On the effects of coating thickness in transient heat transfer experiments using thermochromic liquid crystals

Accepted Manuscript On the effects of coating thickness in transient heat transfer experiments using thermochromic liquid crystals Sebastian Schulz, Stefan Brack, Alexandros Terzis, Jens von Wolfersdorf, Peter Ott PII: DOI: Reference:

S0894-1777(15)00211-3 http://dx.doi.org/10.1016/j.expthermflusci.2015.08.011 ETF 8544

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

13 May 2015 8 July 2015 16 August 2015

Please cite this article as: S. Schulz, S. Brack, A. Terzis, J.v. Wolfersdorf, P. Ott, On the effects of coating thickness in transient heat transfer experiments using thermochromic liquid crystals, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.08.011

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On the effects of coating thickness in transient heat transfer experiments using thermochromic liquid crystals Sebastian Schulza , Stefan Bracka , Alexandros Terzisa,b , Jens von Wolfersdorfa , Peter Ottb a Institute b Group

of Aerospace Thermodynamics (ITLR), University of Stuttgart, Pfaffenwaldring 31, Stuttgart D-70569, Germany ´ of Thermal Turbomachinery (GTT), Ecole Polytechnique F´ ed´ erale de Lausanne, CH-1015 Lausanne, Switzerland

Abstract Transient heat transfer experiments typically employ thermochromic liquid crystals to temporally map surface temperatures. The desired heat transfer coefficient is then calculated from the solution of Fourier’s 1D transient heat conduction equation which is set to model the wall temperature at the solid-fluid interface. However, the experimental conditions do not always justify this assumption due to occurring layers of additional paint shielding the actual liquid crystal from the immediate exposure to the working fluid. The disregard of these additional layers with respect to their thicknesses in the evaluation process produces biased heat transfer results. In order to systematically assess the effect of coating thickness on the evaluated heat transfer, the present investigation reports on the application of three different liquid crystal types in layers in transient experiments. These were conducted for two different flow regimes using separate test facilities, i.e. a flow over a tetrahedra-shaped vortex generator and jet flows from an in-line row of orifices within a low aspect ratio impingement channel. Reynolds numbers of 100,000 and 50,000 based on hydraulic and jet orifice diameter were investigated, respectively. Upon consideration of the actual liquid crystals’ coating thicknesses from measurements, the investigations show that disregarding the layer thicknesses can lead to a significant underestimation of the resulting heat transfer, particularly for large thicknesses. By taking into account the respective coating thicknesses the experimental discrepancies could be reduced from 14% to less than 5%, accomplishing high data redundancy. Keywords: liquid crystal thermography, transient heat transfer, layer thickness measurements, convective heat transfer, vortex generator, jet impingement

1. Introduction Thermal management designs, as encountered in a variety of technical applications, rely on the accurate knowledge of their inherent heat transfer characteristics to ensure proper component functionality. In Email addresses: [email protected] (Sebastian Schulz), [email protected] (Alexandros Terzis) Preprint submitted to Experimental Thermal and Fluid Science

August 20, 2015

the context of better understanding heat transfer phenomena, liquid crystal thermography (LCT) offers a thorough insight into the convective processes at work. Its versatile applicability paired with high spatial detail and the non-intrusive nature has propelled LCT to mature into an attractive tool in convective heat transfer research. In essence, coatings of thermochromic liquid crystals (TLC) are employed to measure surface temperature distributions from which highly resolved heat transfer coefficient (HTC) maps can be deduced. An extensively used experimental approach to measure HTC distributions through LCT is the transient technique, which will be discussed in the subsequent section. In order to stimulate demands for even more reliable HTC data for more complex industrial applications, numerous research efforts have been undertaken to explore more advanced approaches to refine the transient technique. From the vast body of available literature a few examples are given below. When using TLC in experimental heat transfer studies one of the most crucial parts lies in the interpretation of the color-temperature relationship displayed by the crystals. Human perception of color introduces an undesirable uncertainty in the temperature measurement. Hence, Akino et al. [1] described methods to exclude the error stemming from individual color sensation. Furthermore, Baughn [2] reported on the application of narrow-bandwidth liquid crystals, which typically display an active range of around 1K. They appear to have the advantage of being less sensitive to illumination, lighting and viewing angle effects rendering a lower uncertainty in the temperature measurement. Poser et al. [3] concurred with this understanding and further described that peak intensity methods (e.g. the maximum intensity of the green color channel) possess the pivotal advantage to detect even weak TLC indication signals compared to hue methods. Considering the nature of the transient experiment the change in the fluid temperature cannot always be sufficiently approximated in terms of an ideal step due to a rather gradual temperature variation, depending on the experimental setup. Here, Gillespie et al. [4] and Newton et al. [5] described solutions of Fourier’s 1D heat conduction equation using a single and a series of exponential functions, respectively, to model the actual freestream temperature evolution more adequately. Ireland and Jones [6] and Kwak [7] summarized these and other analytical extensions. Conclusively, their respective implementation into the data reduction process yields the potential to significantly reduce the relative error in the HTC calculations. However, these solutions only hold true if the semi-infinite boundary condition is valid. The case of finite wall thickness was addressed by e.g. Vogel and Weigand [8]. Their investigations showed that the classical maximum measurement times could be extended by a factor of 4, accepting the finite wall thickness to affect the evaluated HTC by less than 1%. The problem of wall curvature was discussed by e.g. Buttsworth and Jones [9] and Wagner et al. [10]. The advent of more powerful computational capabilities has increasingly paved the way for innovative signal processing techniques. These methods are designed to best exploit the experimental data. In reference to accurately determining the liquid crystal indication times, Camci et al. [11] introduced a hue-based 2

detection method. Contrarily, Poser et al. [3] devised an advanced approach basing the detection of the TLC indication on the signal’s peak intensity of the green color. Selectively, a signal pre-conditioning was suggested in Poser et al. [12]. Additional elaborate strategies to attain even more robust HTC results gave rise to investigations conducted by, e.g. Wang et al. [13], Talib et al. [14], and Van Treuren et al. [15]. All of their experiments incorporated mixtures of multiple liquid crystals with different activation temperatures. Thus, the temporal tracking of multiple indication events during a transient experiment could be accomplished, yielding several temperature-time correlations. Here, Wang et al. and Talib et al. used the full-intensity history in their data analysis. Wang et al. used a least-squares regression method to scale and match their monochrome intensity histories to ultimately yield heat transfer coefficient distributions, while Talib et al. implemented a pre-calculated lookup table consisting of ideal intensity-histories intended to be matched with the experimental green color signals. Van Treuren et al. applied a peak intensity method. Apart from using the transient TLC histories for the mere determination of heat transfer quantities, the recorded information can also be used to construct and analyze additional, system specific parameters. Ferguson [16] demonstrated the use of experimental data to perform an in-situ TLC calibration next to the determination of HTCs. The advantage of this method, a hue-based technique, is the implicit consideration of calibration parameters, e.g. lighting and viewing angles. Although, approaches such as the one presented by [16] are very attractive, their complexity and sensitivity to small changes challenges their application. Another common approach to calibrate TLC is performed in steady-state fashion. Kakade et al. [17] and Abdullah et al. [18] dedicated their research to investigate several influential parameters and characterize their impact on the optical properties of TLC. The assessment also examined film thickness effects, and it was concluded that TLC coatings should be of sufficient thickness to avoid accelerated aging and a decrease in reflectivity (too thin coatings).

