- Email: [email protected]
Thermographic phosphor thermometry in transient combustion: A theoretical study of heat transfer and accuracy
Available online at www.sciencedirect.com
Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 3603–3610
Combustion Institute www.elsevier.com/locate/proci
Thermographic phosphor thermometry in transient combustion: A theoretical study of heat transfer and accuracy Burak Atakan ⇑, Dennis Roskosch Thermodynamics and CENIDE, IVG, Mechanical and Process Engineering, Faculty of Engineering, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany Available online 12 June 2012
Abstract Thermographic phosphors (TPs) are used in combustion environments to study wall surface temperatures and heat fluxes. Recently they are also applied in unsteady environments like internal combustion engines to study the heat transfer to walls. The present study investigates theoretically some related effects leading to limitations of the method and thus trying to help experimenters to choose proper conditions for their experiments. The influence of absorptivity and film thickness is studied first. Then the unsteady heat flux of a surrounding gas phase is investigated as a function of film thickness and conductivity, including the effect on the temperatures which would be measured using TPs. The errors in temperature measurements and time resolution are investigated for typical cases. Finally the relation between the surface temperature and film thickness is investigated for combinations of two base materials (quartz and steel) coated with layers of Mg2SiO4 or SiO2, as representatives for TP host materials. It is seen that the maximum surface temperature is influenced in unsteady heat transfer processes even by relatively thin layers. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Thermographic phosphor; Surface temperature; Heat transfer
1. Introduction Surface temperatures and heat transfer to surfaces are important in many combustion systems, since most technical combustion takes place in closed environments and is either used to heat another fluid through a wall, or combustion is used within a work process to drive a piston or a turbine. In the latter case the heat transfer to the walls is regarded as a loss process; also, the heat transfer may lead to local flame quenching and combustion
⇑ Corresponding author. Tel.: +49 2033793355.
E-mail address: [email protected] (B. Atakan).
instabilities. Recently within the combustion community a renewed interest arose in an optical method to measure surface temperatures, detecting the temperature dependent phosphorescence of thermographic phosphors (TP) [1–5]. These thermographic phosphors are ceramic materials doped with either rare earth ions or transition metal ions. Several reviews are available explaining different aspects of the method. The host is generally optically inactive while the ions absorb certain wave lengths and emit generally at longer wave lengths. The evaluation of either the lifetime, the total intensity or spectral features can be used to measure surface temperatures [6,7]. The thermographic phosphor is often fixed on a surface
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.05.022
3604
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
to measure the temperature of this surface. The phosphor can either be used as a powder and fixed with an adhesive bonding material or it can be directly deposited on the surface using thin film techniques. The total film thicknesses are, depending on the method, between 0.5 and 60 lm. However, as is generally the case in thermometry, the thermographic phosphor indicates (or measures) its own temperature, thus the relation to the original surface temperature is of interest. This gets even more important when unsteady processes shall be studied using this method. An experimental study was conducted recently by Knappe et al. [8] which attracted our interest and motivated us to rethink the theory of surface temperature measurements using thermographic phosphors. These authors investigated wall temperatures in an optical internal combustion engine (ICE), where parts of the cylinder were made out of quartz. They coated parts of the quartz ring on the inner side, where the combustion takes place and excited the phosphor by a laser beam from either side, once through the quartz and once from the gas side and made crank angle resolved experiments. Using phosphor layers of different thicknesses of 60 lm or lower they found deviations between the two measured temperatures of up to 50 K. This is much larger than the given error bars which are generally below ±13 K for the averaged signals. From their experimental findings the authors gave some recommendations regarding the film thickness. However, it seems that the recommendations mainly hold for this given phosphor and adhesive, while a more general procedure for estimating such effects would be desirable. Theory could help in such cases to select the most appropriate setup and to estimate the remaining errors in the measured temperatures. Also it may be interesting to analyze values for typical film thicknesses, as they are deposited using thin film techniques like CVD or sol-gel methods for TP deposition on surfaces [9–13]. At least three effects or questions are involved here: First of all, assuming that a temperature gradient is present in the film, the question arises: why is it detected? When the laser beam would excite the phosphor in the whole film with small absorption, one would expect that one single decay time and thus one single, somehow averaged temperature would be detected, independent of the excitation direction. Thus one would aim to have a relation between this averaged temperature and the surface temperature. When differences in the temperatures after excitation from both sides are detectable, the absorption of the excitation light source must be important and has to be considered.
The second question is: how large can typical temperature differences between the front and the back side of such a film be expected to be under conditions relevant to IC engines and on which parameters do they depend and how will the temporal resolution of the measurement will be influenced? The final question comes from the often used replacement of the cylinder wall material by a transparent wall like quartz, how is the surface temperature or the temperature measurable by TPs changed by this replacement? The first question can be addressed from a spectroscopic point of view, neglecting details of heat transfer, regarding assumed temperature differences within the film and typical absorption characteristics. The second question can be addressed solving the energy balance for this unsteady one-dimensional conduction problem. And also a combination of both is interesting to get a feeling for the combined effect and the relation between the measured quantity and the physics behind it, which is aimed to be deduced from combustion heat transfer studies. For the third problem the second approach can be repeated using different material constants and material combinations. Thus a one-dimensional unsteady heat transfer modeling investigation is reported here which can also help to select appropriate experimental conditions and help in the interpretation of TP temperature measurements in ICEs. 2. Theory and model 2.1. Laser absorption and spatial averaging effects We will start explaining the procedure for the first problem of the relation between absorption of the excitation light source, temperature gradient in the film and the detected spatially integrated phosphorescence life times. The absorption of the excitation light source leads to the population of an excited state N1 from which the phosphorescence is emitted while returning to a lower lying energetic state with a temperature dependent rate k: @N 1 ¼ kðT Þ N 1 ð1Þ @t z One should keep in mind that the temperature and the population of the excited state generally both depend on the spatial coordinate z and on time t. The excitation should take place very fast at t = 0, which is appropriate for lasers with pulse lengths in the 10 ns regime compared with phosphorescence lifetimes of ls to ms. For this investigation it is assumed that the temporal change of the
