CHAPTER 7 LPV CLOCKING MODELING AND EXPERIMENTAL INTEGRATION
C.4 TIME-RESOLVED HEAT-FLUX
As a final example of the information available in this data set, the time-resolved heat flux will be examined. In this case only the FFT data will be shown in keeping with the principles of minimal processing. It seems certain that the envelope data could also be obtained, however, due to the numerical algorithms used to produce the heat-flux, these will be relatively noisy as compared to the pressure data.
Before presenting the data, it is worthwhile to address the question of “Why should we care about the unsteady heat-flux.” A quick calculation shows that penetration depths of a 10KHz temperature pulse into a metal surface has a characteristic length on the order of fractions of a mil (0.001”) depending on the material. While this is a small dimension, it is not uncharacteristic for thermal barrier coatings. In addition Boley and Weiner [63] discuss the idea of thermal induced vibrations in thin plates and have shown that thin plate configurations similar to the skin on a cooled blade might produce thermal deflections up to twice the static deflections in certain cases5. However, to the
community outside of the engine design world, it is unclear if there is an engineering problem or not. It is clear that the unsteady pressure envelope can have large impact on the cooling system and on high cycle fatigue. It is not clear if a scientific problem exists due to large heat flux oscillations at these high frequencies that if it has been solved, at least in the industrial world, by proper coatings. The only people that know for sure are the blade designers at the engine companies and this data is provided for their
consideration, but a detailed analysis is not really required unless one hypotheses a problem to be solved. However, even without a current problem, there are at least three reasons why one might be interested in the unsteady heat-flux.
1) The data come without cost. By this I mean that to ensure that one has accurate time-averaged data that is not being influenced by the measurement device, one needs very high frequency resolution. Thus, one gets the time resolved data for free. What one does with it is up to the engineer, but an overall measurement of the quality of the time-averaged heat-flux data is the quality of the time-resolved heat-flux data.
5 See sections 12.7 and 10.1 for further discussion
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2) It is unclear how the time resolved heat-flux and the pressure envelopes interact. This may be more of an interest for the pressure data than for the heat-flux data, but it may become more important in the measure of cooling effectiveness
3) We just don’t know what importance the unsteady heat-flux may have. We have long known about the unsteady heat-flux, and my Master’s work at MIT argued that burn-out at the trailing edge of rotor shrouds could be due to the fact that the unsteady heat-flux magnitude remained constant as the flow proceeded from the leading edge to the trialing edge, but the average level decreased dramatically, thus the ratio of the unsteady envelope to the time averaged increased dramatically towards the trailing edge. With machines that are now fully instrumented over large 3-D portions of all airfoils, one can begin to empirically correlate problems with turbine design to areas of high unsteady heat-flux. We may just be much less experienced in this area than we are with the pressure data. I still remember a time when the major engine companies did not think that unsteady pressure envelopes had any engineering design relevance
With the above discussion in mind, the following figures are put forward as examples of the information that can be obtained from a more detailed examination of the unsteady envelopes. As alluded to earlier, the unsteady heat-transfer data is harder to obtain without some extra processing due to the nature of the algorithms. In general, areas of very high unsteady pressure also have high values of unsteady heat-flux. It is those gauges that will be shown below without any extra filtering. Only the HPV and LPV will be shown, since the slip-ring noise on the rotor dominated most frequencies with the exceptions of the data at the tip.
Figure C.11 shows two gauges close together about half way back on the suction side. These were chosen because it shows how the envelope dies out as one moves forward. For both figures the power spectrum of the temperature and the heat-flux are shown. In addition, some of the key frequencies present in the plot are shown.