[Figure 1 about here.] Despite the numerous innovations to inspire heat transfer studies of greater detail, to the authors’ knowledge little attention has been paid to the effect of coating thickness on the calculated HTCs from transient experiments. Therefore, the current study presents the implementation of an analytical model to account for the film thickness of TLC layers. Furthermore, the authors demonstrate, theoretically and experimentally, the impact on the HTC evaluation once the TLC coating thickness is neglected. In addition, two separate transient experiments involving impinging jets and vortex generators (VG) are illustrated. These experiments employ up to three layers of TLC with different indication temperatures, for which the film thicknesses were measured. The results of these experiments indicate the importance to consider the coating thickness in the data analysis. Otherwise, heat transfer coefficients can be significantly underestimated.

3

2. Theoretical Background The underlying principle of the transient technique is to perform heat transfer experiments using the response of TLC to a time-varying heat flux to locally indicate surface temperatures with respect to a previously calibrated indication temperature. Comprehensive reviews on the transient technique can be found in Hippensteele and Poinsatte [19] and Ekkad and Han [20]. Usually, narrow-bandwidth TLC are applied in the context of this method in conjunction with a wall material of low thermal conductivity. During a transient experiment the surface of interest is initially at isothermal state with a known temperature, T0 . As the surface is exposed to a step change in the fluid temperature, Tref , the wall temperature follows the imposed temperature change, depending on the local heat transfer coefficient. By using a calibrated liquid crystal the surface temperature evolution, Tw (t), can visually be traced in time across the area of interest in terms of the TLC’s time-dependent colorplay with a digital color video camera. With respect to the mathematical formulation of this experimental procedure the behavior of the wall temperature can be described by solving Fourier’s 1D transient heat conduction equation for a semi-infinite wall and a convective boundary assumption. The solution to this problem considering a time-invariant heat transfer coefficient, h, can be found in, e.g. Carslaw and Jaeger [21]. Conveniently, the solid-fluid interface (z = 0) is often considered rendering the following equation, Θ=

Tw (t) − T0 = 1 − exp Tref − T0



h2 aw t 2 kw



erfc

 √  h aw t . kw

(1)

Here, aw and kw are the thermal diffusivity and thermal conductivity of the wall material, respectively.

[Figure 2 about here.] [Figure 3 about here.] As the investigation of complex internal cooling designs receives increasing attention, one particular experimental arrangement presides. For intricate geometries the optical accessibility is typically restricted and the surface of interest only available to be observed from the outside of the model. Hence, the TLC application follows a specific sequence. Figure 1(a) illustrates that the liquid crystal is applied to the investigated surface directly, followed by a layer of black paint to better contrast the TLCs colorplay. At this point it is noteworthy that the black backing of the liquid crystal entails a shielding/prevention from direct exposure to the working fluid. When Eq. (1) is now used to evaluate experiments of this kind (Fig. 1), the assumption is made that the temperature change of the working fluid immediately impacts the liquid crystal colorplay. In reality, however, heat conduction effects through the black backing paint delay the activation of the TLC. Therefore, the solution as described by Eq. (1) is inadequate to reasonably assess this experimental circumstance. Nevertheless, the general solution, as derived by [21], can be used to describe the wall temperature 4

at any arbitrary depth of the model material. In view of the fact that differences between the thermal properties of the wall material, the TLC, and the backing paint are relatively small (≤ 4%) ([22], [23]), the following equation, Tw (z, t) − T0 = erfc Tref − T0



z √ 2 aw t



− exp



hz h2 aw t + 2 kw kw



× erfc



√  z h aw t √ + , kw 2 aw t

(2)

can be used to account for layer thickness effects. Here, the variable z resembles the layer thickness of the considered coating. Thus, this expression can also be applied when multiple layers of different liquid crystals are in use, as indicated in Fig. 1(b). The relative deviation (h0 − hz )/hz that occurs when Eq. (1) is selected

over Eq. (2) to evaluate the respective heat transfer experiments is shown in Fig. 2 as a function of the dimensionless temperature, Θ. Here, h0 is the HTC without consideration of any layer thickness, calculated using Eq. (1). Vice versa, hz is determined using Eq. (2). The plots are created for the example case of hz = 200 W/(m2 K). The graphs in Fig. 2 substantiate the notion that with increasing layer thickness the heat transfer coefficient can be tremendously underestimated when thickness is not considered. This can be countered with increasing Θ attenuating the underestimation of the HTC.

3. Experimental Setup Considering the scope of this work separate experiments were conducted at two independent test facilities located at the ITLR and GTT considering two different flow regimes. A flow over a VG of tetrahedra-shaped design ((A), ITLR) and a narrow impingement channel with a single inline row of jet holes ((B), GTT). The test facilities are described below.

Test facility (A) For the experiments with vortex generators the test facility described by [24] was modified and used to investigate the effect of TLC coating thickness on heat transfer. The test rig is depicted in Figure 3(a). The setup employed a vacuum pump which operated in suction mode to generate invariant mass flow conditions. Hence, air was drawn from the ambient through an inlet funnel (1) equipped with a dust filter and, subsequently, passed through a mesh heater (2). The heater was designed according to Wang et al. [25] and Ireland et al. [26]. It had a square cross section and consisted of six stainless steel wire meshes. Respectively three meshes were combined in series. The two resulting modules were each connected to a 9.75kW power supply (150V , 65A), which could arbitrarily be adjusted. Thus, homogeneous temperature profiles and temperature steps ranging between 20K and 60K could be realized. Succeeding the heater the flow was folded in a converging transition piece (3) to match the test section’s rectangular inlet geometry. A honeycomb flow straightener (4) at the entrance of the test section attenuated occurring perturbations in 5

the flow, procuring a homogeneous velocity profile. While it was made of Perspex, the dimensions of the test section (5) can be deduced from Figure 3(b). For the heat transfer measurements a Perspex flat plate (6) was used, which was placed 250mm downstream of the flow straightener at half the channel height. Hence, it divided the test section into two symmetric sub-channels with a hydraulic diameter, Dh , of 80mm each. The flat plate was 30mm thick and 960mm long with a semi-elliptic leading and trailing edge. A trip wire with a diameter of 1mm was located at the leading edge/flat plate junction (60mm downstream of the tip) to ensure a fully turbulent boundary layer at the location of the VG. In the experiments two identical VG were utilized. Their dimensions and arrangement are presented in Fig. 3(b). After passing the test section the flow exited through a system of pipes (7) connecting to the vacuum pump. The piping system included a Venturi nozzle (DIN-ISO 5167) and a flow regulation valve for measurement and regulation of the mass flow rate. Altogether, mass flow measurements ≈ 0.36kg/s were carried out according to the targeted Reynolds number of 100,000.

Measurements of the fluid temperature were carried out in the bottom sub-channel using three pairs of T -type bead thermocouples with a wire diameter of 0.076mm. These were placed 420mm, 720mm, and 1020mm downstream of the flow straightener along the sub-channels center plane. Their respective location is indicated in Fig. 3(b). The temperature data was recorded using a NI-USB6218 data acquisition system incorporating an I.E.D. thermocouple amplifier with reference temperature compensation at a sampling rate of 10Hz, fast enough to guarantee an adequate temporal resolution of the temperature history [7]. For the subsequent data analysis each pair of thermocouple readings was averaged to deduce a representative, timeresolved thermocouple signal at each downstream measurement location. These signals were then applied to Eq. (1) and Eq. (2) while making use of Duhamel’s principle to account for a non-ideal temperature step, as can be found in e.g. [7]. Additionally, several 35W warm white (3000K) fluorescent lamps were positioned appropriately to illuminate the test surfaces uniformly. Thus, the liquid crystal’s colorplay could be recorded with a digital color video camera (SONY DFW-X710) at a frame rate of 15Hz which was positioned above the test section. [Figure 4 about here.] Test facility (B) [Table 1 about here.] Experiments were also carried out in the impingement cooling test rig of GTT (EPFL) which has been successfully used in the past for the investigation of different geometries of narrow impingement channels, e.g. Terzis et al. [27, 28, 29]. Therefore, only a brief overview will be given here. Figure 4(a) shows a 3D representation of the test facility which mainly consists of an inlet flare (1), a metallic fast response heater mesh (2) which increases the temperature of the flow for the transient experiment, a wooden plenum (3) in 6

order to eliminate thermal losses with the surroundings and the narrow impingement channel (4) placed at the top of the test rig. The air source of this open circuit wind tunnel, operated in suction mode, was a oil dealed rotary vane pump (SOGEVAC SV 1200). The overall mass flow was controlled with a laminar flow element (Tetratec 50 MCO2-06) and the jet average Reynolds number, based on the jet diameter (Dj ), was determined as follows, ReDj =