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
temperature distribution is much slower than the phosphorescence lifetime and thus can be regarded as decoupled. This is justified by the La2O2S : Eu phosphor investigated in [8] its properties will be used here, having lifetimes in the ls regime and the results regarding the heat transfer, which will be described later, being at least 1–2 orders of magnitude slower. The initial distribution of ions in the excited state comes from the laser beam absorption, which is attenuated according to Beer Lambert’s law: IðzÞ ¼ I 0 expðaa zÞ
ð2Þ
leading to a initial relative distribution of the ions in the excited state, which follows the absorbed intensity: N 1;z;t¼0 ¼ b
I N 0 ¼ b N 0 expðaa zÞ I0
ð3Þ
aa is the total absorption coefficient (unit:1/m) while b 6 1 is the part of the absorbed intensity which is transfered to the excited radiating state in relation to the total absorbed intensity, since other non-emitting states may also be populated by the incoming light. Also, if a binder or adhesive is used, it may also be absorbing the excitation wave length to some amount and thus, reducing b. A related approach which also includes scattering was reported for isothermal systems by Feist and Heyes[14]. For lifetime evaluations, absolute intensities or number densities are not needed, so the main point is that the population in the excited state decreases exponentially along the z axis for a film of thickness L. In the following a finite volume scheme will be applied to solve the heat transfer problem, leading to Nmax finite volumes along the z axis with equal volumes, with z = 0 being at the surface and z = L being at the back side of the film, where it is in contact with the substrate. The phosphorescence is originated from all these finite volumes at different temperatures and with different initial populations of the excited state N1,0: I ph ðtÞ ¼ c
N max X
N 1;0 ðnÞekðT ðnÞÞt
ð4Þ
n¼0
The constant c (in units of Wm) is introduced for the conversion of population density to intensity. Since only relative values are needed in the present work, it can be set to an arbitrary value. The temperature dependence for the lifetime of this phosphor was taken from the literature [15], where a function was given, valid for temperatures between 420 and 508 K: kðT Þ ¼ ð5:240 expð0:02896 T ÞÞ1
ð5Þ
Thus the resulting spatially integrated time dependent phosphorescence intensity could be fitted to this function for temperature evaluation. In the
3605
results section the effect of the absorption coefficient on the total life time and thus on the evaluated surface temperatures will be discussed for different temperature gradients in the film. 2.2. Time dependent film heating From heat transfer text books [16] it is well known, that two characteristic dimensionless numbers should help to classify an unsteady conduction process, in order to get a feeling for characteristic time scales and the importance of temperature gradients within the solid, compared to temperature gradients in the boundary layer. These are the Fourier number and the Biot number. at Fo ¼ 2 ð6Þ L aL ð7Þ Bi ¼ k Within these formula k is the thermal conductivity a is the convection coefficient, a is the thermal diffusivity (a = k/(q cv) with the density q and the capacity of heat cv), t is the time and L is a characteristic length, in our case the thermographic phosphor film thickness. Now, one problem arises from the missing knowledge of the thermal parameters of the thermographic phosphor films, often embedded in an adhesive or binder, so that only typical regimes can be evaluated. Using a film thickness of 60 lm and an upper limit for the convection coefficient of a = 4500 W/(m2 K) [17] and values for fused silica [16] and for Mg2SiO4 which is the resulting substance coming from the HPC binder used in [8], one obtains Bi numbers of 0.2–0.1,which are in a regime where temperature gradients within the film start to get important, depending on the temperature deviation which may be tolerated, while a Fourier number of unity is reached at times around 4 ms. The latter are time scales which are not short for internal combustion engines. Thus, temperature gradients within such a film can be expected to play some role and it seems reasonable to perform some calculations for 1D unsteady conduction. The energy balance for the given unsteady 1Dsystem is straight forward: @T @ @T qcv ¼ k ð8Þ @t @z @z The spatial variable (z) extends from the thermographic phosphor surface at 0 to the outer surface of the wall G. Since the curvature of a quartz (or steel) ring within an engine cylinder is small, simple Cartesian coordinates are used and the curvature is neglected. The values of the material properties change with position, within the TP film (0 6 z 6 L) the values differ from the values above L. As thermographic phosphor host or
3606
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
binder two substances were investigated here: MgSiO2,SiO2 in order to evaluate the importance of the used material. Below, extending from L to G, there was always a 1 cm thick silicon dioxide or steel substrate, this thickness is enough to ensure that the heat flux through the outer wall is negligibly small in the period regarded (50 ms), so that thicker walls would not change the result. At the outer side (z = G) an isothermal boundary condition was used, while the boundary condition for the front side of the thermographic phosphor (z = 0) was a convective one. In order to simulate an ignition process with subsequent expansion, a simple gaussian temporal temperature shape was assumed in the gas phase, starting at 478.15 K (205 °C) and increasing to 1573 K (1300 °C), the maximum being at 15 ms with r = 1.5 ms. These seemed to be reasonable for the regarded case and resembles the profiles from [8]. The convection coefficients in engines are known to change with crank angle and with gas phase temperature. In the present study we used again the same gaussian temporal function for the convection coefficient as we did for temperature starting with a value of 250 W/m2 K and having a peak value of 2000 W/m2 K, as shown in Fig. 1. These values resemble the curve measured in an Otto engine from Bargende cited in [17]. The partial differential equation was solved numerically with the finite volume package FiPy [18] which is publicly available. For most calculations, the grid is chosen so that 10 points were set in the first 100 nm, 190 points within the following 95 lm and the remaining distance up to z=G was covered by 25 further grid points. In some test cases, the spatial resolution was increased by a factor of 5, but this did not influence the results, so the mentioned values were selected. The temporal integration was always performed up to 50 ms
Fig. 1. Change of the convection coefficient with time, the same relative profile is also used for the temperature profile.
with steps between 0.1 ls to 0.1 ms, again showing no important difference. The 50 ms were chosen to reflect an engine cycle speed of 1200 rpm. 3. Results and discussion 3.1. Laser absorption and spatial averaging effects Steady state conditions and resulting phosphorescence decays were evaluated for three cases. First a 60 lm film is regarded, which is at 500 K at its front side and at 450 K at its back side, where a quartz plate could follow. The absorption coefficients were varied for all cases between 6 104/m and 6 107/m. The resulting excitation intensities and the evaluated spatially integrated phosphorescence decay curves are shown in Fig. 2. The increasing absorption coefficient clearly leads to an increased spatial resolution, the probed region gets nearer and nearer to the
Fig. 2. Temporal phosphorescence decay(a) and spatial excitation intensity (b) for a film of 60 lm thickness; the excitation took place from the front side at z = 0. The absorption coefficient (in units of 1/m) (for both graphs) were 6 104(dashed line), 6 105(dotted line), 6 106 (crosses), 6 107(solid line) and the phosphorescence decay directly at the uppermost layer (circles). The dash dotted line in (b) is the assumed spatial temperature profile, values are on the right axes.
