[american institute of aeronautics and astronautics 48th aiaa aerospace sciences meeting including...

Window Temperature Impact on IR Thermography for Heat Transfer Measurements

Jonas P. R. Gustavsson*, Jonas Hylén†, Mats Kinell‡ and Esa Utriainen§ Siemens Industrial Turbomachinery AB, 612 83 Finspong, Sweden

Using time-resolved temperature measurements obtained through IR thermography, the film cooling effectiveness and heat transfer coefficient can be determined simultaneously from a single test for the entire observed surface. This is a type of test ideally suited for studying the heat load and cooling configuration efficiency on a gas turbine blade or guide vane. As shown in this paper, accurate measurements require special care to be taken of the window material and temperature. This issue stems from the non-unity internal transmittance of the window through which the test article is observed, coupled with the unusual feature of the test rig window in this kind of setup frequently being heated at a faster rate than the test object during a test. It is exasperated by the strong coupling between the two parameters being sought, making the output sensitive to small changes in the input. Approaches for measuring the window temperature are outlined and uncertainty estimates in the determination of the heat transfer coefficient and film cooling effectiveness given as 23% and 0.08, respectively.

Nomenclature

A. Latin c = guide vane chord length [m] DL = digital level – raw 14-bit output of IR camera [1] h = heat transfer coefficient [W/(m2K)] Nuc = Nusselt number based on chord length, Nuc=hc/k [1] k = thermal conductivity of guide vane material [W/(mK)] T = temperature [K]

B. Greek = thermal diffusivity of guide vane material [m2/s] = emissivity of guide vane [1] = recovery temperature Reynolds number dependence exponent [1] = film cooling effectiveness [1] = reflectance of window [1] = transmittance of window [1] = surface-normal coordinate measured from guide vane surface inward [m]

C. Subscript bg = background c = cooling f = film i = initial s = guide vane surface

* Consulting Test Engineer, AIAA Senior Member † Senior Measurement Engineer ‡ Senior Measurement Engineer § Technology Lead – Turbine

American Institute of Aeronautics and Astronautics

1

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-670

Copyright © 2010 by Siemens Industrial Turbomachinery AB. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

w = window ∞ = free-stream

I. Introduction HE main route for increasing thermal efficiency of a gas turbine is through increasing the temperature of the air leaving the combustor.1 Given that the combustor is often operating near the lean blowout limit, this can be

easily achieved. The problem is the increased heat loading on combustor liner along with the first turbine stages. To avoid fatigue failure of the material, various methods are used, e. g. use of single crystal turbine components, thermal barrier coating with ceramic materials, conduction cooling through the combustion chamber liner and turbine blade and vane walls and film cooling. Film cooling involves the injection of relatively cool air bled of from the compressor into combustor and turbine areas subjected to especially high thermal loads. Since the air bypasses the combustion chamber, it leads to a decrease in thermal efficiency, meaning that the flow needs to be kept as low and used as carefully as possible. The purpose of this investigation was to determine the heat transfer coefficient, h (W/(m2K)) and film cooling effectiveness, (dimensionless) on the surface of a scaled-up and two-dimensionalized gas turbine guide vane, allowing various cooling configurations to be compared and numerical simulations of these configurations to be validated. The measurement technique employed was the transient method previously used by e. g. Ekkad et al.,2 Drost3, Reiss,4 and Vedula and Metzger,5 which allows both parameters to be determined in a single test through time-resolved measurements of the surface temperature following the application of a step change in the gas temperature. The goal was to provide a dataset for numerical code validation as well as directly allowing different cooling configurations to be compared and cooling flows to be optimized. During testing, the impact of window temperature was noted and the correction of this effect is the topic of this paper.