4m ˙ , nπDj µ

(3)

where n is the number of jets, in this case five. The narrow impingement channel, shown in Figure 4(b), is manufactured of transparent acrylic material, an hence, the evolution of the liquid crystals on the target plate of the narrow passage is recorded from the backside of the target plate, as illustrated in Fig. 1. The narrow impingement channel consists of a single row of five impingement holes. The jet spacing in streamwise direction and the channel width are X/Dj =6.67 and Y /Dj =5.33, respectively. The channel height is Z/Dj =2. All impingement jets are supplied from the common plenum, and hence, they are fed from the same total pressure. Several ReDj , based on the jet diameter Dj , were investigated from which the case of ReDj = 50, 000 is currently presented. The evolution of the flow temperature, acquired by a NI-9213 module, is obtained with five K-type thermocouples with exposed junction (Omega 5SC Series, 0.076mm wire diameter) and equally inside the wooden plenum from TC1 to TC5, as shown in Figure 4(b). Note also that due to the low plenum velocities, i.e. 61m/s, which are typical for this kind of experiments and when the jets are plenum fed, thermal inertia of commercial thermocouples causes a delay, lagging from the real plenum temperature history. Therefore, the evolution of the driving temperature was corrected for thermocouple time constants according to Terzis et al.[30] prior to their application in Eq. (1) and Eq. (2) considering again Duhamel’s superposition principle. The evolution of the liquid crystal colour-play on the target plate of the cooling cavity is recorded at 25fps with CCD camera (AVT Pike F210C). Uniform illumination through the complete length of the channel is provided by two fluorescent white lights mounted on both sides of the test rig eliminating shadows and reflections. [Figure 5 about here.] The liquid crystal test surfaces Following the description of the two test facilities, the two experimental cases are referred to as (A) and (B) from here on. For the heat transfer experiments multiple liquid crystals of different indication temperatures were used in both test facilities and applied to the respective test surface using an air brush technique. The various TLCs were spray painted in layers, not as a mixture, in two distinct sequences, namely ΨI -descending order and ΨII -ascending order (in terms of their indication temperature). Finally, these layers were covered with a single layer of black backing paint, as shown in Fig. 5. 7

The preparation of the flat plate in the case of (A) entailed a division of the area of interest into two segments, namely AT LC and BT LC (see Fig. 3(b)). Onto both sides three liquid crystals by Hallcrest (G30C1W, G35C1W, G40C1W) were sprayed individually. Prior to their application the liquid crystals and the black paint were mixed with distilled water at a ratio of νH20 /νT LC = 1/5. The total amount consumed was about 0.03ml/cm2 for all layers. The order in which the TLCs were applied onto one side was opposite with respect to the other. Hence, it is possible by means of one experiment to, independently, investigate the impact of the TLC layers’ sequence - ascending/descending order - on the HTC results while retaining identical experimental conditions. From Table 1 the sequence assigned to each side can be deduced.

[Figure 6 about here.] In view of the case of (B) the impingement plate was also equipped with three layers of liquid crystals by Hallcrest (R35C1W, R38C1W, R41C1W) in the fashion described above. Similarly, each liquid crystal layer and the black paint were mixed with distilled water at a ratio of νH20 /νT LC = 2/3 and the amount of mixture consumed was about 0.025ml/cm2 for all layers. However, in contrast to the approach taken in the case of the flat plate, two separate, yet similar, experiments were conducted to obtain HTC data for both TLC sequences.

[Figure 7 about here.] In both cases, the overall coating thickness, δ, of the dried TLC including the black paint was carefully measured. In the case of (A) the thickness was mechanically gauged with an accuracy of ±10µm, whereas

for (B) an integral coating thickness gauge (Elcometer 456) typically used for non-ferrous materials was used (±2µm). Therefore, a polished copper bar, with similar surface roughness as the acrylic model, was simultaneously painted during the spraying procedure. The overall thickness measurements provided an area-averaged value of 160 and 120µm in the case of (A) and 25 and 28µm for (B) for the ascending (ΨII ) and descending (ΨI ) TLC paint sequence, respectively. Considering the application of equal amounts of paint for each layer, a mean value for the thickness of each individual layer can be estimated presuming equidistant layer separation. Based on these layer thicknesses it is defined for the following analysis that the liquid crystals’ indications occur in the intermediate plane of each layer (Fig. 5), yielding the thickness values, z, in Table 1. Detailed information for the thicknesses of liquid crystals can be found in Table 1. The various liquid crystals are labelled according to their indication temperature in ascending order. The crystals’ individual indication temperature was determined with respect to the maximum intensity of the green color signal. For case (A) the calibration procedure is detailed in [31], and for case (B) the reader is referred to [32]. 8

Peak Detection Due to the fact that three TLC were used in both investigations to temporally map surface temperatures, peak detection methods were applied during the data post processing to identify maximum intensities of the entire RGB intensity history. However, only the peak values of the green color signal were finally considered, corresponding to each TLCs designated indication temperature, similar to Waidmann et al. [33]. In the case of (A) the WA Multiscale Peak Detection VI algorithm implemented in the Advanced Signal Processing Toolkit by LabVIEWr was employed in the data reduction process to locate each green intensity peak in time. However, the available video signals from the CCD camera were first preprocessed according to [12] to render the peak detection process feasible. Contrarily, in the case of (B) the base intensity level, which is mainly affected by the black paint, was removed first by a subtraction between all the images of the video sequence and a reference image that does not contain any liquid crystal information. The evolution of the green signal in time for each pixel was then filtered by a Savitzky-Golay digital filter that can be applied for smoothing purposes without greatly distorting the signal. The position of each peak in time was determined using a peak detection algorithm in MATLABr . The indication time of each individual liquid crystal sublayer could, therefore, be determined on a pixel size level. Figures 6(a) and (b) display a single frame from the entire experimental recording of each test case to give an impression of the liquid crystals’ indication sequence. Furthermore, Fig. 7 shows an example of the normalized noise-filtered green intensity histories for a single pixel. With regard to this procedure, three different indication time matrices were generated for the same experiment - one for each TLC. These were imported into the data analysis processes along with the local temperature information from the experiments to evaluate the local heat transfer coefficients. Critical Layer Thickness For Multi-TLC Experiments To ensure a correct evaluation of the experimental data it is necessary to assign every peak in the green intensity history doubtlessly to the corresponding liquid crystal. As long as the heat flux penetrates the multiple liquid crystal layers in the direction from the lowest indication temperature (TLC 1) to the highest indication temperature (TLC 3) and the time difference between two indications is greater than the reciprocal of the recording frame rate, the order of the liquid crystal indication is known beforehand. In this case (here ΨII ) the TLC closest to solid-fluid interface will indicate first then the TLC in the intermediate sublayer and finally the TLC closest to the perspex. For the other experiments the TLCs indicate in the same order as long as a critical sublayer thickness ∆zcrit is not exceeded. If one dimensional heat conduction in the sublayers of constant height ∆z and an ideal step change in the fluid temperature is assumed ∆zcrit depends on the three indication temperatures TG,max,1 , TG,max,2 , TG,max,3 , the initial temperature T0 , the 9

reference temperature Tref , the HTC, and thermal conductivity of Perspex kw . According to Barenblatt [34] the problem can be described by three different dimensionless variables ∆Θ, Θ1 , and Bicrit , ∆Θ =