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
3607
strongly absorbing films. The expected temperature deviation values between the real surface temperature and the evaluated one, would have to be analysed with the concrete parameters of a given thermographic phosphor film. However, absorption coefficients of such films should be characterized in future also, since they are rarely available.
surface from which the light enters. Similar calculations (not included in the figure) were also performed for the laser beam entering from the colder back side and for two other cases a 6 lm thick layer with temperature gradients of 50 K or 5 K, respectively. The resulting temperatures from fitting the integral decay curves, integrated for a time interval from 0 to 20 ls, are summarized in Table 1. For low absorption coefficients, some average temperature is evaluated, however it is always biased towards the lower temperature, because the life times at lower temperatures are longer and thus the phosphorescence intensity from this region is higher and dominates. Only for very high absorption coefficients where only the first 1–2 lm of the layer is excited, values within 0.5 K of the real surface temperatures would be evaluated for the 60 lm film, as long as the gradient is not too high, as it is the case for the 6 lm film with 50 K temperature difference. Curvatures of the time resolved emission curves are observed in Fig. 2 for low values of the absorption coefficient. In experiments the dynamic range of a detector is in general limited and an integration time from 0 to 20 ls would include probably some interval below the detection limit or the noise level. Thus it was also tested how the integration time influences the resulting temperature, by coupling the integration time to the dynamic range and evaluating only ranges from I/I0 = 1 to I/I0 = 2d. This leads directly to shorter integration times (below (10 ls). Reducing d leads to a shift of both evaluated temperatures to higher values, but even reducing d to a value of 0.5, leading to integration times of 1.63 ls only, results in evaluated temperatures of 477.5 K and 476.6 K from excitation through the frontside and backside, respectively, in the case of the lowest evaluated absorption (aa = 6 1004/m). Such a low d value means that only intensity decays by 30% from I0 to 0.7 I0 would be evaluated, this would not be considered by most experimentalist. Thus, a further reduction of d does not seem to be meaningful, since the precission would also be reduced strongly if such small intensity decays are evaluated. In total, for measuring surface temperatures both is helpful, using very thin films, best with thicknesses around 1 lm and having
3.2. Time dependent film heating Typical results for the temporal temperature evolution at the top and the bottom of 60 lm thick coatings are shown in Fig. 3. Only the first 30 ms are shown, since the different temperatures converge for longer times. The evolution of the gas phase temperature Tg, which is an input to the calculation, is also included (with the values on the right axis). The top image is calculated with the material parameters of pure Mg2SiO4, while the properties of SiO2 were used in the lower part, both on a silicon dioxide substrate. The first obvious thing which is recognized is that the top surface temperatures Tf (solid lines) deviate by nearly 40 K for the maxima of the two cases. The dashed lines, showing the calculated temperatures of the bottom Tb of the phosphor layers deviate from the value at the top by 21 and 51 K, respectively. Although the Biot numbers are small, it is seen that the deviations of the two are not negligible, however they disappear within a few milliseconds. Also, a phase shift between the appearance of the maximum values is recognized between the gas phase and the top surface temperature and between the top and the bottom of the coating layer. The latter does not show a pronounced maximum as it is found for the top temperature. It should be mentioned that these two layer materials were chosen, because Mg2SiO4 is a material which is used in binders while silicon dioxide has a lower conductivity and is the base material at the same time, so the ’unperturbed’ surface temperature can be seen there. Also the conductivities of real coatings are expected to be lower than the values for pure materials due to voids and impurities, thus the lower diagram may even be more representative for real Mg2SiO4 layers. Another point should be emphasized: If it is aimed to measure the
Table 1 Resulting temperatures from spatially integrated phosphorescence decays and two different film thicknesses. f: laser enters from the front side, b: laser enters from the back side. L DT aa/(1/m) 04
6 10 6 1005 6 1006 6 1007
60 lm 50 K Tfit/K
6 lm 50 K Tfit/K
6 lm 5K Tfit/K
f
b
f
b
f
b
469.0 472.0 492.8 499.6
468.3 465.6 454.5 450.4
468.7 469.0 472.0 492.8
468.6 468.3 465.6 454.5
497.3 497.4 497.7 499.5
497.3 497.3 496.9 495.5
3608
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
Fig. 3. Thick film: comparison of modeled temperatures and temperatures which would be measurable with thermographic phosphors for two material combinations on SiO2: Mg2SiO4 (top) and SiO2 (bottom). The dotted line (Tg) is the assumed gas phase temperature (right scale). The solid line is the surface temperature (Tf) and the dashed line is the temperature at the bottom (Tb) of a 60 lm film. In between are the calculated temperatures which would be measurable for front illumination and aa = 3 105/m (dashed dotted), aa = 6 104/m (fine dots) and both for back side illumination(crosses and dots, respectively).
surface temperature of the silicon dioxide substrate in a combustion environment, the peak temperature would be underestimated by approximately 40 K, thus mainly if thick films shall be used, the temperature conductivities of the layer and the substrate should be matched as far as possible. Using the same procedure as described above, the spatially integrated time resolved phosphorescence intensities were calculated with the temperature profiles within the layers for each time step and TP temperatures were deduced from these profiles. This was done for illumination from the front and the back side. If the absorption is strong (aa 6 6 105/m) the temperature of the side from which the illumination takes place is reproduced within 1 K, thus these curves are not included in the figure. For less absorbing films some average temperature would be measured with phosphor thermometry, with an absorption coefficient of aa = 3 105/m differences would be measured
Fig. 4. Thin film: comparison of modeled temperatures and temperatures which would be measurable with thermographic phosphors for two material combinations on SiO2: Mg2SiO4 (top) and SiO2 (bottom). The dotted line (Tg) is the assumed gas phase temperature (right scale). The solid line is the surface temperature (Tf) and the dashed line is the temperature at the bottom (Tb) of a 6 lm film. In between, calculated temperatures which would be measurable for different absorption coefficients are plotted, but they cannot be distinguished from the upper surface temperature curve.
