nuclear Instruments and Methods in Physics Research A 738 (2014) 25–33
pulses (number, pulse duration, repetition rate). The laser acoustooptical modulator adjustments provided the laser pulses of nearly rectangular shape for the applied repetition rates νL ¼2 Hz to 1 kHz. Laser pulse duration was τL ffi 0.5/νL. The pyrometer system comprised two Kleiber pyrometers: KGAF 274C-LWL (pyro-1) and KGAF 740-HS (pyro-2) of (600– 2600 K) and (500–1300 K) temperature range, respectively. Both the pyrometers (1.58–2.2 mm spectral range, time constant t98% ¼ 15 ms) were applied in consecutive order for temperature measurements. An optical lens system was used to image the heated zone ( ffi 500 mm diameter) onto the entrance of the pyrometer fibre (1.5 m length, 200 mm diameter). The pyrometers were with “direct” outputs to provide the exit signal (Volts) proportional to the photon flux. The pyrometers were calibrated with the black body etalon source. All the data were recorded by a computer system and processed by MATLAB software. 3.2. Sample Fig. 5 presents the sample with a carbon deposited layer on TEXTOR graphite tile with different zones under study. The sample has already been under deposited layer characterisation [6,18]. From these studies, the sample may be described as follows. Zones A1 and A2 are without the deposited carbon layer which has suffered overheating and was destroyed by laser ablation. In (B, C, D) zones, the carbon deposited layer is not homogeneous and of a different thermal contact with a substrate. The layer thickness is 33713 mm, 47 2 mm, E 10 mm for zones B, C, and D respectively. In zone D, the deposited layer is visibly detached from the graphite tile. 3.3. Experimental results and simulations
Fig. 1. TEXTOR graphite layer on the TEXTOR graphite substrate, d¼ 100 μm. The surface plots of the phase shift dependence on νL and h. r0 ¼ 100 μm (d), 1000 μm (e), 10,000 μm (f).
pyrometer system, optical systems for laser beam transportation and optical focusing, and a generator to trigger laser pulses. The pulse repetition rate laser (Nd:YAG, 1064 nm, 10–100 W amplitude power) was used for sample surface heating. A fusion quartz optical fibre (32 m length, 1 mm diameter) was used for laser beam transportation and to provide homogeneous intensity distribution (flat-top) of the laser beam spot. An optical system was used for laser beam focusing on the sample surface (2 mm diameter spot). A photodiode was used to register the laser power reflected from the surface to provide laser beam control. A pulse generator (Princeton, DG535) was used to control the applied laser
Zones B, C, and D with a carbon deposited layers were under laser heating with the laser repetition rate frequencies νL ¼2– 1000 Hz. The laser power was carefully adjusted to avoid the layer overheating which may affect the initial layer properties and results in undesirable modification in surface features. The applied laser power was P ¼12 W for zone B (33713 mm layer thickness), P¼ 12 W or 16 W for zone C (4 72 mm layer thickness), while for zone D (E10 mm layer thickness, detached), the laser power was P ¼8 W to provide the condition (ΔT o1000 K) for any zone under heating, regardless of the layer thickness, thermal contact quality and applied repetition rate frequency. The experimental heating temperatures evolutions were determined for all the zones under study. For zone B, the evolutions of experimental heating temperature are given in Fig. 6. The maximal temperature and modulation amplitude decrease with the increasing of laser repetition rate frequency. For zone C and zone D, the heating temperature evolutions are quite similar to those obtained for zone B. With the 3D modelling (see Section 2), it was possible to calculate the heating temperature with a good temporal and spatial resolution. In our simulations, the graphite properties for the TEXTOR tile (substrate) were taken as in Ref. [9]: density ρs ¼ 1680 kg/m3, porosity ps ¼25%, mass specific heat Cs ¼ 1500 J/ (kg K), thermal conductivity ks ¼60 W/(m K). The fitting for the experimental/calculated temperatures for zones (B, C, and D) was made. For zones B, C, and D, respectively, Figs. 7–9 present the best temperature fitting obtained with the adjusted carbon layer properties. The set of the layer parameters corresponding to the best fit of the experimental/simulation results was considered as the layer properties. Table 1 presents the adjusted mean carbon layer properties and thermal contact coefficient determined by active laser pyrometry with E 10% accuracy (for a given layer thickness d) for TEXTOR tile as a substrate.
