CHAPTER 7 LPV CLOCKING MODELING AND EXPERIMENTAL INTEGRATION
B.3 MAJOR DATA ANALYSIS TECHNIQUES
B.3.2 Airfoil passing envelope technique development
The next two sections discuss techniques for examining the time-resolved data.
These are related in that they look at the same data, but they do it through different perspectives. The FFT technique (which is more common and discussed in the next section) looks at the data in the frequency regime, whereas this technique looks at the data from a time perspective.
The idea relates back to the basic physics of the problem, that the generation of power from a gas turbine comes from the interaction between a rotating and stationary blade row. This produces a periodic pattern. One would expect that this pattern should be repeatable given proper manufacturing tolerances and stable operating conditions.
This periodic pattern contains information about the flow characteristics. Comparing patterns from different blade locations can help the experimentalist infer what is
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happening in those areas, e.g. shock reflection, separation, etc. The pattern arises from some sort of averaging of the many passing events that occur in a given time window.
0.1 0.2 0.3 0.4 0.5 0.6
113 113.5 114 114.5 115
Raw Time-Resolved Data
50% Span, 10% Wetted Distance
Normalized Pressure
TIME (ms) Blade Passing
Figure B.15 Raw Time Data for PR42
Figure B.15 is an example of the raw data. The individual blade passing events are clearly seen in this figure. The question becomes one of generating an average plot for this blade-passing event by adding up all the different passages that occur.
There are lots of different ways to do this. These techniques are sometimes referred to as “ensemble plotting” techniques and involve a process of mapping one passage onto another and then averaging it. Sometimes, one plots the exact same physical passage onto itself (requiring several revolutions). Other times one is just interested in plotting a passage onto its neighbor, so that for a revolution of data that has 38 vanes, the blade sensors would have 38 passages all averaged together. The data can be either in encoder space (which makes the alignment easier) or it can be time-based and some amount of interpolation is needed. The time-based techniques involve creating
“ensemble” plots that phase lock the data so that for any gauge location, points are averaged together which are in the same relative locations in the passage. These can be done in several ways, and one can perform this operation on blades that are in the high vane wakes, or that are upstream of the low vane. The easiest way to think about it is to position yourself on the gauge in question and then think about what other airfoils you
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see going by you. If you are on the blade, you see both the HPV and the LPV go by you, but the other blades seem stationary to you.
In the ensemble average, you try to average together points that occur at the exact same placement in the blade passage. As a specific example, think about a sensor on the blade that is being affected by the low vane. We want to average all the points together that occur when the low vane leading edge is closest to the blade trailing edge. Similarly, you want to move to a slightly different part of the passage and average all these points together.
Having said that, there are a lot of ways to perform this operation. Probably the easiest to understand occurs when the time-dependent data is sampled at specific circumferential locations controlled by an encoder mounted on the rotor shaft. The encoder for this entry was a 500-pulse encoder, meaning that we know the exact time (to within 1E-7 Sec) the blade changes position 1/500 of a revolution. Since one knows the blade and vane count, one can back out which data point lies where in a passage, and it is relatively easy to sort the points out and align them to do the averaging. An example of this procedure may help.
In this case, assume 500 samples in a revolution and that one revolution of data is being examined, and that each sample corresponds to the rotor changing position 1/500 of a revolution. Further, assume that there are 72 blades and 38 vanes. If we are on the rotor, we see 38 vanes go by, and thus we have 500/38 =3.15789 samples/vane passage.
Clearly, a sensor mounted on one blade will not be in exactly the same relative location within the vane passage until 19 vane passages go by (250 samples), and thus one could say that there are 2 integer passages in a revolution, each integer passages consisting of 19 vanes and 36 blades, If you displayed each integer passage and put the next one on top if it, there would be 2 points at each of 250 locations (500 total) and one could
averages these points together to get a shape that describes how the pressure changes with the location in the integer passage (which comprises 19 vane passages).
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One can usually go a step further, since one knows that the second vane in a 19 passage combination is off by a fixed amount, one can move those data points over and place them in the proper relative position on the first vane passage. The same holds true with the third, fourth, etc.. The end result is that one can get increased resolution on one vane passage (in this case 250 points per passage), each point consisting of the average of 2 points. This type of technique is well documented and has been used extensively in the past [62].
Often one does not want to sample data based on the encoder (there are some technical reasons for this that are not critical to the discussion), and as a result one may interpolate from data acquired at fixed increments in time (time-based), into data that is based on fixed rotor positions (encoder based) if one has the encoder position stored as a function of time, which is how our data is usually acquired. However, any linear
interpolation scheme will always tend to attenuate the peaks.