TG,max,2 − TG,max,1 TG,max,3 − TG,max,2 = , Tref − T0 Tref − T0 TG,max,1 − T0 h∆zcrit Θ1 = , Bicrit = , Tref − T0 kw

(4)

while the temperature difference between the indication temperatures of TLC 2 and TLC 1, as well as TLC 3 and TLC 2 is identical. Fig. 8 presents the numerically calculated critical Biot numbers for three different dimensionless indication temperatures Θ1 , for which TG,max,1 of TLC 1 is varied, plotted against the dimensionless indication temperature difference ∆Θ between the TLCs. These lines represent the value combinations of Θ1 , ∆Θ, and Bicrit leading to a simultaneous indication of two TLCs. Additionally the maximal Biot-numbers for the three different experiments are marked in the diagram verifying that the green intensity peaks can always be assigned doubtlessly to the correct liquid crystal. The dimensionless temperature difference ∆Θ for every experiment was, therefore, calculated as the average value of the differences Θ2 − Θ1 and Θ3 − Θ2 using Table 1. [Figure 8 about here.]

RESULTS [Figure 9 about here.] [Figure 10 about here.] In the following section the heat transfer results for both test cases are presented. Thus, the discussion comprises a detailed assessment of the VG investigations ((A)) as well as the jet impingement scenario ((B)) considering the results for ReDh = 100, 000 and ReDj = 50, 000, respectively. Figures 9(a) and (b) examplarily display the heat transfer coefficient surface contours from the current VG and jet impingement investigations obtained from the analysis of TLC 2 taking into account the occuring thicknesses of zII,2 = 100µm and zII,2 = 15.3µm for ΨII , respectively. Generally, the well-documented, characteristic patterns of the HTC distribution behind a vortex generator and from impinging jets can be observed here, too. The distinct footprints of elevated HTC values are related to either the vortex flow system convecting downstream of the VG or the imminent impingement of the jets. A detailed discussion on the heat transfer phenomenology of both cases is, however, beyond the scope of this study. Therefore, the reader is referred to, e.g. [35, 36], and [27, 28, 29], respectively.

[Figure 11 about here.] 10

[Figure 12 about here.] In Figures 10(a) - (d) the lateral HTC averages of TLC 1 through TLC 3 for both investigations ((A) and (B)) considering ΨI and ΨII are plotted. The TLC/paint thickness was not considered in the evaluation. Upon comparison of the two graphs in Figs. 10(a) - (b) for the VG investigations the influence of the TLC application sequence can readily be discerned. With regards to ΨI (Fig. 10(a)) a distinct staggering effect of the heat transfer results can be observed. Consequently, TLC 1 (i.e. lowest indication temperature → short

activation times) displays the lowest HTC values, whereas for TLC 3 (i.e. highest indication temperature → late activation times) the highest HTC values can be detected. Here, the overall maximum deviation

with respect to TLC 3 is about 14%. In contrast to this finding, the HTC distributions for ΨII (Fig. 10(b)) all collapse onto one trend line within an overall deviation of ≈ 3%. Equivalent conclusions can be inferred for the results of the impingement jet experiments. Although, the differences between the reported HTC

values of the different liquid crystals are lower for ΨI (Fig. 10(c)) indicating a weaker dependence on the layer arrangement, the coinciding trend lines for ΨII can also be detected (Fig. 10(d)). The explanation for this phenomenon can be found upon consideration of the layer depths and application sequence of the TLC, yielding distributions similar to Fig. 2. For the subsequent discussion a generic distribution showing the underestimation in the HTC for a single point with hz = 100W/(m2 K) is adopted to allow the assessment of both experimental cases, i.e. the VG and the jet impingement scenario. The resulting graphs are shown in Figs. 11(a) and (b). Here, the following definitions are concluded: for the dimensionless temperatures - Θ1 < Θ2 < Θ3 , and for the coating thicknesses - z1 < z2 < z3 . Gererally, for every liquid crystal used in an experiment a specific value for Θ can be calculated with respect to the experimental conditions and the individual crystal’s calibrated indication temperature. For the current study, these values are listed in Table 1. Consequently, these Θ values can be used in conjunction with the graphs in Fig. 11 to identify the level of underestimation, ε, in the evaluated HTC introduced by disregarding the coating thickness. In this sense, an explanation for the discrepancies of the present study, particularly observed in Figs. 10(a) and (c), can also be retrieved. Essentially, it can be seen in Fig. 11(a) that for low values in Θ the disregard of relatively large coating thicknesses provokes higher underestimation levels in the HTC calculations. These deviations are primarily due to conduction effects within the above layer(s) which ultimately delay the activation of the actual liquid crystal with respect to its typical response to the change in fluid temperature. Consequently, increasing values of Θ and decreasing coating thicknesses attenuate the thickness effect towards lower ε and, thus, less erroneous HTC values. Considering the current study with regards to the TLC layer order of ΨI , this understanding is very well reflected by the staggering trends of Fig. 10(a). Although, the line averages of Fig. 10(c) also display this behavior, the effect is less pronounced due to higher Θ values and lower coating thicknesses (Table 1). Conclusively, for the aforementioned example of hz = 100W/(m2 K), the disregard 11

of the TLC layer thicknesses causes an underestimation of the HTC values up to 16.1% for Θ1 = 0.26 and zI,1 = 105µm, and 2.6% for ΘI,1 = 0.44 and zI,1 = 25µm for the VG and jet impingement investigations, respectively. Moreover, the relative differences of ∆ε1,2 and ∆ε2,3 lie between 7.6% to 4.6% and 1% to 0.2% for both cases. However, from Figs. 10(b) and (d) it can be deduced that coating thickness effects are of apparently the same magnitude, given the well agreeing HTC distributions. In reference to Fig. 11(b) this notion is substantiated. Here, it can be seen that the order of liquid crystal layers with regards to ΨII is favorable to mitigating conduction effects through the coating and their impact on subsequent HTC evaluation. Hence, the underestimation, ε, is be kept low with minimal relative deviations ∆ε. Considering the example case along with the experimental circumstances of (A), maximum values in underrating the HTC reach ≈ 8%

with a relative difference of ≈ 1%. Quantitatively, these levels in underrating the HTC are even lower for (B) attaining an overall value of about 1% with relative deviations less than that.

Figures 12(a) - (d) display the spanwise averaged HTC distributions when the absolute thickness values for each liquid crystal layer are incorporated into the evaluation process through Eq. 2 according to Fig. 1. As expected, it can generally be stated that the overall heat transfer levels are higher compared to the case when the layers’ thicknesses are neglected. Furthermore, it can be discerned for the particular case of ΨI that accounting for the individual thicknesses diminishes the overall relative discrepancies in the HTC distributions from formerly 14% (Fig. 10(a)) to actually below 5%. In this regard, the graphs of ΨII (Figs. 12(b) and (d)) evidently appear unaffected while their HTC levels are also raised. Thus, a consideration of the individual paint thicknesses leads to a fair independence of the layering (Ψ).