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Fig. 2. TEXTOR graphite layer on the TEXTOR graphite substrate, d ¼100 μm. The phase shift dependence on νL at different h (panel a) and on h at different νL (panel b). r0 ¼1000 μm.
Fig. 4. The general scheme of the experimental installation.
Fig. 5. TEXTOR graphite tile with different zones under study.
Fig. 3. The phase shift dependences on νL and on h. r0 ¼1000 μm (panel a), r0-1 (panel b). Sample is TEXTOR graphite substrate with a layer (d ¼40 μm).
To complete the above layer characterisation made by active laser pyrometry, lock-in thermography was applied to determine thermal contact coefficient (hph) by phase shifts measurements on different laser repetition rate frequencies. To determine the experimental phase shifts, the temperature evolution traces obtained by pyrometer measurements (Fig. 6) were used. Theoretical phase shifts were simulated with a new model for rapid calculations (see Section 2). Both the experimental and theoretical phase shifts versus laser repetition rate frequency for zones B, C, and D are presented in Figs. 10–12, respectively. The phase shifts in these figures correspond to the Fourier component with n ¼1, that is, to the Fourier component on laser repetition rate frequency νL.
The phase shift modelling was made with the adjusted layer properties obtained by laser active pyrometry (see Table 1) and layer/surface thermal contact coefficient hph was a given parameter. From the above Figures, for zones B, C, and D, respectively, the thermal contact coefficients are hph E10 kW/(m2 K), hph E10– 100 kW/(m2 K), and hph E 1 kW/(m2 K). Table 2 presents the thermal contact coefficients determined by active laser pyrometry (halp) along with the coefficients determined by lock-in thermography (hph). From Table 2, one may conclude that the results obtained by both methods are quite comparable. Though there was no gain in the measurements accuracy, lock-in measurements have demonstrated their advantage as being much more rapid. For zones (A1) and (A2) without the deposited carbon layer, the obtained phase shifts were almost the same and equal to zero for all the applied νL ¼ (20–1000) Hz (Fig. 13).
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Fig. 6. Temperature evolutions for zone B (337 13 mm layer thickness). P¼ 12 W, νL ¼ (2–1000) Hz.
4. Conclusions Active laser pyrometry and lock-in thermography were applied for in situ non-destructive characterisation of micrometric carbon
layer (10–40 mm thickness, different thermal contact quality) deposited on TEXTOR graphite tile. The study was aimed to crosscheck the layer thermal contact coefficients obtained by active laser pyrometry and lock-in thermography. The modified experimental
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Fig. 7. Theoretical fit of the heating temperatures for zone B (337 13 mm layer thickness). P¼ 12 W, νL ¼100 Hz. Panel (a) presents the results for the 45th laser pulse in the saturation regime for mean temperature. Panel (b) presents the profiles of the minimal and maximal heating temperatures for 50 laser pulses on the whole temperature trace.
Fig. 8. Theoretical fit of the heating temperatures for zone C (4 7 2 mm layer thickness). P ¼16 W, νL ¼100 Hz. Panel (a) presents the results for the 45th laser pulse in the saturation regime for mean temperature. Panel (b) presents the profiles of the minimal and maximal heating temperatures for 50 laser pulses on the whole temperature trace.
Fig. 9. Theoretical fit of the heating temperatures for zone D ( E10 mm layer thickness, detached). P¼ 8 W, νL ¼ 100 Hz. Panel (a) presents the results for the 95th laser pulse in the saturation regime for mean temperature. Panel (b) presents the minimal and maximal heating temperatures for 100 laser pulses on the whole temperature trace.
Table 1 The adjusted mean properties of the carbon layer deposited on the TEXTOR tile determined by active laser pyrometry. The accuracy of the results is mainly determined by the accuracy of the layer thickness d. Carbon layer parameters
Zone B
Zone C
Zone D (detached)
d [mm] ρ l [kg/m3] C l [J/(kg K)] k l [W/(m K)] α l [1 μm 1] Rl h alp [kW/(m2 K)]
33 713 650 1500 0.1 1 0.7 3.925
4 72 1792 1500 10 2.13 0.23 14
10 450 1500 0.1 1 0.9 0.325
installation comprised a Nd:YAG pulsed repetition rate laser (1 Hz to 1 kHz repetition rate frequency, homogeneous spot) and a homemade pyrometer system based on two pyrometers for the temperature consecutive measurements in (500–2600)K range. Both for active laser pyrometry and lock-in thermography, the layer characterisation was provided by the best fit of the experimental results and simulations. The experimental results obtained by active laser pyrometry were simulated by 3D model for heating temperatures. The experimental phase shifts determined by lockin thermography were simulated by the developed model for rapid phase shift calculations. The layer thermal contact coefficients determined by active laser pyrometry (halp) and those by the
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Fig. 10. Zone B. Simulated phase shifts (a-f) versus νL for different h (kW/(m2 K)). For (a) h r 0.001, (b) h ¼ 0.01, (c) h ¼ 0.1, (d) h ¼ 1, (e) h ¼ 10, (f) h Z 100. The layer thickness in the simulations is d ¼ 33 μm, and the laser beam radius r0 ¼ 1000 μm. The experimental results are given by points with errors bars.