T

II. Method The results presented in the current paper were obtained through applying the method of Vedula and Metzger5 on

unsteady temperature measurements on the surface of a guide vane model to obtain the heat transfer coefficient and film cooling effectiveness over this surface. Rather than the thermochromic liquid crystal method used by Vedula and Metzger, IR thermography is used in a manner similar to Ekkad et al.2 The heat power per unit area transferred at a point on the surface, q (W/m2), is determined by the temperature of the gas film outside that point on the surface, Tf(K), the local wall temperature, Tw(K) and the local heat transfer coefficient, h (W/(m2K)):

)( wf TThq (1)

The local film temperature can be defined at the local adiabatic wall temperature, i. e. the temperature attained at the guide vane surface when thermal equilibrium has been reached and there is no more net heat transfer to or from the surface. In the current film cooling setup, the film temperature is given by the local mixture of cool film cooling air and hot freestream combustor exhaust gas. These streams have temperatures Tc(K) and Tg(K), respectively, which are used to define the local film cooling effectiveness as:

cg

fg

TT

TT

(2)

Note that the efficiency is 0 where the film temperature is equal to the hot gas temperature and 1 where it is equal to the cooling air temperature. The heat transfer across the surface forms one of the boundary conditions for the heat transfer Laplacian partial differential equation,

t

TkT

)( (3)

Here k(W/(mK)) is the thermal conductivity of the material below the surface. In the case of constant thermal conductivity and 1D heat transfer perpendicularly to the surface this simplifies to:


2

t

TTk

2

2

(4)

Here (m) is a surface-normal coordinate with =0 at the surface. Continuity of the heat transfer at the surface, where no heat accumulation is possible, produces one boundary condition and the other stems from the assumption of a semi-infinite slab of material:

i

f

TxT

TThT

kq

)(

))0((0 (5)

A further constraint is the uniform initial temperature:

iTtT )0( (6)

The problem specified by Eqns. 4-6 may be solved using the Laplace transform approach after having been made homogenous by the subtraction of the initial temperature Ti. Here only the surface temperature, Ts=T(=0), which is what is accessible to measure, is of interest:

))(1()))(1()(()(k

therfcxTTTTTtT igicis

(7)

Erfcx is the conjugated error function, erfcx(x)=exp(x2)erfc(x). The relevant gas temperature, Tg, is the so-called recovery temperature, which adds the effect of friction heating to the static temperature, T∞, of the flow.3

P

g C

UTT

2Pr

2

(8)

The exponent has the value ½ for a laminar and 1/3 for a turbulent boundary layer. In practice, this will produce recovery temperatures that more closely approximate the stagnation than the local static temperature.

III. Experimental Setup A test rig for testing various cooling

configurations on guide vanes has been constructed at Siemens Industrial Turbomachinery at Finspong, Sweden. The experimental setup consists of rig hardware for supplying the hot freestream and cooling flows, data acquisition equipment for flow, pressure and temperature measurements and an IR thermography system as detailed below.

A. Test Rig The test rig main flow is supplied by a blower

capable of delivering 3 kg/s of air at pressures of up to 0.5 barg. The cooling flow is supplied from the in-house compressed air network at 7 bar, delivering up to 40 g/s of air measured through a Massflo 6000 mass flow meter mounted upstream


3

Figure 1. Test section side view. The right section is the bypass switch section with bypass exhaust on the back side. To the left is the test section where the guide vane model is mounted as indicated by white curve.

of a pressure regulator. The flow is then distributed over four cooling plena, which may be independently controlled through in-line valves. Through a pneumatically controlled three-way valve, the main flow can be switched very quickly (<1 s) between the bypass and test section. Initially, the bypass is used to allow the heat naturally generated by the blower to heat up the upstream section of the test rig while leaving the test section at ambient temperature until the valve is switched. The main flow rate is determined from a calibrated V-cone pressure differential measurement upstream of the bypass valve. When the desired conditions have been achieved – typically 58°C and 3.0 kg/s main flow – the flow is allowed to pass through the test section and data and images are acquired. A photograph of the test section and bypass valve section is shown in Figure 1.

B. Test Objects The test articles consist of several guide vane models with different cooling configurations manufactured

through rapid prototyping in PA2200 polyamide. The vanes have a chord length of 0.45 m and a span of 0.1 m. The vanes have 3-4 internal cooling plena feeding 9-10 rows of 8-9 cooling holes each, allowing various cooling flows to be tested for each configuration. The guide vanes, which have skin thicknesses of 10 mm, are fitted with three Type N thermocouples each to monitor the internal heat conduction and ensure that a uniform temperature has been attained prior to initiating a test.