[Figure 13 about here.] Conclusively, Fig. 13 indicates the impact of coating thickness on the underestimation of the HTC for ΨII with regards to the indication event history for both experimental cases. Here, the spatial distribution of indication times from the experiments are projected onto the abscissa and are, therefore, indicative of the corresponding corrected heat transfer coefficient. As a result, each data point corresponds to a single pixel. In consideration of Fig. 11(b), which alludes to the underestimation’s (ε) independence of Θ for the considered case of ΨII , it can be argued with confidence that the overall order of the trend lines in Fig. 13 is a pure artifact of increasing thickness. This notion is further substantiated by the large discrepancies found between the trend lines of (A) and (B) for similar Θ values, particularly for an almost identical Θ of 0.5. From an experimental point of view it can be drawn from Fig. 13 that the results of both test cases ((A) and (B)) complement each other in terms of the increasing underestimation of the HTC with growing paint layer depths, which is also consistent with the overall understanding from theory. The staggering trends discerned for each set of experimental results underscore the conformity of the experiments. As already 12

mentioned Fig. 13 discloses the effect of layer thickness on the underestimation of the HTC with regards to the indication time. Based on the experimental results it can be seen that for small coating thicknesses ((B)) the response of the TLC to the imposed heat pulse is less affected, even for overall rather medium Θ values and small indication times (high HTC), causing small errors within 5%. On the contrary, large coating thicknesses ((A)) prolong the penetration time of the heat pulse delaying the activation of the respective liquid crystal. Thus, larger errors are produced.

3.1. Uncertainty Analysis Overall experimental assessment The uncertainties of the calculated heat transfer coefficients were evaluated using the root-sum-square method (RSS) [37, 38], which has been applied by several researchers in transient liquid crystal experiments [39, 40, 41, 42] for the solid-fluid interface (negligible paint thickness, z=0). In this study, however, the paint thickness of the multi-liquid crystal layer has been considered in the uncertainty analysis as a stochastic error given the experimental determination each individual depth on the model material. The individual uncertainty terms of the measured parameters (±2σ) are combined in order to provide the 95% confidence interval of the level of heat transfer coefficients, as follows Ph2



2  2 ∂h ∂h 2 = + Pt + Pz2 ∂t ∂z  2  2 ∂h ∂h + Pa2w + Pk2w , ∂aw ∂kw ∂h ∂Θ

2

PΘ2



(5)

[Table 2 about here.] where z is the depth of the liquid crystal layer. Table 2 indicates a detailed example of the uncertainty level of the measured parameters and the thermal properties of the model material, and their individual error propagation on the final result considering a nominal value for the heat transfer coefficient, 100W /(m2 K) and five different paint thicknesses, z. Note however that for the actual repeatability of the experiments, the thermal properties of the model material should not be considered because it is a systematic error which does not change on repeated experiments. The effect of the measured temperature, the indication time of liquid crystals and the contribution of material properties on the evaluation of heat transfer coefficients are well documented in the literature. Therefore, in this section particular attention will be given for the uncertainty term introduced by the model thickness (depth of evaluation). As expected, the heat transfer coefficients are increased when corrected for paint thickness effects and the increase is higher at thicker coatings. The RMS-error in the calculation of heat transfer coefficients is also slightly increased with the depth on the model material. For example for z=10µm 13

and 150µm is ±11.5W /(m2 K) and ±14.2W /(m2 K), respectively. For relatively thin coatings, however, the

uncertainty caused by the paint thickness is very small. In particular, (∂h/∂z×Pz )2 is about 0.02 and 0.25 for z=10µm and 30µm, respectively, indicating no significant effect on the uncertainty propagation compared to the other measured variables. However, as the thickness of the coating is increased, the uncertainty level becomes comparable with the other measurement variables, while at very large depths, e.g. z=150µm, (∂h/∂z×Pz )2 is significantly higher compared to any other measured variable approaching the uncertainty propagation of the model material thermal properties. This means that for a given transient liquid crystal experiment, if the coating thickness of the black paint or the multi-liquid crystal layers is determined with an acceptable accuracy, e.g. 15%, the uncertainty propagation of z on the evaluation of the HTC for typical TLC coatings, e.g. 10µm≤z≤50µm, is in the order of 1%, although the underestimation of heat transfer coefficient can easily reach 10% under the same thicknesses. Therefore, considering the coating thickness on the evaluation of the HTC introduces no significant increase in uncertainty on the final result. [Figure 14 about here.] The contribution of layer depth A more detailed consideration of the uncertainty level of z is presented in this subsection for both TLC sequences, ΨI and ΨII . Although the contribution is rather small compared to the other variables, an interpretation of the local error propagation of z is useful for the overall assessment of the optimum TLC paint sequence in terms of the overall experimental uncertainties as well. Figure 14 shows the local (∂h/∂z)2 ×Pz2 at the centerline of the measurement surfaces for both test

facilities (A) and (B) and all TLCs. As expected (∂h/∂z)2 ×Pz2 is spatially varied depending on the local heat transfer coefficients (Θ and t). It can be clearly observed that for both ΨI and ΨII the uncertainty

propagation of z follows the patterns of heat transfer coefficients indicating that the contribution of z on the overall uncertainty is higher for higher h. For ΨI and both test facilities, (∂h/∂z)2 ×Pz2 is higher for

lower Θ values as TLC1 is painted first on the perspex surface, and hence, it lies on a depth of 105µm and 21µm for the vortex generator and the impingement channel, respectively. On the other hand, for ΨII , an opposite trend can be observed as TLC3 is painted first on the perspex surface. However, the differences between the (∂h/∂z)2 ×Pz2 levels for all TLC layers and ΨII are considerably lower compared to ΨI , and the data somehow collapse between them even at high heat transfer coefficients, although the uncertainty of TLC3 is slightly higher over the full length of the heat transfer area. This can be better observed for the narrow impingement channel and the stagnation region of the downstream jets. As a result, for a given paint thickness, the contribution of z on the uncertainty of h is reduced as Θ is increased. Therefore, one can conclude that TLC with higher indication temperatures should be painted in order to have a higher depth of evaluation. Although, z is increased, which causes a negative impact on the uncertainty propagation, 14

the increased Θ values somehow balance the overall contribution of z on the evaluation of heat transfer coefficients.

4. Conclusions The focus of the current study was to investigate the effect of coating thickness on the evaluation of heat transfer coefficients using the transient liquid crystal technique and provide an analytical assessment coupled with an extensive experimental basis for validation. The experiments were performed using two separate test facilities allowing to assess two different flow regimes, i.e. a flow over a tetrahedra-shaped vortex generator((A), ITLR) and an impingement jet flow from an in-line row of orifices within a low aspect ratio narrow impingement channel ((B), GTT). Furthermore, three different liquid crystal types with varying indication temperatures were applied to the test surfaces in different layers, for which the coating thicknesses were accurately measured. The investigation also considered the impact of the TLC layer sequence (ascending or descending in terms of indication temperatures) on the heat transfer evaluation. The results are reported for Reynolds numbers of 100,000 ((A)) and 50,000 ((B)) based on hydraulic and jet orifice diameter, respectively. The heat transfer experiments showed that if a black paint is sprayed above the liquid crystal layer in order to provide high intensity signals or multiple liquid crystal layers are used, and the paint thicknesses are not considered, the heat transfer coefficients can be significantly underestimated. More specifically, the results show that the evaluated heat transfer coefficient is affected by the sequence and the level of paint layer thickness. Moreover, this effect is augmented the more, the higher the heat transfer coefficient level. Therefore, when transient liquid crystal experiments are conducted and the optical access is according to Fig. 1(a), a consideration of paint thickness is of vital importance in order to provide a reliable evalution of the heat transfer level. In consideration of the two different test facilities, this finding is evident from and independently consistent for both investigations. Finally, using multiple liquid crystal layers and considering the respective paint thicknesses (depth of evaluation) as an additional parameter, the overall measurement precision is slightly reduced (increased uncertainty) compared to the ideal solid-fluid interface solution (z=0µm), however, the accuracy of the measurements is increased since the heat transfer coefficients are calculated for the realistic depth on the model material, and hence, they approach a more realistic level. This can be crucial when dealing with thermal designs of various components in automotive, aerospace and other industrial applications, given that accurate knowledge of the heat transfer coefficients are essential in order to ensure proper component functionality eliminating risks of material failure.