depending on the side of illumination, however, both would be not the correct boundary temperatures near the peak values. The deviations being larger for front side illumination than for back side illumination. Finally, if the film would be mainly transparent, the maximum surface temperature would be underestimated by 10–30 K. For comparison the results for 6 lm films on quartz are shown in Fig. 4. It is seen that the temperature gradient between the front and the back side is relatively small now, thus surface temperatures could be measured with good accuracy. 3.3. Comparison of silicon dioxide with steel Obviously quartz is only used as part of the engine cylinder, to obtain optical access. However, it is clear that wall temperatures due to different conductivities and capacities of heat will differ between a quartz and a steel wall, with or without a coating on the wall. Therefore a series
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
of calculations were performed, where the unsteady heat flux was calculated using the same temporal change in gas phase temperature and convection coefficient, but now for different material combinations. The substrate material was once chosen as steel and once as quartz, while coatings of SiO2 and Mg2SiO4 were considered on top of them, having different layer thicknesses between 200 nm and 60 lm. The results for the maximum temperatures on each film side are shown in Fig. 5. The first thing which is obvious for all combinations is that the difference in maximum temperatures between the front and the back side vanish with lowering the film thickness. It should be kept in mind that for most of the time, along a (modeled) ignition cycle the temperatures on both side are virtually the same, only at short times near ignition these differences are
Fig. 5. Modeled maximum temperatures (top) and temperature differences between the top and the bottom of each layer (bottom) for different material combinations as a function of film thickness. The solid lines and filled symbols are throughout surface temperatures, while the dotted lines and open symbols are always calculated for the boundary between film and substrate. From top to the bottom the curves represent the combinations of SiO2/SiO2 (triangles-left), Mg2SiO4/ SiO2 (squares), SiO2/steel (triangles), Mg2SiO4/steel (circles). In the lower graph also two analytical solutions are included (see: Eq. 9) for quartz (dotted) and Mg2SiO4 (dashed), details are explained in the text.
3609
obtained (compare also Fig. 3 at t 6 10 ms or t P 2 ms). The difference is most pronounced for the silicon dioxide film on both substrates, being largest on steel. In the lower part of the figure the maximum of the temperature difference is plotted, which is not the same as the difference in the maximum values between top and bottom, since there is a phase shift between both profiles. In the worst case modeled here, the deviations could reach 78 K and is also not negligible for layers of 10 lm. The situation relaxes for layers of higher conductivity. The maximum temperatures at the surface converge to a single value for the same substrate material, as it is expected. The differences in the maximum surface temperatures are substantial for coated surfaces compared to uncoated surfaces as can be compared for the quartz substrate case and also for the comparison of coated steel with coated quartz having the same coating thickness and material. However, the difference between coated steel and coated quartz is substantial throughout. The question remains how surface measurements using thermographic phosphors should be performed. The influence of the coating on the surface temperature can only be judged using some detailed heat transfer modeling, which finally will also be the best way to include such results into ICE models. The order of magnitude of the temperature difference within the layer can be judged reasonably well using the analytical formula for transient heat transfer into a semi-infinite homogeneous wall ([16]). In order to estimate the highest possible temperature difference within a film, the highest expected convection coefficient and the maximum gas phase temperatures (Tg) can be used in the formula, which can then be evaluated for typical times of 1 ms, leading to reasonable results (but are independent from the substrate below the film). The results for the differences evaluated at values for Tg = 1500 °C and a = 2000 W/(m2 K) at 1 ms are included for the two substrate materials. The formula from [16] is: T T0 x ax a2 a t ¼ erfc pffiffiffiffiffiffiffiffi exp þ 2 T g;1 T 0 k 2 at k pffiffiffiffiffiffiffiffi x a at ð9Þ erfc pffiffiffiffiffiffiffiffi þ k 2 at This formula may be most convenient for a fast estimation of typical errors due to temperature gradients within the thermographic phosphor film. 4. Conclusions A few points can be concluded from the work presented here, regarding temperature measurements
3610
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
with thermographic phosphors in transient combustion environments. Temperature gradients within the TP film may be important, even in films of thicknesses around 10 lm. The absorption coefficient of the film (including any binder) is an important parameter, if it is high the measured temperature is much nearer to the surface temperature than for low absorption coefficients, where biased average temperatures are measured. Surface temperatures of coated surfaces generally deviate substantially from those of uncoated surfaces, this is even more important when the substrate material is changed. Thus such transient measurements will be only valuable in an interplay of experiment and (heat transfer) modeling. Generally a matching of the thermal properties of the phosphor and the substrate material will not be possible, thus film thickness will remain the most important parameter which may be influenced by experimentalists. It should also be mentioned that some effects were not regarded yet, like the thermal radiation flux from and to the surface and the possibility of film heating by the excitation laser which might get important for highly absorbing films. These topics will be addressed in future work.
Acknowledgment Financial support by the DFG is gratefully acknowledged.
References [1] A. Omrane, F. Ossler, M. Alde´n, Exp. Therm. Fluid Sci. 28 (2004) 669–676. [2] M. Remie, G. Sa¨rner, M. Cremers, et al., Int. J. Heat Mass Transfer 51 (2008) 3144–3152. [3] H. Seyfried, M. Richter, K.-H. Nilsson, M. Alde´n, H. Schmidt, in: Collect. Tech. Pap. Aeros. Sci. Meet., Volvo Aero Corporation, Department 6660HS, SE461 81 TrollhSttan, vol. 18, 2011, pp. 12794–12802. [4] J. Bru¨bach, J. Zetterberg, A. Omrane, Z. Li, M. Alde´n, A. Dreizler, Appl. Phys. B 84 (2006) 537–541. [5] B. Bo¨hm, J. Brnbach, C. Ertem, A. Dreizler, Flow Turbul. Combust. 80 (2008) 507–529. [6] S. Allison, G. Gillies, Rev. Sci. Instrum. 68 (1997) 2615–2650. [7] A. Khalid, K. Kontis, Sensors 8 (2008) 5673–5744. [8] C. Knappe, P. Andersson, M. Algotsson, M. Richter, J. Linden, M. AldTn, M. Tuner, B. Johansson, SAE International 2011-01-1292, 2011. [9] C. Pflitsch, D. Viefhaus, B. Atakan, Chem. Vapor Depos. 13 (2007) 420–426. [10] C. Pflitsch, R. Siddiqui, C. Eckert, B. Atakan, Chem. Mater. 20 (2008) 2773–2778. [11] C. Pflitsch, R. Siddiqui, B. Atakan, Appl. Phys. A 90 (2008) 527–532. [12] A. Nebatti, C. Pflitsch, C. Eckert, B. Atakan, Prog. Org. Coat. 68 (2010) 146–150. [13] C. Eckert, C. Pflitsch, B. Atakan, Prog. Org. Coat. 68 (2010) 126–129. [14] J.P. Feist, A.L. Heyes, Heat Transfer Eng. 30 (2009) 1087–1095. [15] J. Bru¨bach, A. Dreizler, J. Janicka, Meas. Sci. Technol. 18 (2007) 764–770. [16] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, Hoboken, NJ, 2007. [17] G.P. Merker, C. Schwarz, Grundlagen Verbrennungsmotoren, Simulation der Gemischbildung, Verbrennung, Schadstoffbildung und Aufladung, Vieweg+Teubner Verlag, Wiesbaden, 2009. [18] J.E. Guyer, D. Wheeler, J.A. Warren, Comput. Sci. Eng. (2009) 6–15.
Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 3603–3610
Combustion Institute www.elsevier.com/locate/proci
Thermographic phosphor thermometry in transient combustion: A theoretical study of heat transfer and accuracy Burak Atakan ⇑, Dennis Roskosch Thermodynamics and CENIDE, IVG, Mechanical and Process Engineering, Faculty of Engineering, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburg, Germany Available online 12 June 2012
Abstract Thermographic phosphors (TPs) are used in combustion environments to study wall surface temperatures and heat fluxes. Recently they are also applied in unsteady environments like internal combustion engines to study the heat transfer to walls. The present study investigates theoretically some related effects leading to limitations of the method and thus trying to help experimenters to choose proper conditions for their experiments. The influence of absorptivity and film thickness is studied first. Then the unsteady heat flux of a surrounding gas phase is investigated as a function of film thickness and conductivity, including the effect on the temperatures which would be measured using TPs. The errors in temperature measurements and time resolution are investigated for typical cases. Finally the relation between the surface temperature and film thickness is investigated for combinations of two base materials (quartz and steel) coated with layers of Mg2SiO4 or SiO2, as representatives for TP host materials. It is seen that the maximum surface temperature is influenced in unsteady heat transfer processes even by relatively thin layers. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Thermographic phosphor; Surface temperature; Heat transfer
1. Introduction Surface temperatures and heat transfer to surfaces are important in many combustion systems, since most technical combustion takes place in closed environments and is either used to heat another fluid through a wall, or combustion is used within a work process to drive a piston or a turbine. In the latter case the heat transfer to the walls is regarded as a loss process; also, the heat transfer may lead to local flame quenching and combustion
⇑ Corresponding author. Tel.: +49 2033793355.
E-mail address: [email protected] (B. Atakan).
instabilities. Recently within the combustion community a renewed interest arose in an optical method to measure surface temperatures, detecting the temperature dependent phosphorescence of thermographic phosphors (TP) [1–5]. These thermographic phosphors are ceramic materials doped with either rare earth ions or transition metal ions. Several reviews are available explaining different aspects of the method. The host is generally optically inactive while the ions absorb certain wave lengths and emit generally at longer wave lengths. The evaluation of either the lifetime, the total intensity or spectral features can be used to measure surface temperatures [6,7]. The thermographic phosphor is often fixed on a surface
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.05.022
3604
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
to measure the temperature of this surface. The phosphor can either be used as a powder and fixed with an adhesive bonding material or it can be directly deposited on the surface using thin film techniques. The total film thicknesses are, depending on the method, between 0.5 and 60 lm. However, as is generally the case in thermometry, the thermographic phosphor indicates (or measures) its own temperature, thus the relation to the original surface temperature is of interest. This gets even more important when unsteady processes shall be studied using this method. An experimental study was conducted recently by Knappe et al. [8] which attracted our interest and motivated us to rethink the theory of surface temperature measurements using thermographic phosphors. These authors investigated wall temperatures in an optical internal combustion engine (ICE), where parts of the cylinder were made out of quartz. They coated parts of the quartz ring on the inner side, where the combustion takes place and excited the phosphor by a laser beam from either side, once through the quartz and once from the gas side and made crank angle resolved experiments. Using phosphor layers of different thicknesses of 60 lm or lower they found deviations between the two measured temperatures of up to 50 K. This is much larger than the given error bars which are generally below ±13 K for the averaged signals. From their experimental findings the authors gave some recommendations regarding the film thickness. However, it seems that the recommendations mainly hold for this given phosphor and adhesive, while a more general procedure for estimating such effects would be desirable. Theory could help in such cases to select the most appropriate setup and to estimate the remaining errors in the measured temperatures. Also it may be interesting to analyze values for typical film thicknesses, as they are deposited using thin film techniques like CVD or sol-gel methods for TP deposition on surfaces [9–13]. At least three effects or questions are involved here: First of all, assuming that a temperature gradient is present in the film, the question arises: why is it detected? When the laser beam would excite the phosphor in the whole film with small absorption, one would expect that one single decay time and thus one single, somehow averaged temperature would be detected, independent of the excitation direction. Thus one would aim to have a relation between this averaged temperature and the surface temperature. When differences in the temperatures after excitation from both sides are detectable, the absorption of the excitation light source must be important and has to be considered.
The second question is: how large can typical temperature differences between the front and the back side of such a film be expected to be under conditions relevant to IC engines and on which parameters do they depend and how will the temporal resolution of the measurement will be influenced? The final question comes from the often used replacement of the cylinder wall material by a transparent wall like quartz, how is the surface temperature or the temperature measurable by TPs changed by this replacement? The first question can be addressed from a spectroscopic point of view, neglecting details of heat transfer, regarding assumed temperature differences within the film and typical absorption characteristics. The second question can be addressed solving the energy balance for this unsteady one-dimensional conduction problem. And also a combination of both is interesting to get a feeling for the combined effect and the relation between the measured quantity and the physics behind it, which is aimed to be deduced from combustion heat transfer studies. For the third problem the second approach can be repeated using different material constants and material combinations. Thus a one-dimensional unsteady heat transfer modeling investigation is reported here which can also help to select appropriate experimental conditions and help in the interpretation of TP temperature measurements in ICEs. 2. Theory and model 2.1. Laser absorption and spatial averaging effects We will start explaining the procedure for the first problem of the relation between absorption of the excitation light source, temperature gradient in the film and the detected spatially integrated phosphorescence life times. The absorption of the excitation light source leads to the population of an excited state N1 from which the phosphorescence is emitted while returning to a lower lying energetic state with a temperature dependent rate k: @N 1 ¼ kðT Þ N 1 ð1Þ @t z One should keep in mind that the temperature and the population of the excited state generally both depend on the spatial coordinate z and on time t. The excitation should take place very fast at t = 0, which is appropriate for lasers with pulse lengths in the 10 ns regime compared with phosphorescence lifetimes of ls to ms. For this investigation it is assumed that the temporal change of the
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