C. Data Acquisition Equipment To monitor rig and test object temperatures, flows and pressures during the test, one or two PSI 9010 pressure

transducer blocks, a DataScan 7220 general analog signal input device were employed. These devices were connected to a PC using a serial interface and each channel was read at a rate of approximately 1 Hz during the experiment using a LabView-based program.

D. IR Thermography System The IR thermography system is based on a Cedip Titanium 560M MWIR camera fitted with a 50mm/2.0 lens

having an effective detection wavelength range of 1.5-5.1 m. The exposure time used was 1 ms, providing good signal-to-noise ratio while effective eliminating temporal smear. The camera was connected to a PC running the Altair program for image acquisition. Normally, images at full 640×512 pixel resolution were acquired at a rate of 5 Hz for 40 s starting a few seconds prior to the switch of the bypass valve. To reduce the memory and processing load, in most cases 2x2 spatial binning was used and only every other frame was processed.

IV. Observations

A. Initial Tests During initial testing, the acquired IR images were analyzed using conventional processing where the test section

sapphire window was ascribed a certain transmittance but was implicitly assumed to remain at ambient temperature during the test. When studying the temperature inside the cooling holes in the IR images, it was surprising to note that these increased substantially during the test. While the indicated temperature was always substantially lower than that of the uncooled guide vane surface, an increase of the order of 10K during the test could not be explained physically given the strength of forced convective cooling versus conductive heat transfer in the cooling holes. Given the high heat conductivity of sapphire and its limited transmittance near 5 m, it was suspected that the indicated film hole temperature increase was actually due to emission from the sapphire window increasing as the window got warmer during a test. This was confirmed in later tests where a spot of high-emissivity paint was applied to the outer window surface, allowing its temperature to be measured at every instant during the test. Results from a sample test shown in Figure 2 demonstrate that the window

Figure 2. Window temperature as measured using IR thermography on a paint spot on the outside of the window.


4

temperature increases substantially from 26 to 44°C during the test, necessitating a correction.

B. Model Refinements The signal detected by the IR camera may be considered a sum of contributions from three sources: the test

object, the window and the background. If the test object has low emissivity, a fourth contribution from the inside of the test rig must also be considered, greatly complicating matters when the inside of the test rig is not uniformly heated, e. g. during film cooling experiments. This source was minimized in the present experiments where the test object was painted with black paint whose emissivity had been determined experimentally to be >99% in the wavelength region of interest.

The background contribution, due primarily to reflections in the window front and back surface, but when the

test object emissivity is low also due to reflections in this, is relatively easy to correct for since the background temperature typically remains constant during the test. Furthermore, it is frequently lower than the test object temperature, reducing its relative signal contribution. One thing to bear in mind is that in order for the background contribution to be small and low, it is very important to avoid reflections of hot objects, e. g. light sources, in the window of test object. In the current experiments this was achieved through mounting a black screen in such a manner that its reflection in the window blocked the rest of the room from the camera’s point-of-view. The high index of refraction of sapphire, 1.65, produces a reflectance of about 0.06 in each surface, making this arrangement crucial. A substantially more challenging issue is the contribution from the sapphire window emission. In the literature, a wide range of transmittance curves of sapphire around 5 m have been found. Because of the low temperatures measured during the current experiments, the Planck distribution predicts a photon flux maximum near 10 m, implying that only the shortest tail of the radiation wavelength distribution entered the region of interest, making the optical properties of the system near 5 m most important. To accurately measure the transmittance of the sapphire window under the experimental conditions, a separate experiment was carried out, producing an internal transmittance of 0.88 for the 2 mm thick window. When it comes to measuring the window temperature during the test, two different approaches were tested:

Black spot measurements: To allow the window temperature to be measured and corrected for during the transient test used to measure the guide vane heat transfer parameters, a 5-mm diameter spot of high-emissivity paint was applied near a corner of the outside of the sapphire window, as seen in Figure 5. The benefit of this approach is that the window temperature is obtained for the same run conditions as the guide vane data, making correction straightforward. The drawback is that the spatial distribution of temperatures over the window is unknown. The size of the paint spot required is determined by depth-of-field of the optical arrangement.