15

5. Acknowledgement The authors gratefully acknowledge the financial support of this research project provided by the “Deutsche Forschungsgemeinschaft” (DFG). 6. References References [1] Akino, N., Kunugi, T., Ichimiya, K., Mitsushiro, K., Ueda, M., 1989, “Improved Liquid-Crystal Thermometry Excluding Human Color Sensation”, Journal of Heat Transfer, Vol. 111, pp. 558-565. [2] Baughn, J. W., 1995, “Liquid Crystal Methods For Studying Turbulent Heat Transfer”, International Journal of Heat and Fluid Flow, Vol. 16, pp. 365-375. [3] Poser, R., v. Wolfersdorf, J., Lutum, E., 2007, “Advanced Evaluation Of Transient Heat Transfer Experiments Using Thermochromic Liquid Crystals”, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 221, pp. 793-801. [4] Gillespie, D. R. H., Wang, Z., Ireland, P. T., 1998, “Full Surface Local Heat Transfer Coefficient Measurements In a Model Of An Integrally Cast Impingement Cooling Geometry”, Journal of Turbomachinery, Vol. 120, pp. 92-99. [5] Newton, P. J., Yan, Y., Stevens, N. E., Evatt, S. T., Lock, G. D., Owen, M. J., 2003, “ Transient Heat Transfer Measurements Using Thermochromic Liquid Crystal. Part 1: An Improved Technique”, International Journal of Heat and Fluid Flow, Vol. 24, pp. 14-22. [6] Ireland, P. T., Jones, T.V., 2000, “Liquid Crystal Measurements Of Heat Transfer And Surface Shear Stress”, Measurement Science and Technology, Vol. 11, pp. 969-986. [7] Kwak, J. S., 2008, “Comparison Of Analytical And Superposition Solutions Of The Transient Liquid Crystal Technique”, Journal of Thermophysics and Heat Transfer, Vol. 22, pp.290-295. [8] Vogel, G., Weigand, B., 2001, “A New Evaluation Method For Transient Liquid Crystal Experiments”, National Heat Transfer Conference, NHTC2001-20250, California, USA. [9] Buttsworth, D. R., Jones, T. V., 1997, “Radial Conduction Effects In Transient Heat Transfer Experiments”, The Aeronautical Journal, pp. 209-212. [10] Wagner, G., Kotulla, M., Ott, P., Weigand, B., v. Wolfersdorf, J., 2005, “The Transient Liquid Crystal Technique: Influence Of Surface Curvature And Finite Wall Thickness”, Journal of Turbomachinery, Vol. 127, pp. 175-182. [11] Camci, C., Kim, K., Hippensteele, S. A., 1992, “A New Hue Capturing Technique for Quantitative Interpretation Of Liquid Crystal Images Used In Convective Heat Transfer Studies”, Journal of Turbomachinery, Vol. 114, pp. 765-775. [12] Poser, R., Ferguson, J. R., v. Wolfersdorf, J., 2009, “Temporal Signal Preprocessing And Evaluation Of Thermochromic Liquid Crystal Indications In Transient Heat Transfer Experiments”, 8th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, pp. 785-795. [13] Wang, Z., Ireland, P. T., and Jones, T. V., 1995, “An Advanced Method Of Processing Liquid Crystal Video Signals From Transient Heat Transfer Experiments”, Journal of Turbomachinery, Vol. 117, pp. 184-189. [14] Talib, R. A., Neely, A. J., Ireland, P. T., Mullender, A. J., 2004, “A Novel Liquid Crystal Image Processing Technique Using Multiple Gas Temperature Steps To Determine Heat Transfer Coefficient Distribution And Adiabatic Wall Temperature”, Journal of Turbomachinery, Vol. 126, pp.587-596. [15] Van Treuren, K. W., Wang, Z., Ireland, P. T., Jones, T. V., 1994, “Detailed Measurements Of Local Heat Transfer Coefficient And Adiabatic Wall Temperature Beneath An Array Of Impinging Jets”, Journal of Turbomachinery, Vol. 116, pp. 369-374.

16

[16] Ferguson, J. R., 2007, “Simultaneous Thermochromic Liquid Crystal Calibration And Calculation Of Heat Transfer Coefficients”, Proceedings of ASME Turbo Expo, Montreal, Canada, GT2007-28124. [17] Kakade, V. U., Lock, G. D., Wilson, M., Owen, J. M., Mayhew, J. E., 2009, “Accurate Heat Transfer Measurements Using Thermochromic Liquid Crystal. Part 1: Calibration And Characteristics Of Crystals”, International Journal of Heat and Fluid Flow, Vol. 30, pp. 939-949. [18] Abdullah, N., Talib, A. R.A., Saiah, H. R. M., Jaafar, A. A., Salleh, M. A. M., 2009, “Film Thickness Effects On Calibrations Of A Narrowband Thermochromic Liquid Crystal”, Experimental Thermal and Fluid Science, Vol. 33, pp. 561-578. [19] Hippensteele, S. A., Poinsatte, P. E., 1993, “Transient Liquid-Crystal Technique Used To Produce High-Resolution Convective Heat Transfer Coefficient Maps”, Tech. Rep., Lewis Research Center, Cleveland, Ohio, USA. [20] Ekkad, S. V., Han, J.-C., 2000, “A Transient Liquid Crystal Thermography Technique For Gas Turbine Heat Transfer Measurements”, Measurement Science and Technology, Vol. 11, pp. 957-968. [21] Carslaw, H. S., Jaeger, J. C., 1959, “Conduction Of Heat In Solids”, Second edition, Oxford Science Publications. [22] LCR Hallcrest, “TLC Products For Use In Research And Testing Applications”, LCR Hallcrest Research & Testing Products, Rev. 1, pp. 1 - 18. [23] Heidmannn, J. D., 1994, “Determination Of A Transient Heat Transfer Property Of Acrylic Using Thermochromic Liquid Crystals”, NASA Tech. Report, NSN 7540-01-280-5500. [24] Liu, C.-L., v. Wolfersdorf, J., Zhai, Y.-N., 2014, “ Time-Resolved Heat Transfer Characteristics For Steady Turbulent Flow With Step Changing And Periodically Pulsating Flow Temperatures, International Journal of Heat and Mass Transfer, Vol. 76, pp. 184-198. [25] Wang, Z., Gillespie, D., and Ireland, P. T., 1996, “Advances In Heat Transfer Measurements Using Liquid Crystals, Proceedings of the Turbulent Heat Transfer Conference, San Diego, CA, USA. [26] Ireland, P. T., Neely, A. J., Gillespie, D. R. H., and Robertson, A. J., 1999, “Turbulent Heat Transfer Measurements Using Liquid Crystals, International Journal of Heat and Fluid Flow, Vol. 20, pp. 355-367. [27] Terzis, A., Wagner, G., von Wolfersdorf, J., Ott, P., Weigand, B., 2014, ‘Effect Of Hole Staggering On The Cooling Performance Of Narrow Impingement Channels Using The Transient Liquid Crystal Technique”, Journal of Heat Transfer, Vol. 136, pp. 071701-1-9. [28] Terzis, A., Ott, P., von Wolfersdorf, J., Weigand, B., Cochet, M., 2014, “Detailed Heat Transfer Distributions Of Narrow Impingement Channels For Cast-In Turbine Airfoils”, Journal of Turbomachinery, Vol. 136, pp. 091011-1-9. [29] Terzis, A., Ott, P., Cochet, M., von Wolfersdorf, J., Weigand, B., 2015, “Effect Of Varying Jet Diameter On the Heat Transfer Distributions Of Narrow Impingement Channels”, Journal of Turbomachinery, Vol. 137, pp. 021004-1-9. [30] Terzis, A., von Wolfersdorf, J., Weigand, B., Ott, P., 2012, “Thermocouple Thermal Inertia Effects On Impingement Heat Transfer Experiments Using The Transient Liquid Crystal Technique”, Measurement Science and Technology, Vol. 23, pp. 115303-1-13. [31] Poser, R. and von Wolfersdorf, J., 2010, “Transient Liquid Crystal Thermography In Complex Internal Cooling Systems”, VKI Lecture Series - Internal Cooling in Turbomachinery, von Karman Institute for Fluid Dynamics, (VKI LS 2010-05). [32] Terzis, A., 2014, “Detailed Heat Transfer Distributions Of Narrow Impingement Channels For Integrally Cast Turbine Airfoils”, Dissertation, EPFL, Switzerland. [33] Waidmann, C., Poser, R., von Wolfersdorf, J., 2013, “Application Of Thermochromic Liquid Crystal Mixtures For Transient Heat Transfer Measurements”, 10th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Lappeenranta, Finland. [34] Barenblatt, G. I., 1987, “Dimensional Analysis”, Gordon & Breach, New York. [35] Henze, M., von Wolfersdorf, J., Weigand, B., Dietz, C. F., Neumann, S. O., 2011, “Flow And Heat Transfer Characteristics