temperature distribution is much slower than the phosphorescence lifetime and thus can be regarded as decoupled. This is justified by the La2O2S : Eu phosphor investigated in [8] its properties will be used here, having lifetimes in the ls regime and the results regarding the heat transfer, which will be described later, being at least 1–2 orders of magnitude slower. The initial distribution of ions in the excited state comes from the laser beam absorption, which is attenuated according to Beer Lambert’s law: IðzÞ ¼ I 0 expðaa zÞ
ð2Þ
leading to a initial relative distribution of the ions in the excited state, which follows the absorbed intensity: N 1;z;t¼0 ¼ b
I N 0 ¼ b N 0 expðaa zÞ I0
ð3Þ
aa is the total absorption coefficient (unit:1/m) while b 6 1 is the part of the absorbed intensity which is transfered to the excited radiating state in relation to the total absorbed intensity, since other non-emitting states may also be populated by the incoming light. Also, if a binder or adhesive is used, it may also be absorbing the excitation wave length to some amount and thus, reducing b. A related approach which also includes scattering was reported for isothermal systems by Feist and Heyes[14]. For lifetime evaluations, absolute intensities or number densities are not needed, so the main point is that the population in the excited state decreases exponentially along the z axis for a film of thickness L. In the following a finite volume scheme will be applied to solve the heat transfer problem, leading to Nmax finite volumes along the z axis with equal volumes, with z = 0 being at the surface and z = L being at the back side of the film, where it is in contact with the substrate. The phosphorescence is originated from all these finite volumes at different temperatures and with different initial populations of the excited state N1,0: I ph ðtÞ ¼ c
N max X
N 1;0 ðnÞekðT ðnÞÞt
ð4Þ
n¼0
The constant c (in units of Wm) is introduced for the conversion of population density to intensity. Since only relative values are needed in the present work, it can be set to an arbitrary value. The temperature dependence for the lifetime of this phosphor was taken from the literature [15], where a function was given, valid for temperatures between 420 and 508 K: kðT Þ ¼ ð5:240 expð0:02896 T ÞÞ1
ð5Þ
Thus the resulting spatially integrated time dependent phosphorescence intensity could be fitted to this function for temperature evaluation. In the
3605
results section the effect of the absorption coefficient on the total life time and thus on the evaluated surface temperatures will be discussed for different temperature gradients in the film. 2.2. Time dependent film heating From heat transfer text books [16] it is well known, that two characteristic dimensionless numbers should help to classify an unsteady conduction process, in order to get a feeling for characteristic time scales and the importance of temperature gradients within the solid, compared to temperature gradients in the boundary layer. These are the Fourier number and the Biot number. at Fo ¼ 2 ð6Þ L aL ð7Þ Bi ¼ k Within these formula k is the thermal conductivity a is the convection coefficient, a is the thermal diffusivity (a = k/(q cv) with the density q and the capacity of heat cv), t is the time and L is a characteristic length, in our case the thermographic phosphor film thickness. Now, one problem arises from the missing knowledge of the thermal parameters of the thermographic phosphor films, often embedded in an adhesive or binder, so that only typical regimes can be evaluated. Using a film thickness of 60 lm and an upper limit for the convection coefficient of a = 4500 W/(m2 K) [17] and values for fused silica [16] and for Mg2SiO4 which is the resulting substance coming from the HPC binder used in [8], one obtains Bi numbers of 0.2–0.1,which are in a regime where temperature gradients within the film start to get important, depending on the temperature deviation which may be tolerated, while a Fourier number of unity is reached at times around 4 ms. The latter are time scales which are not short for internal combustion engines. Thus, temperature gradients within such a film can be expected to play some role and it seems reasonable to perform some calculations for 1D unsteady conduction. The energy balance for the given unsteady 1Dsystem is straight forward: @T @ @T qcv ¼ k ð8Þ @t @z @z The spatial variable (z) extends from the thermographic phosphor surface at 0 to the outer surface of the wall G. Since the curvature of a quartz (or steel) ring within an engine cylinder is small, simple Cartesian coordinates are used and the curvature is neglected. The values of the material properties change with position, within the TP film (0 6 z 6 L) the values differ from the values above L. As thermographic phosphor host or
3606
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
binder two substances were investigated here: MgSiO2,SiO2 in order to evaluate the importance of the used material. Below, extending from L to G, there was always a 1 cm thick silicon dioxide or steel substrate, this thickness is enough to ensure that the heat flux through the outer wall is negligibly small in the period regarded (50 ms), so that thicker walls would not change the result. At the outer side (z = G) an isothermal boundary condition was used, while the boundary condition for the front side of the thermographic phosphor (z = 0) was a convective one. In order to simulate an ignition process with subsequent expansion, a simple gaussian temporal temperature shape was assumed in the gas phase, starting at 478.15 K (205 °C) and increasing to 1573 K (1300 °C), the maximum being at 15 ms with r = 1.5 ms. These seemed to be reasonable for the regarded case and resembles the profiles from [8]. The convection coefficients in engines are known to change with crank angle and with gas phase temperature. In the present study we used again the same gaussian temporal function for the convection coefficient as we did for temperature starting with a value of 250 W/m2 K and having a peak value of 2000 W/m2 K, as shown in Fig. 1. These values resemble the curve measured in an Otto engine from Bargende cited in [17]. The partial differential equation was solved numerically with the finite volume package FiPy [18] which is publicly available. For most calculations, the grid is chosen so that 10 points were set in the first 100 nm, 190 points within the following 95 lm and the remaining distance up to z=G was covered by 25 further grid points. In some test cases, the spatial resolution was increased by a factor of 5, but this did not influence the results, so the mentioned values were selected. The temporal integration was always performed up to 50 ms
Fig. 1. Change of the convection coefficient with time, the same relative profile is also used for the temperature profile.
with steps between 0.1 ls to 0.1 ms, again showing no important difference. The 50 ms were chosen to reflect an engine cycle speed of 1200 rpm. 3. Results and discussion 3.1. Laser absorption and spatial averaging effects Steady state conditions and resulting phosphorescence decays were evaluated for three cases. First a 60 lm film is regarded, which is at 500 K at its front side and at 450 K at its back side, where a quartz plate could follow. The absorption coefficients were varied for all cases between 6 104/m and 6 107/m. The resulting excitation intensities and the evaluated spatially integrated phosphorescence decay curves are shown in Fig. 2. The increasing absorption coefficient clearly leads to an increased spatial resolution, the probed region gets nearer and nearer to the
Fig. 2. Temporal phosphorescence decay(a) and spatial excitation intensity (b) for a film of 60 lm thickness; the excitation took place from the front side at z = 0. The absorption coefficient (in units of 1/m) (for both graphs) were 6 104(dashed line), 6 105(dotted line), 6 106 (crosses), 6 107(solid line) and the phosphorescence decay directly at the uppermost layer (circles). The dash dotted line in (b) is the assumed spatial temperature profile, values are on the right axes.