Black window run: To get temperature values for every point in the window, separate runs were carried out with the entire inside of the sapphire window painted black. In these runs, it was noted that towards the end of a run, the temperature variation across the window could be as much as 3K, making this approach the one chosen for correcting the current set of guide vane measurements. The major challenge with this approach is that it is necessary to carefully match the guide vane test with the corresponding black window test – in space, time and temperatures to obtain an appropriate point-by-point correction of the guide vane temperatures.

As was mentioned above, the majority of the radiation produced in the present experiment is longer than the sensitivity range of the camera, lens and window. As the temperature of the test object increases, the total emitted radiation will not only grow faster according to the T4 law of Stefan-Boltzmann, but also be shifted towards shorter wavelength, into the detection system range, as suggested by Planck’s law. This produces a signal that grows very rapidly with increasing temperature. After calibration against a calibrated blackbody source over the temperature range of interest, 293<T<333 K, the signal of the camera was found to be DL=611.8+1.4335×1017T8.2533, where DL is the digital level (14 bit) raw output of the camera and T is the blackbody temperature in kelvin. The first term is a constant offset while the second is Itot – the total signal detected by the camera.


5

The different contributions to the camera signal are illustrated in Figure 3. The goal of this analysis is to determine the guide vane temperature through removing the background and window contributions from the total camera signal and apply the camera calibration.

window

I7 I6I5

I1 I4 I3I2

camera

guide vanewindow

I7 I6I5

I1 I4 I3I2

camera

guide vane

Figure 3. Contributions to camera signal. 1, 5, 7: from background, 2, 4, 6: from window, 3: from test object. Note that the series of signals is truncated at three places.

In the present case, =0.88, =0.06, =0.99, which made the geometric series of higher order reflections, omitted in Figure 3, converge rapidly. Note that it has been assumed, as shown in Figure 3, that radiation reflected in the guide vane surface comes from the direction of the window. This is not always true and in cases where the guide vane reflects diffusively, the reflected radiation will be a locally weighted average of background, window and tunnel temperatures. Given the small reflectivity of the guide vane, this complication has been neglected here. I1=0.060Ibg, I2=0.113Iw, I3=0.769Is, I4=0.006Iw, I5=0.041Ibg, I6=0.001Iw and adding the truncated terms gives a total of Itot=0.107Ibg+0.120Iw+0.773Is. That is, when the background, window and guide vane all have the same temperature, 77% of the camera signal comes from the guide vane while the rest is evenly split between the background and window. However, in a more typical film cooling situation with a background temperature of 295K, window temperature of 323K and guide vane temperature of 313K, Iw=2.11Ibg, Is=1.63Ibg. In this case 6.6% of the signal comes from the background, 15.6% from the window and 77.8% from the guide vane. These temperatures will be used as an example to show the results obtained through applying several different assumptions in the calculations of Ts based on known Tbg and Itot from measurements.

1. No correction Completely neglecting both the reflection and the emission of the window assuming =1 for the guide vane

means that Ts is obtained directly from Itot=Is, giving Ts=Tbg(Itot/Ibg)1/8.2533= 312.7K. This is only 0.3K too low since

the lowering contribution from the cold background almost exactly cancels out the increasing contribution from the hot glass.

2. Correcting for guide vane emissivity Still ignoring the window impact but using =0.99 for the vane surface produces Is=1.6246Ibg, which gives an

indicated surface temperature of Ts=312.9K. This is an even better result than above, but as will be demonstrated in Section IV.D, a correct temperature at one time instant does not guarantee correct h and values when the time constant of the window heating is different than that for the guide vane heating.

3. Using theoretical window reflectance Using the index of refraction of sapphire and assuming normal incidence the reflectance =0.0602 is obtained

for each sapphire surface. The window internal transmittance is still set to 1, assuming either that the window remains as cold as the background or that its external transmittance is only reduced by window reflections. This produces a weighing of Itot=0.1256Ib+0.8744Is. Solving for the surface temperature now gives Ts=314.8 K, 1.8K too high as the signal is corrected for too cold contributions for the window reflections.