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0 0.02 0.04 0.06 0.08 0.1
0 1 104 2 104 3 104 4 104 5 104
0 10000 20000 30000 40000 50000
Run9, 1 Rev FFT Data
HPV 50% Span, 50% Wetted Distance (Suction Side)
HV16: Temp HV16: Heat-Flux
Peak Temp (Deg C) Heat-Flux (W/M^2)
Frequency (Hz)
Measures Key freq:
10640Hz
12688 and 13276
Blade Passing (Calc): 10776 Hz
0 0.02 0.04 0.06 0.08 0.1
0 5000 1 104 1.5 104 2 104 2.5 104
0 10000 20000 30000 40000 50000
Run9, 1 Rev FFT Data
HPV 50% Span, 40% Wetted Distance (Suction Side)
HV28: Temp HV28: Heat-Flux
Peak Temp (Deg C) Heat-Flux (W/M^2)
Frequency (Hz) Measures Key freq:
12766 Hz 10477 Hz 25490 Hz
Blade Passing (Calc): 10776 Hz
Figure C.11 HPV 50% span Power Spectrum, Selected Gauges
These data are shown over one revolution using the interpolation techniques describe earlier (actual FFT resolution is 149 Hz). For the gauge at 50% location (HV16), one can see that the main peak in both temperature and heat flux occurs at 10.6 KHz which is very close to the calculated blade passing frequency. There are other characteristic frequencies that show up at 12688 and 13276. The 13276 Hz number is interesting because it represents a combined frequency of the rotor blade count and 1/2 of the vanes. However, clearly it is a very low signal. Just a little forward of this location at 40% span (HV28), the main blade passing frequency is almost completely gone. There is more action on the LPV as is shown in Figure C.12.
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0 0.01 0.02 0.03 0.04 0.05
0 5000 1 104 1.5 104 2 104 2.5 104
0 10000 20000 30000 40000 50000
Run9, 1 Rev FFT Data
LPV 50% Span, 26.7% Wetted Distance (Suction Side)
Temp Heat-flux
Peak Temp (Deg C) Heat-Flux (W/M^2)
Frequency (Hz)
Measures Key freq:
10793 Hz 15058 Hz 21629 Hz
Blade Passing (Calc): 10776 Hz
0 0.01 0.02 0.03 0.04 0.05
0 5000 1 104 1.5 104 2 104 2.5 104
0 10000 20000 30000 40000 50000
Run9, 1 Rev FFT Data
LPV 50% Span, 40% Wetted Distance (Suction Side)
HLV32: Temp HLV32: Heat-flux
Peak Temp (Deg C) Heat-Flux (W/M^2)
Frequency (Hz)
Measures Key freq:
10782Hz 13667 Hz 21535Hz
Blade Passing (Calc): 10776 Hz
0 0.01 0.02 0.03 0.04 0.05
0 5000 1 104 1.5 104 2 104 2.5 104
0 10000 20000 30000 40000 50000
Run9, 1 Rev FFT Data
LPV 50% Span, 90% Wetted Distance (Suction Side)
HLV34: Temp HLV34: Heat-flux
Peak Temp (Deg C) Heat-Flux (W/M^2)
Frequency (Hz)
Measures Key freq:
10733Hz
Blade Passing (Calc): 10776 Hz
Figure C.12 LPV 50% span Power Spectrum, Selected Gauges
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In this figure, three different locations on the LPV suction surface are shown.
One can see the main frequency decay as one moves downstream. What is interesting is that there is some action at 15KHz for the 27% location, and a slightly lower frequency (that 13KHz number) for the 40% location. In addition, the 40% location clearly has multiple harmonics while the first harmonic seems to die away by the 90% location.
Another interesting point is that the frequency content remains viewable even as one processes the temperature data into heat-flux suggesting that relative sizes of the unsteady envelopes should be obtained from the raw temperature data instead of the heat-flux sensors if one wanted to try to reduce noise.
As a final comparison, Figure C.13 shows how the data compares for HV16 from different runs (in the same group).
0 500 1000 1500 2000 2500
0 0.0002 0.0004 0.0006 0.0008 0.001
0 10000 20000 30000 40000 50000
Run5, 1 Rev FFT Data
HPV 50% Span, 50% Wetted Distance (Suction Side)
HV16: Nusselt Number HV16: Stanton Number
Peak Nusselt Number Stanton Number
Frequency (Hz)
Measures Key freq:
10717 Hz 15769 Hz 21494 - 22361 Hz
Blade Passing (Calc): 10760 Hz
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
HPV 50% span, 50% Wetted Distance (Suction side) Comparision Runs 5 and 9
HV16: Run 5 HV16: Run 9
Peak Temp (deg C)
Frequency (Hz) Main Freq:
Run 5- 10711 Hz Run 9- 10640 Hz
15762 Hz 16281 Hz (also at 12688 and 13276) 21491 Hz 21908 Hz
Figure C.13 Comparison between Runs
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As one would expect, the Nusselt number and Stanton number calculations contain the same frequency data, and the variation between run 9 and run 5 is due primarily to frequency shifts due to slight changes in speed.