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
3607
strongly absorbing films. The expected temperature deviation values between the real surface temperature and the evaluated one, would have to be analysed with the concrete parameters of a given thermographic phosphor film. However, absorption coefficients of such films should be characterized in future also, since they are rarely available.
surface from which the light enters. Similar calculations (not included in the figure) were also performed for the laser beam entering from the colder back side and for two other cases a 6 lm thick layer with temperature gradients of 50 K or 5 K, respectively. The resulting temperatures from fitting the integral decay curves, integrated for a time interval from 0 to 20 ls, are summarized in Table 1. For low absorption coefficients, some average temperature is evaluated, however it is always biased towards the lower temperature, because the life times at lower temperatures are longer and thus the phosphorescence intensity from this region is higher and dominates. Only for very high absorption coefficients where only the first 1–2 lm of the layer is excited, values within 0.5 K of the real surface temperatures would be evaluated for the 60 lm film, as long as the gradient is not too high, as it is the case for the 6 lm film with 50 K temperature difference. Curvatures of the time resolved emission curves are observed in Fig. 2 for low values of the absorption coefficient. In experiments the dynamic range of a detector is in general limited and an integration time from 0 to 20 ls would include probably some interval below the detection limit or the noise level. Thus it was also tested how the integration time influences the resulting temperature, by coupling the integration time to the dynamic range and evaluating only ranges from I/I0 = 1 to I/I0 = 2d. This leads directly to shorter integration times (below (10 ls). Reducing d leads to a shift of both evaluated temperatures to higher values, but even reducing d to a value of 0.5, leading to integration times of 1.63 ls only, results in evaluated temperatures of 477.5 K and 476.6 K from excitation through the frontside and backside, respectively, in the case of the lowest evaluated absorption (aa = 6 1004/m). Such a low d value means that only intensity decays by 30% from I0 to 0.7 I0 would be evaluated, this would not be considered by most experimentalist. Thus, a further reduction of d does not seem to be meaningful, since the precission would also be reduced strongly if such small intensity decays are evaluated. In total, for measuring surface temperatures both is helpful, using very thin films, best with thicknesses around 1 lm and having
3.2. Time dependent film heating Typical results for the temporal temperature evolution at the top and the bottom of 60 lm thick coatings are shown in Fig. 3. Only the first 30 ms are shown, since the different temperatures converge for longer times. The evolution of the gas phase temperature Tg, which is an input to the calculation, is also included (with the values on the right axis). The top image is calculated with the material parameters of pure Mg2SiO4, while the properties of SiO2 were used in the lower part, both on a silicon dioxide substrate. The first obvious thing which is recognized is that the top surface temperatures Tf (solid lines) deviate by nearly 40 K for the maxima of the two cases. The dashed lines, showing the calculated temperatures of the bottom Tb of the phosphor layers deviate from the value at the top by 21 and 51 K, respectively. Although the Biot numbers are small, it is seen that the deviations of the two are not negligible, however they disappear within a few milliseconds. Also, a phase shift between the appearance of the maximum values is recognized between the gas phase and the top surface temperature and between the top and the bottom of the coating layer. The latter does not show a pronounced maximum as it is found for the top temperature. It should be mentioned that these two layer materials were chosen, because Mg2SiO4 is a material which is used in binders while silicon dioxide has a lower conductivity and is the base material at the same time, so the ’unperturbed’ surface temperature can be seen there. Also the conductivities of real coatings are expected to be lower than the values for pure materials due to voids and impurities, thus the lower diagram may even be more representative for real Mg2SiO4 layers. Another point should be emphasized: If it is aimed to measure the
Table 1 Resulting temperatures from spatially integrated phosphorescence decays and two different film thicknesses. f: laser enters from the front side, b: laser enters from the back side. L DT aa/(1/m) 04
6 10 6 1005 6 1006 6 1007
60 lm 50 K Tfit/K
6 lm 50 K Tfit/K
6 lm 5K Tfit/K
f
b
f
b
f
b
469.0 472.0 492.8 499.6
468.3 465.6 454.5 450.4
468.7 469.0 472.0 492.8
468.6 468.3 465.6 454.5
497.3 497.4 497.7 499.5
497.3 497.3 496.9 495.5
3608
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
Fig. 3. Thick film: comparison of modeled temperatures and temperatures which would be measurable with thermographic phosphors for two material combinations on SiO2: Mg2SiO4 (top) and SiO2 (bottom). The dotted line (Tg) is the assumed gas phase temperature (right scale). The solid line is the surface temperature (Tf) and the dashed line is the temperature at the bottom (Tb) of a 60 lm film. In between are the calculated temperatures which would be measurable for front illumination and aa = 3 105/m (dashed dotted), aa = 6 104/m (fine dots) and both for back side illumination(crosses and dots, respectively).
surface temperature of the silicon dioxide substrate in a combustion environment, the peak temperature would be underestimated by approximately 40 K, thus mainly if thick films shall be used, the temperature conductivities of the layer and the substrate should be matched as far as possible. Using the same procedure as described above, the spatially integrated time resolved phosphorescence intensities were calculated with the temperature profiles within the layers for each time step and TP temperatures were deduced from these profiles. This was done for illumination from the front and the back side. If the absorption is strong (aa 6 6 105/m) the temperature of the side from which the illumination takes place is reproduced within 1 K, thus these curves are not included in the figure. For less absorbing films some average temperature would be measured with phosphor thermometry, with an absorption coefficient of aa = 3 105/m differences would be measured
Fig. 4. Thin film: comparison of modeled temperatures and temperatures which would be measurable with thermographic phosphors for two material combinations on SiO2: Mg2SiO4 (top) and SiO2 (bottom). The dotted line (Tg) is the assumed gas phase temperature (right scale). The solid line is the surface temperature (Tf) and the dashed line is the temperature at the bottom (Tb) of a 6 lm film. In between, calculated temperatures which would be measurable for different absorption coefficients are plotted, but they cannot be distinguished from the upper surface temperature curve.
depending on the side of illumination, however, both would be not the correct boundary temperatures near the peak values. The deviations being larger for front side illumination than for back side illumination. Finally, if the film would be mainly transparent, the maximum surface temperature would be underestimated by 10–30 K. For comparison the results for 6 lm films on quartz are shown in Fig. 4. It is seen that the temperature gradient between the front and the back side is relatively small now, thus surface temperatures could be measured with good accuracy. 3.3. Comparison of silicon dioxide with steel Obviously quartz is only used as part of the engine cylinder, to obtain optical access. However, it is clear that wall temperatures due to different conductivities and capacities of heat will differ between a quartz and a steel wall, with or without a coating on the wall. Therefore a series
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
of calculations were performed, where the unsteady heat flux was calculated using the same temporal change in gas phase temperature and convection coefficient, but now for different material combinations. The substrate material was once chosen as steel and once as quartz, while coatings of SiO2 and Mg2SiO4 were considered on top of them, having different layer thicknesses between 200 nm and 60 lm. The results for the maximum temperatures on each film side are shown in Fig. 5. The first thing which is obvious for all combinations is that the difference in maximum temperatures between the front and the back side vanish with lowering the film thickness. It should be kept in mind that for most of the time, along a (modeled) ignition cycle the temperatures on both side are virtually the same, only at short times near ignition these differences are
Fig. 5. Modeled maximum temperatures (top) and temperature differences between the top and the bottom of each layer (bottom) for different material combinations as a function of film thickness. The solid lines and filled symbols are throughout surface temperatures, while the dotted lines and open symbols are always calculated for the boundary between film and substrate. From top to the bottom the curves represent the combinations of SiO2/SiO2 (triangles-left), Mg2SiO4/ SiO2 (squares), SiO2/steel (triangles), Mg2SiO4/steel (circles). In the lower graph also two analytical solutions are included (see: Eq. 9) for quartz (dotted) and Mg2SiO4 (dashed), details are explained in the text.