4. Including cold window transmittance An experimentalist familiar with the non-unity transmittance of sapphire may attempt to correct the results

through using a measured transmittance instead of only including the effect of surface reflections. This may be achieved through measuring the temperature of a black body at a known temperature through a window at ambient temperature and adjusting the transmittance until the correct value of Ts is obtained. Using this approach but still


6

assuming the window to be at ambient temperature implies carrying out the corrections with Iw=Ibg, giving Itot=0.227Ibg+0.773Is, which produces a surface temperature estimate of Ts=316.8K, a 3.8K overestimate. When finding h and from the calculated T(t) curve, the film cooling effectiveness will be underestimated since the actual contribution from the hot window will be interpreted as a hotter guide vane surface in this model. The heat transfer coefficient, which is proportional to the temperature increase rate divided by (1- when Tt=Tc, will also be underestimated when using the cold window model. As will be shown in Section IV.D, assuming a cold window can generate substantial errors in both parameters.

C. Corrected Tests At a point where the film cooling effectiveness is and the heat transfer coefficient is h, the guide vane

temperature will be given by Eqn. 7. The time t is measured from the application of a step change in gas temperature from Ti to T∞, i. e. from the switching of the bypass valve in the current setup. When the temperature T(t) is known from the IR thermography measurements in the current test, Eqn. 1 can be used to find h and as the parameters giving the best fit to the experimental data. To obtain the best possible guide vane surface temperatures, the window temperature was measured in a separate black window test. This test was run with the inside of the sapphire window painted black with a high-emissivity paint in each point, allowing the instantaneous window temperature to be calculated, after accounting for background reflection. After overlapping the test results in time and space and correcting for minor differences in free-stream gas temperature and cooling air temperature between the two tests, data in each pixel in the guide vane measurement could be accurately corrected. In Figure 4, such corrected data from a single pixel is presented. As can be seen, the fit is excellent with all measured temperatures within 0.5 K of the curve produced by the h and values obtained.

When this technique is applied to every pixel in the IR camera images, h and fields as shown in Figure 5 are

obtained. The pentagonal window shape stems from it being cut from a 100 mm diameter circular window and the desire to maintain as wide a view as possible at the upstream end of the window. The flow direction is from the bottom to the top in these images from the guide vane suction side. The small dots seen on the guide vane surface are blind holes used for image alignment and transformation. The larger dot at the bottom right corner is a paint spot on the window used in some tests for window temperature measurement. The streaks in the streamwise direction are produced by a two spanwise rows of film cooling holes located just upstream of the bottom of the window.

Figure 4. Guide vane surface temperature after applying window and background corrections. Blue dots are measured data and the solid red curve is the fit giving indicated valued of h and .


7

Figure 5. Heat transfer coefficients (left) and film cooling effectiveness (right) on the suction side of a guide vane. The pentagon shape is the sapphire window through which the vane is observed. Flow is from bottom to top.

D. Sensitivity One issue with any form of deconvolution method, such as the correction of window reflection and emission, is how sensitive the results are to the values of correction parameters. In this case, a major source of concern

is the way the two sought parameters affect the measured T(t) curves in a similar manner as shown in Figure 6. Here it is seen that if the heat transfer coefficient, h, is increased by 50% from 200 to 300 W/(m2K) and

the film cooling effectiveness, at the same time is increased by 12% from 0.50 to 0.56, two very similar temperature time traces are obtained, differing no more than 1K from each other over the 30 s covered. This implies that just a minor change in the T(t) slope will affect both parameters obtained from a fit substantially. In addition to suggesting that an error in calibration slope for the camera can have a dramatic impact, it means that the window transmittance must be known accurately. The reason for this is that it essentially acts as a weighing factor which affects how the measured temperature in each point is affected by the window temperature, which as we have seen varies in a similar manner with time as the sought surface temperature, potentially producing the kind of error shown in

Figure 6 if the transmission is chosen poorly. In order to quantify the impact of the window transmittance on h and , the same data set was processed with two different window transmittance values, =0.80 and =0.84 as shown in Figure 7. These values were chose as they are centered on the value =0.82 found to give the best results in comparison to silicon window runs as discussed in Section IV.F.


8

Figure 6. Temperature versus time under indicated run conditions for two different values of h and .

Figure 7. Heat transfer coefficient (top) and film cooling effectiveness (bottom) for one run evaluated using two different window transmittances, =0.80 (left) and =0.84 (right).