Fig. 11. Zone C. The simulated phase shifts (a–f) versus the applied νL for different h (kW/(m2 K)). For (a) h r 0.001, (b) h ¼ 0.01, (c) h ¼ 0.1, (d) h ¼1, (e) h ¼ 10, (f) h Z 100. The experimental results for zone C given by points with errors bars. P ¼12 W and 16 W.
Fig. 12. Zone D. Simulated phase shifts (a-f) versus the νL for given h (kW/(m2 K)). For (a) h r0.001, (b) h ¼0.01, (c) h ¼ 0.1, (d) h ¼ 1, (e) h ¼ 10, (f) h Z 100. The experimental results are given by points with errors bars. P¼ 8 W.
Table 2 Thermal contact coefficients determined by solely active laser pyrometry (hfit ) and those by lock-in thermography (hph) used complementary. Carbon layer zones B, C, and D on the TEXTOR tile under study. Thermal contact coefficient
Zone B
Zone C
Zone D (detached)
halp [kW/(m2 K)] hph [kW/(m2 K)]
4 70.5 h 10
147 2 h 10–100
0.3 7 0.05 0.1o h o1.0
lock-in thermography (hph ) were quite comparable (see Table 2). Though there was no gain in the measurements accuracy, lock-in measurements have proved their advantage as being much more rapid for determination of thermal contact coefficient for deposited layers of micrometric thickness. Based on the comparison of
Fig. 13. Zones (A1 – A2) ablated by laser. The experimental phase shifts versus applied νL. For. zone A1, P¼ 12 W. For zone A2, P ¼40 W.
the obtained results, it was concluded that lock-in thermography may provide a more rapid determination of thermal contact coefficient for deposited layers of micrometric thickness. To improve lock-in thermography measurements of the phase shifts, the following considerations should be taken into account. Careful adjustment of the laser repetition rate is required. The laser pulse energy should not be too high to avoid any modifications in the layer properties resulting from the excessive heating of the surface layer. For the zones with a poor thermal contact, the rapid increase in the surface temperature may result in the layer surface modifications. In this case, it is not evident whether the measured phase shifts are attributed to different thermal contact quality or to the resulted layer modifications. For surface properties characterisation by lock-in thermography or active laser pyrometry, it may be advised to use a pyrometer of (330–1300 K) temperature measurements range which may provide measurements of a rather low temperature modulation of the surface under heating. At the low temperature modulation, the layer properties may be regarded as constant, and the phase shifts measurements are not sensitive to the layer properties dependence on a heating temperature. In addition, the undesirable surface oxidation may be avoided. To decrease laser heating fluence, it may be advised to increase the laser spot diameter on the layer surface. For the temperature measurements in this case, the infrared camera rather than the pyrometer should be used. The infrared camera may offer the advantage of making the sample surface thermography and phase measurements simultaneously for each pixel of the camera. For in situ measurements by active laser pyrometry and lock-in thermography in fusion installations (tokamaks), an optical scheme for laser beam transportation and thermal signal collection should be adjusted to the optical windows of the vacuum chamber. With optical windows of 100 mm diameter and adequately chosen optical system inside the vacuum chamber, a large surface of the inner walls of the vacuum chamber may be tested. For example, an optical scheme which was used for LIBS in situ measurements on JET [24,25] can be also applied for active laser thermography. In general, with additional plasma-facing mirrors, no special problems may be expected with the zone accessibility. In this case, to ensure the required optical mirror transmission and dust-free quality, a regular laser cleaning of the mirrors should be provided [26,27].
Acknowledgements The authors would like to express their gratitude to Mr. D. Farcage (DPC/SEARS/LISL, CEA Saclay) for the assistance in the development of the experimental setup scheme.
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