17

Behind Vortex Generators - A Benchmark Dataset”, International Journal of Heat and Fluid Flow, Vol. 32, pp. 318-328. [36] Terzis, A., von Wolfersdorf, J., Weigand, B., Ott, P., 2015, “A Method To Visualise Near Wall Fluid Flow Patterns Using Locally Resolved Heat Transfer Experiments”, Experimental Thermal and Fluid Science, Vol. 60, pp. 223-230. [37] Kline, S. J., McClintock, F. A., 1953, “Describing The Uncertainties In Single Sample Experiments”, Mechanical Engineering, pp. 38. [38] Moffat, R. J., 1988, “Describing The Uncertainties In Experimental Results”, Experimental Thermal and Fluid Science, Vol. 1, pp. 3-17. [39] Owen, J. M., Newton, P. J., Lock, G. D., 2003, “Transient Heat Transfer Measurements Using Thermochromic Liquid Crystal. Part 2: Experimental Uncertainties”, International Journal of Heat and Fluid Flow, Vol. 24, pp. 2328. [40] Yan, Y., Owen, J. M., 2002, “Uncertainties In Transient Heat Transfer Measurements With Liquid Crystal”, International Journal of Heat and Fluid Flow, Vol. 23, pp. 2935. [41] Poser, R., von Wolfersdorf, J., Semmler, K., 2005, “Transient Heat Transfer Experiments In Complex Passages”, Proceedings of ASME Summer Heat Transfer Conference, HT2005-72260, 17-22 July, San Francisco, California, USA. [42] Rao, Y., Xu, Y., 2012, “Liquid Crystal Thermography Measurement Uncertainty Analysis And Its Application To Turbulent Heat Transfer Measurements”, Advances in Condensed Matter Physics,Vol. 2012,pp. 18.

18

NOMENCLATURE a

[m2 /s]

Thermal diffusivity

A

[−]

Label of flat plate side

B

[−]

Label of flat plate side

Bi

[−]

Biot Number

D

[m]

Diameter

h

[W/(m2 K)]

Heat transfer coefficient

k

[W/(mK)]

Thermal conductivity

L

[m]

Length of impingement channel

m ˙

[kg/s]

Mass flow

n

[−]

Mathematical variable

P

[%]

Probability

t

[s]

Time

T

[K]

Temperature

x, y, z

[−]

Cartesian coordinates

X, Y, Z

[−]

Distances

δ

[m]

Coating thickness

∆

[−]

Difference



[%]

Relative underestimation

Θ

[−]

Dimensionless temperature

µ

[kg/(ms)]

Dynamic viscosity

ν

[l]

Amount of substance

π

[−]

Mathematical constant

Ψ

[−]

TLC sequence

Subscripts 0

initial conditions

1, 2, 3

enumeration within a sequence

crit

critical

D

diameter

G, max

maximum green color intensity

19

h

hydraulic

j

jet

ref

reference temperature

w

wall

δ

thickness

Abbreviations GT T

Group of Thermal Turbomachinery at EPFL

IT LR

Institute of Aerospace Thermodynamics, University of Stuttgart

H2 O

Water

HT C

Heat transfer coefficient

LCT

Liquid crystal thermography

Re

Reynolds number

TC

Thermocouple

T LC

Thermochromic liquid crystals

VG

Vortex generator

20

List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Illustration of (a) TLC application sequence, (b) consideration of layer thickness for the semiinfinite wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative underestimation for various layer thicknesses for hz = 200W/(m2 K) . . . . . . . . . Schematic of the experimental setup of the test facility (A) at ITLR . . . . . . . . . . . . . . Schematic of the experimental setup of the test facility (B) at GTT . . . . . . . . . . . . . . Illustration of the investigated TLC Layer Sequences . . . . . . . . . . . . . . . . . . . . . . . Single Frame of the TLC indication sequence for (a) VG, (b) jet impingement . . . . . . . . . Green intensity history for a single pixel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical layer thickness for three different TLC . . . . . . . . . . . . . . . . . . . .
. . . . . . Local heat transfer coefficient distribution h/href for (a) VG, href = 220W/ m2 K , (b) jet
2 impingement, href = 400W/ m K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spanwise averaged heat transfer coefficient distribution for (a), (b) VG experiments and (c), (d) jet impingement experiments considering z = 0µm . . . . . . . . . . . . . . . . . . . . . . Schematic of relative HTC underestimation for various layer thicknesses for hz = 100W/(m2 K) considering (a) ΨI , (b) ΨII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spanwise averaged heat transfer coefficient distribution for (a), (b) VG experiments and (c), (d) jet impingement experiments considering the various penetration depths z . . . . . . . . . Range of HTC underestimation for both experimental cases (A) and (B) with respect to indication history of ΨII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial contribution of the TLC layer depth to the RSS error taken at the centerline . . . . .

21

22 23 24 25 26 27 28 29 30 31 32 33 34 35

Perspex

TLC Paint

δ

Observer

.....

Flow

kw, aw

z (a)

(b)

Figure 1: Illustration of (a) TLC application sequence, (b) consideration of layer thickness for the semiinfinite wall

22

0

(h0 − hz )/hz

[%]

−20 −40

z

10µm 30µm 50µm 90µm 130µm

−60 −80

−100

0

0.2

0.4

0.6

0.8

1

Θ

Figure 2: Relative underestimation for various layer thicknesses for hz = 200W/(m2 K)

23

(1)

(2)(3)

(4)

(6)

(5)

CCD

Vortex Generator xVG(

(7)

120

Camera

A - A 6

BTLC

ATLC y

16

16

Wall Liquid Crystal Black Paint

Flow

VG Thermocouples

A Flow

Trip 60

VG 405

x

A Flow Straightener

(a) Test facility

Thermocouples

(b) Test section

Figure 3: Schematic of the experimental setup of the test facility (A) at ITLR

24

150

Flat Plate

z

z

60

X

X Y

(b) Narrow impingement channel

(a) Impingement cooling test facility

Figure 4: Schematic of the experimental setup of the test facility (B) at GTT

25

Z

P e rs pe x

δ z I,1

zI,2

TLC 1

TLC 3

TLC 2

TLC 2

TLC 3

TLC 1

zI,3

zII,3

zII,1

Bla ck ΨI

zII,2

Ψ II

Figure 5: Illustration of the investigated TLC Layer Sequences

26

(a) Vortex generator

(b) Jet impingement

Figure 6: Single Frame of the TLC indication sequence for (a) VG, (b) jet impingement