9

As expected based on the reasoning above, a small increase in window transmittance, producing a weaker compensation for window temperature, does produce a significant drop in both h and indicated on the guide vane. A systematic study of the effect point by point across an area downstream of the cooling holes shown in Figure 7 made it possible to quantify how much the parameters varied as a function of the parameter values themselves. The results of this investigation are presented in Figure 8 as a scatter plots with a third-degree polynomial fit in h and , respectively. Some validation has been performed to try to reduce the number of spurious data points taken from areas too close to the cooling holes to allow the 1D conduction model to be applied, while retaining enough points to cover wide ranges of h and . The heat transfer coefficient data covers the range 0-500 W/(m2K) and show that the relative deviation in h is greatest for small h and gradually gets smaller as h approaches 500 W/(m2K), going from -8 to -4 over this range. For the film cooling effectiveness, the variation over the range is more complex, but it remains between -2 and -1 for 0.3<<0.8. Hence, a single percent relative error in transmittance can generate up to 8% error in h and 2% error in . The large scatter seen in the plots is a result of the fit algorithm not having converged over the small number of iterations set to allow quick execution, combined with the fact that the cancellation between the two transmittance runs amplifies relative differences.

Figure 8. Relative change in h (left) and (right) relative a change in window transmittance as a function of h and , respectively. Blue dots: pixel data, red curve: curve fit.

To further demonstrate the importance of correcting the acquired data for the window temperature, the same data set was also processed with the window transmittance set to 1 and its index of refraction set to 2.096 rather than 1.65 as is the proper value for sapphire. Using these parameter values will eliminate the window temperature from the analysis but will maintain the same cold external transmittance (77%) as for a sapphire window with the correct transmittance and index of refraction, in line with Model 4 in Section IV.B. The results are shown in Figure 9 and clearly demonstrate that this approach generates large errors in both parameters with h underestimated by 20-50%. For the film cooling effectiveness the largest errors are found in the cooling streaks where not accounting for the contributions from the hot window lead to relative underestimates of by up to 70%.


10

Figure 9. Relative heat transfer coefficient (left) and film cooling effectiveness (right) obtained when processing data assuming a cold window compared to a properly processed case. This comparison was based on a sapphire transmittance of 0.88.

E. Temperature dependence of effective transmittance Given the great sensitivity to window transmittance found in Section IV.D. and the rapid growth of DL with

temperature due to the emission spectrum moving into the range transparent to sapphire and detectable with the current MWIR system, it was decided that the variation in effective window transmittance with radiation wavelength and hence guide vane surface temperature needed to be checked. Since many optical parameters, including the camera sensitivity across the spectrum, the lens and sapphire window transmission spectrum as well as the guide vane paint emissivity spectrum were unknown, only a coarse simulation could be made based on the best guesses for these parameters as shown in Figure 10. The emission spectra at the two temperatures shown, 20 and 60°C, have been based on the assumption of constant emissivity across this region of the spectrum. The sapphire internal transmission spectrum is adapted from the Melles Griot catalog. No data could be found for the lens performance, except that it was designed for use over the 3.5-5 m range of the spectrum, so it was assumed to have 0.9 transmittance at these wavelengths and a smooth function going to zero transmission at 3 and 6 m was applied. For the camera, a generic InSb sensitivity curve obtained from the manufacturer was used for the camera after extrapolating to zero at the spectral ends. Given the many assumptions made in this simulation, it was reassuring to find that the predicted detected signal varied with the absolute temperature to the power 9.8 between the two temperatures tested. A power 8.25 dependency had been found in calibrations, suggesting that the cutoff of the optical system may lie towards somewhat longer wavelengths. As suggested by the figure to the right, the shift to the right in the detected spectrum as the temperature is increased is very small, despite the overly strong wavelength signal-versus-temperature dependency noted. With the current model, the effective (weighted average over relevant spectral portion) transmittance of the sapphire was 0.873 at 20°C and 0.882 at 60°C, a change in 1.0% over the interval studied.


11

Figure 10. Left: Spectra for various system components along with blackbody spectra at two temperatures. Right: Spectral distribution of photos detected by the sensor using these spectra.