3609
obtained (compare also Fig. 3 at t 6 10 ms or t P 2 ms). The difference is most pronounced for the silicon dioxide film on both substrates, being largest on steel. In the lower part of the figure the maximum of the temperature difference is plotted, which is not the same as the difference in the maximum values between top and bottom, since there is a phase shift between both profiles. In the worst case modeled here, the deviations could reach 78 K and is also not negligible for layers of 10 lm. The situation relaxes for layers of higher conductivity. The maximum temperatures at the surface converge to a single value for the same substrate material, as it is expected. The differences in the maximum surface temperatures are substantial for coated surfaces compared to uncoated surfaces as can be compared for the quartz substrate case and also for the comparison of coated steel with coated quartz having the same coating thickness and material. However, the difference between coated steel and coated quartz is substantial throughout. The question remains how surface measurements using thermographic phosphors should be performed. The influence of the coating on the surface temperature can only be judged using some detailed heat transfer modeling, which finally will also be the best way to include such results into ICE models. The order of magnitude of the temperature difference within the layer can be judged reasonably well using the analytical formula for transient heat transfer into a semi-infinite homogeneous wall ([16]). In order to estimate the highest possible temperature difference within a film, the highest expected convection coefficient and the maximum gas phase temperatures (Tg) can be used in the formula, which can then be evaluated for typical times of 1 ms, leading to reasonable results (but are independent from the substrate below the film). The results for the differences evaluated at values for Tg = 1500 °C and a = 2000 W/(m2 K) at 1 ms are included for the two substrate materials. The formula from [16] is: T T0 x ax a2 a t ¼ erfc pffiffiffiffiffiffiffiffi exp þ 2 T g;1 T 0 k 2 at k pffiffiffiffiffiffiffiffi x a at ð9Þ erfc pffiffiffiffiffiffiffiffi þ k 2 at This formula may be most convenient for a fast estimation of typical errors due to temperature gradients within the thermographic phosphor film. 4. Conclusions A few points can be concluded from the work presented here, regarding temperature measurements
3610
B. Atakan, D. Roskosch / Proceedings of the Combustion Institute 34 (2013) 3603–3610
with thermographic phosphors in transient combustion environments. Temperature gradients within the TP film may be important, even in films of thicknesses around 10 lm. The absorption coefficient of the film (including any binder) is an important parameter, if it is high the measured temperature is much nearer to the surface temperature than for low absorption coefficients, where biased average temperatures are measured. Surface temperatures of coated surfaces generally deviate substantially from those of uncoated surfaces, this is even more important when the substrate material is changed. Thus such transient measurements will be only valuable in an interplay of experiment and (heat transfer) modeling. Generally a matching of the thermal properties of the phosphor and the substrate material will not be possible, thus film thickness will remain the most important parameter which may be influenced by experimentalists. It should also be mentioned that some effects were not regarded yet, like the thermal radiation flux from and to the surface and the possibility of film heating by the excitation laser which might get important for highly absorbing films. These topics will be addressed in future work.
Acknowledgment Financial support by the DFG is gratefully acknowledged.
References [1] A. Omrane, F. Ossler, M. Alde´n, Exp. Therm. Fluid Sci. 28 (2004) 669–676. [2] M. Remie, G. Sa¨rner, M. Cremers, et al., Int. J. Heat Mass Transfer 51 (2008) 3144–3152. [3] H. Seyfried, M. Richter, K.-H. Nilsson, M. Alde´n, H. Schmidt, in: Collect. Tech. Pap. Aeros. Sci. Meet., Volvo Aero Corporation, Department 6660HS, SE461 81 TrollhSttan, vol. 18, 2011, pp. 12794–12802. [4] J. Bru¨bach, J. Zetterberg, A. Omrane, Z. Li, M. Alde´n, A. Dreizler, Appl. Phys. B 84 (2006) 537–541. [5] B. Bo¨hm, J. Brnbach, C. Ertem, A. Dreizler, Flow Turbul. Combust. 80 (2008) 507–529. [6] S. Allison, G. Gillies, Rev. Sci. Instrum. 68 (1997) 2615–2650. [7] A. Khalid, K. Kontis, Sensors 8 (2008) 5673–5744. [8] C. Knappe, P. Andersson, M. Algotsson, M. Richter, J. Linden, M. AldTn, M. Tuner, B. Johansson, SAE International 2011-01-1292, 2011. [9] C. Pflitsch, D. Viefhaus, B. Atakan, Chem. Vapor Depos. 13 (2007) 420–426. [10] C. Pflitsch, R. Siddiqui, C. Eckert, B. Atakan, Chem. Mater. 20 (2008) 2773–2778. [11] C. Pflitsch, R. Siddiqui, B. Atakan, Appl. Phys. A 90 (2008) 527–532. [12] A. Nebatti, C. Pflitsch, C. Eckert, B. Atakan, Prog. Org. Coat. 68 (2010) 146–150. [13] C. Eckert, C. Pflitsch, B. Atakan, Prog. Org. Coat. 68 (2010) 126–129. [14] J.P. Feist, A.L. Heyes, Heat Transfer Eng. 30 (2009) 1087–1095. [15] J. Bru¨bach, A. Dreizler, J. Janicka, Meas. Sci. Technol. 18 (2007) 764–770. [16] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, Hoboken, NJ, 2007. [17] G.P. Merker, C. Schwarz, Grundlagen Verbrennungsmotoren, Simulation der Gemischbildung, Verbrennung, Schadstoffbildung und Aufladung, Vieweg+Teubner Verlag, Wiesbaden, 2009. [18] J.E. Guyer, D. Wheeler, J.A. Warren, Comput. Sci. Eng. (2009) 6–15.