27

1 TLC3 TLC2 TLC1

I / Imax

0.8 0.6 0.4 0.2 0 0

10

20

30 t [s]

40

50

60

Figure 7: Green intensity history for a single pixel

28

2 Θ1 = 0.2 Θ1 = 0.4 Θ1 = 0.6 VG Θ1 = 0.26, ∆Θ = 0.13 Jet ΘI,1 = 0.44, ∆Θ = 0.07 Jet ΘII,1 = 0.46, ∆Θ = 0.075

Bi =

h∆z kw

1.5 1 0.5 0

0

0.05

0.1

0.15 ∆Θ

0.2

0.25

0.3

Figure 8: Critical layer thickness for three different TLC

29

(a) TLC 2 (zII,2 = 100µm)

y/LV G

1.54 0 −1.54

0

2

4

8 10 x/LV G

6

12

14

16

(b) TLC 2 (zII,2 = 15.3µm) y/L j

0.16 0 −0.16

0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

x/L j h/hre f

0

0.2

0.4


2 Figure 9: Local heat transfer coefficient distribution h/h for (a) VG, h = 220W/ m K , (b) jet ref ref
2 impingement, href = 400W/ m K

30

100

100

TLC 1 TLC 2 TLC 3

80

90


[W / m2 K ]


[W / m2 K ]

90

80 70

60 50

h

h

70

0

4

8 x/LV G

12

60 50

16

0

4

(a) (A): ΨI

16

300
[W / m2 K ]

300
[W / m2 K ]

350

250

250

200

200

150

h

h

12

(b) (A): ΨII

350

100 50

8 x/LV G

150 100

0

0.2

0.4

0.6

0.8

50

1

0

0.2

0.4

0.6

x/L j

x/L j

(c) (B): ΨI

(d) (B): ΨII

0.8

1

Figure 10: Spanwise averaged heat transfer coefficient distribution for (a), (b) VG experiments and (c), (d) jet impingement experiments considering z = 0µm

31

ε2

ε1,2,3

(h0 − hz )/hz

[%]

0

(h0 − hz )/hz

[%]

0 ε3

ε1 z1 z2 z3

Θ1

Θ2

z1 z2 z3

Θ1

Θ3

Θ2

Θ3 Θ

Θ (b)

(a)

Figure 11: Schematic of relative HTC underestimation for various layer thicknesses for hz = 100W/(m2 K) considering (a) ΨI , (b) ΨII

32

100

100

TLC 1: zI,1 = 105µm TLC 2: zI,2 = 75µm TLC 3: zI,3 = 45µm

80

80 70

60

h

h

70

50

TLC 1: zII,1 = 60µm TLC 2: zII,2 = 100µm TLC 3: zII,3 = 140µm

90


[W / m2 K ]


[W / m2 K ]

90

0

4

8 x/LV G

12

60 50

16

0

4

(a) (A): ΨI 350

TLC 1: zI,1 = 25µm TLC 3: zI,3 = 10.5µm

350

TLC 2: zI,2 = 17.5µm

16


[W / m2 K ]

TLC 2: zII,2 = 15.3µm

250

200

200

150

h

h

TLC 1: zII,1 = 9.2µm TLC 3: zII,3 = 21.4µm

300

250

100 50

12

(b) (A): ΨII


[W / m2 K ]

300

8 x/LV G

150 100

0

0.2

0.4

0.6

0.8

50

1

0

0.2

0.4

0.6

x/L j

x/L j

(c) (B): ΨI

(d) (B): ΨII

0.8

1

Figure 12: Spanwise averaged heat transfer coefficient distribution for (a), (b) VG experiments and (c), (d) jet impingement experiments considering the various penetration depths z

33

0 [%]

−5

(h0 − hz )/hz

−10 −15

Test facility (A) Θ1 =0.26/zII,1=60µm

−20 −25

0

20

Test facility (B) ΘII,1=0.46/zII,1=9.2µm

Θ2=0.38/zII,2=100µm

ΘII,2=0.54/zII,2=15.3µm

Θ3=0.52/zII,3=140µm

ΘII,3=0.61/zII,3=21.4µm

40

60 t

80

100

[s]

Figure 13: Range of HTC underestimation for both experimental cases (A) and (B) with respect to indication history of ΨII

34

60

40 30 20 10 0

1

2

(∂ h/∂ z)2 × Pz2

30 20

1

2

(a) (A): ΨI

(b) (A): ΨII

30

40

20 10

0.2

0

x/LV G

TLC 1: zI,1 = 25µm TLC 2: zI,2 = 17.5µm TLC 3: zI,3 = 10.5µm

0

0

3

x/LV G

40

0

40

10

(∂ h/∂ z)2 × Pz2

0

TLC 1: zII,1 = 60µm TLC 2: zII,2 = 100µm TLC 3: zII,3 = 140µm

50 (∂ h/∂ z)2 × Pz2

50 (∂ h/∂ z)2 × Pz2

60

TLC 1: zI,1 = 105µm TLC 2: zI,2 = 75µm TLC 3: zI,3 = 45µm

0.4

0.6

0.8

x/L j

TLC 1: zII,1 = 9.2µm TLC 2: zII,2 = 15.3µm TLC 3: zII,3 = 21.4µm

30 20 10 0

1

3

0

0.2

0.4

0.6

0.8

x/L j

(c) (A): ΨI

(d) (A): ΨII

Figure 14: Partial contribution of the TLC layer depth to the RSS error taken at the centerline

35

1

List of Tables 1 2

TLC characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2 2 . . . . . . . . . . . . . . . . . . . . . . 38 Experimental uncertainties in terms of (∂h/∂Xi ) PX i

36

Table 1: TLC characteristics

1. TLC1 2. TLC2 3. TLC3

TG,max [o C] 30.49 34.77 39.76

Test Facility A ΨI Θ zI [µm] (AT LC ) 0.26 105 0.38 75 0.52 45

ΨII zII [µm] (BT LC ) 60 100 140

37

Test Facility B TG,max [o C] 35.01 38.29 40.89

ΘI 0.44 0.52 0.58

ΘII 0.46 0.54 0.61

ΨI zI [µm] 25 17.5 10.5

ΨII zII [µm] 9.2 15.3 21.4

2

2 Table 2: Experimental uncertainties in terms of (∂h/∂Xi ) PX i

Parameter Units o T0 C o Tref C o Tw C t s k W /(mK) a (×10−7 ) m2 /s Paint thickness, δ

Value PX,i 20.11 ±0.10 58.77 ±0.15 38 ±0.12 15 ±0.1 0.19 ±10% 1.081 ±10% µm ±15% HTC-W /(m2 K) RMS Error h % Repeatability %

z=0µm 0.99 1.65 1.29 0.11 100 25 100 11.3 11.3 2.01

z=10µm 1.02 1.70 1.32 0.12 101.9 26 0.02 100.9 11.5 11.4 2.05

38

z=30µm 1.08 1.81 1.41 0.13 106.5 28.3 0.24 103.2 11.8 11.5 2.16

z=60µm 1.18 1.97 1.53 0.14 113.5 32.1 1.05 106.6 12.3 11.6 2.43

z=100µm 1.33 2.22 1.73 0.17 123.8 38.1 3.37 111.3 13.1 11.8 2.97

z=150µm 1.55 2.61 2.02 0.21 138.5 47.4 9.06 117.7 14.2 12.1 3.93

Highlights We performed transient heat transfer experiments using vortex generators and impinging jets We used multiple liquid crystals We investigated the effect of layer/paint thickness on the evaluated heat transfer coefficient If the layer/paint thicknesses are neglected the heat transfer coefficient can be significantly underestimated We additionally performed a thorough uncertainty analysis