F. Comparison to data obtained with a silicon window Based on the sensitivity of the method to window transmittance presented in the present paper, it was decided to

replace the sapphire window with one having very high transmittance in the 3.5-5 m range. There are two primary candidates for reasonably robust window materials in this range, silicon and germanium. After installing an anti-reflex coated silicon window, the runs were repeated and the results could be compared side by side. The results from this comparison are shown in Figure 11. From the raw data, it is clear that the contrast is substantially higher in the silicon run, as could be expected because of the effect of the even window heating on the sapphire window. It is also clear that with a judicious choice of window transmittance, here =0.82, good overall agreement can be obtained between runs with the two window materials. It can, however, also be seen how the deconvolution process required to produce reasonable values from the sapphire run produces much larger pixel-to-pixel noise than is present in the silicon window run. This could probably be greatly reduced by a using a more thorough fit algorithm to find h and from the measured T(t) curve in each point, ensuring complete convergence.


12

Figure 11. Comparison of data from run with sapphire (left) and silicon (right) window. Top: raw digital level DL from camera, Center: film cooling effectiveness, , Bottom: heat transfer coefficient, h (W/(m2K)).

G. Uncertainty Analysis Due to the complexity of the test and the indirect manner in which h and are determined, there are numerous

sources of uncertainty in the determination of these parameters, e. g.

IR camera signal (shot noise, error in calibration)

Background temperature uncertainty

Window temperature uncertainty


13

Uncertainty in observation angle (affecting and of window)

Uncertainty in window properties, particularly

Guide vane property uncertainty, , k,

Uncertainty in thermocouple measurements of free-stream temperature and cooling air temperature

Alignment error between guide vane and window temperature measurements

Neglected contributions in radiometric model, e. g. reflections in guide vane surface of hot objects

Deviations from the mathematical 1D conduction method used The camera uncertainty is given in the specifications as ±1K in over the studied range, which has also been

confirmed in a calibration against a calibrated blackbody source. It is important to note that the type of error is more important than the magnitude of it for these kinds of test. A bias error is of little concern and a random uncertainty has little impact because of the highly over-determined system of equation used for determining h and . What is of great importance is that the slope of the camera calibration is correct since an error here will affect proportionally to the relative slope error. The relative error in h will be half as large. After the calibration the remaining slope error was estimated at 1% over the 20-60°C interval of interest.

When it comes to window properties, the uncertainty in transmittance was estimated as ±0.02 based on the

scatter between different tests and the temperature dependence discussed in Section IV.E. As was noted in Section IV.F. above, the best fit with silicon data was found at =0.82, which is 0.06 less than the 0.88 estimated based on optics databases, and simulations, suggesting that a larger uncertainty may be more appropriate if reference tests are not available. Angle uncertainties of as much as 10° could be expected, but because of the high index of refraction of sapphire, the transmittance was affected less than 0.001 by this, rendering the error negligible. The impact on the reflectance was also negligible for unpolarized radiation. An error in transmittance will produce an improper weighing of the signal contributions from the guide vane and window which will be problematic when the difference in temperature between the two of them is large. As discussed in Section IV.D, the amplification is 8 and 2, respectively for h and , producing an error of 18% in h and 4.5% in .

The uncertainty in guide vane material parameters is, in the present case, primarily due to the anisotropy of the

material introduced as part of the rapid prototyping process, introducing an uncertainty in h of 5% while is unaffected by this.

The uncertainty in thermocouple measurements is taken as 1.5 K. Here the offset error is of interest since it is the

difference between cooling air and hot gas temperatures that is of interest in the determination of , producing a contribution of 0.06 for this parameter but not affecting h.

The alignment error can be estimated as the strongest temperature gradient observed multiplied by an alignment

error estimate of 2 pixels. Using a gradient of 0.05K/pixel in the black window run, the temperature error is 0.1K, which in the worst case of a slope error produces an error of 0.003 in and 0.15% in h.

An upper bound for the error introduced by the emissivity uncertainty on the guide vane can be obtained through

assuming that the reflection is specular and comes from the low ambient temperature. From comparisons with other surfaces, the uncertainty in emissivity is taken as 0.04, producing an error in the vane temperature of 0.6K, corresponding to 0.016 in or 0.1% in h.

Deviations from the 1D conduction model that is used to derive the formula for T(t) based only on local values

of h and come in many different forms. It is well established that heat conduction in the plane of the surface become important near the cooling holes,3 but also in regions with well-developed cooling streaks downstream of the cooling holes as discussed by von Wolfersdorf.6 The error is dependent on the second derivative of temperature in the spanwise direction, d2T/dz2, as well as the time constant of the heating. Von Wolfersdorf found deviations of up to 22% in and 43% in h at the center of the cooling streaks. The errors here are smaller because of the higher heat transfer rates, producing estimates of 8% in and 14% in h from this source.


14


15

Using quadratic error propagation, the total uncertainties are 0.08 in and 23% in h. Using the conventional window model, would be underestimated by 0.07 and h overestimated by 3.5% as the guide vane temperature would have been too high and increased too rapidly without taking the contribution from the heated window into account. The uncertainties in the measurement would have otherwise been similar. A more in-depth discussion of uncertainty analysis for a similar transient heat transfer experiment is given by Moffat.7

V. Conclusion Accurate temperature measurements through viewing ports on a test facility require careful consideration of the

transmittance and temperature of the window material. This is particularly important when the window is hotter than the object whose temperature is being sought and when the method used by Vedula & Metzger,5 Ekkad et al.2 and others is employed to determine both film cooling effectiveness and heat transfer coefficient in a single test. There are three approaches to achieving accurate measurements:

Ensure that the windows are kept at a low, constant temperature during the test, e. g. through use of a strong forced air cooling system on the inside of the windows to keep the hot air away from them.

Use a window material with near-unity internal transmittance in wavelength region of interest, e. g. silicon or germanium for MWIR measurements.

Measure and correct for window temperature as detailed in the current paper. The uncertainty in the method applied in the current paper was found to be 0.08 in film cooling effectiveness and

23% in heat transfer coefficient. These may be reduced substantially be improving accounting for 3D heat conduction effects and employing a window material with high transmittance. Given that the ultimate goal is the determination of Nuc in the model for application on the guide vane, the uncertainty in guide vane material can be eliminated. With further calibrations and corrections, errors of the order of 0.01 and 1%, respectively, appear feasible. Given the large sensitivity to the optical properties of the window material, it is essential to both use a high- material and correct the results for any deviations. Ignoring the effect of the heated window would have led to significant errors in the determination of and h – at the example conditions demonstrated in Figure 9, both parameters would have been underestimated by on the order of 50%.

Acknowledgments The authors would like to thank Siemens for the permission to publish this paper. This work is part of an on-

going effort at Siemens Industrial Turbomachinery to refine the film cooling test rig. The assistance and fundamental work performed on this rig by Bengt Petterson, Daniel Edebro, Emelie Algebrant and Lars Hedberg is gratefully acknowledged. The authors are also grateful for the helpful suggestions by Sven-Gunnar Sundkvist.

References

1 Han, J.-C., Dutta, S., Ekkad, S. V., Gas turbine heat transfer and cooling technology, Taylor & Francis, New York, NY, USA, 2000.

2 Ekkad, S. V., Ou, S., Rivir, R. B., “A transient infrared thermography method for simultaneous film cooling effectiveness and heat transfer coefficient measurements from a single test“, GT2004-54236, ASME Turbo Expo, Vienna, Austria, June 14-17, 2004.

3 Drost, U., An experimental investigation of gas turbine airfoil aero-thermal film cooling performance, Dissertation 28, EPFL, Lausanne, Switzerland, 1998.

4 Reiss, H., Experimental study on film cooling of gas turbine airfoils using shaped holes, Dissertation 31, EPFL, Lausanne, Switzerland, 2000.

5 Vedula, R. P., and Metzger, D. E., “A Method for the Simultaneous Determination of Local Effectiveness and Heat Transfer Distribution in a Three Temperature Convective Situation”, ASME Paper 91-GT-345, ASME Turbo Expo, Orlando, FL, USA, June 3-6, 1991.

6 von Wolfersdorf, J., “Influence of lateral conduction due to flow temperature variations in transient heat transfer measurements”, International Journal of Heat and Mass Transfer, 50, pp. 1122-1127, 2007.

7 Moffat, R. J., “Using Uncertainty Analysis in the Planning of an Experiment”, Journal of Fluids Engineering, 107 (6), pp. 173-178, 1985.

[american institute of aeronautics and astronautics 48th aiaa aerospace sciences meeting including...

Documents