0 0.2 0.4 0.6 0.8 1 1.2
0 50 100 150 200
Original Data (Deg deg Res)
Interpretation Time base (36 Deg Res)
Amplitude
Angle (Deg)
Sample Data to Show How Peaks are Attenuated
Note: you can only capture max value if one of the interpolation points lines up on a max vale
Attemuation
Figure B.16 Sample Data Showing Interpolation Attenuation The data shown in Figure B.16 illustrates this attenuation and was achieved using a simple sine wave and changing the X data from a 10 deg resolution to a 36 deg
resolution. One can see that in this scheme, that the best the interpolated data can due is to capture the peak only if it lines up with the peak (only if the blue dots occur at the peak value). Otherwise it will attenuate the peak a little. Usually this is not a problem, when
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one is looking at general shapes, but when one is comparing these patterns for changes due to clocking (which we expect will be small) one could easily confuse clocking effects with interpolation errors.
The procedure used to avoid this problem was not to interpolate the data from time-base to encoder base, but rather to use the data in the time base and pass in one revolution of data. Doing so requires one to state how many real passages exist in this data. Depending on the speed of the rotor, one might have 800-900 samples in a revolution. The program does a similar job as stated above, but because there are not defined numbers of samples in a rotor revolution, one can get non-rational numbers for the number of samples per passage. This can be accounted for by grouping values that are very close together to perform the average. The end result is that in this case one gets uncertainty bands that occur both in the passage direction (X Axis) and in the amplitude (Y-Axis). A sample of the result of this technique with its uncertainty bands is shown below for the same data shown in Figure B.15.
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
0 0.5 1 1.5 2
Periodic Envelope for PR42, Run 9_M HPB 50% Span 10% W.D. (Suction Side)
Normalized Pressure Envelope
Blade Passing
This is the Range of the Envelope
Y Range Bars are the STD of the average at that location in the passage
X Range bars are the STD of the Location used in the binning operation
Figure B.17 Example of Time Based Ensemble Plots
In these plots, two passages are generally shown (although they are exact duplicates) to aid in seeing the pattern. The trade-off using this technique is that one can combine variations that occur naturally with each passage with the variations in the X position and these are grouped together into the uncertainty band. This is very clear in PR42 at about
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0.65% of passage where the uncertainty range on that point is due to some of the data being used to generate the average is closer in x location to the lower point and others are closer to the higher point. For this work, it was decided that this trade-off was
worthwhile since the main peaks are not being attenuated in the interpolation, but the data could easily be processed in encoder space if desired. We will mainly be interested in the envelopes sizes, which come from the maximum and minimum of the envelope. The overall size of the envelope can be compared between clock positions computationally as well as visually. Because of the large amount of data involved, the envelope size
becomes a great way to characterize the envelope with just one data point, although some sample plots will be shown of the actual envelopes themselves.
As a comparison with the more involved time envelopes discussed previously, one can get an initial estimate of the periodic envelope just from basic statistics of the data. Shown below is an example of this technique.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
-100 -50 0 50 100
Different Methods for Characterizing Periodic Envelope HPV 50% Span
1 Rev Average From Ensemble Technique 2 Rev Average (Straight)
2 Rev Average + STD over averaging period 2 Rev Average - STD over averaging period
Normalized Pressure
% WETTED DISTANCE
For Ensemble Technique (Red) Bars Represent Average Max and Min Values for a passage For Straight Average (Blue) Bars Represent Max and Min Values
Figure B.18 Comparison of Techniques for Estimating Periodic Envelope
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In this figure, the time average values for the HPV at 50% span are plotted. The red dots are a 1 revolution average, the blue dots are an average over two revolutions.
One can see that the averages line up with each other (as expected). The range bars for the red signal come from the maximum and minimum of the envelope calculations.
These maximum and minimums are an average passage maximum and minimum. The blue range bars represent the absolute maximum and minimum from the data array used to generate the average (in this case a two revolution period). The black lines represent the standard deviation of the signal over this same period.
One can immediately see that the standard deviation of the array tracks the overall envelopes as calculated by the much more computationally intensive operation of
generating the passage plots. The blue lines overestimate the range dramatically which is not surprising since these measurements do not include any averaging techniques and are just representations of the absolute maximum and minimum signals measured over this time period (there is no filtering here). The HPV was chosen for this plot because one can see that on the pressure side, where there is essentially no envelope, the standard
deviation repeats this result well. However, on the trailing edge on the suction side where there is a lot of interaction between the blade and the vanes, the standard deviation reproduces that envelope well. Examining the blue range bars, one can see that on the pressure side of the vane there is a much larger variation in the input signal. This is due to the fact that this location is the most sensitive to variations in the facility input
parameters. However, using the standard deviation of the signal puts these variations in perspective and illustrates that though one may have data points that are far outside of the expected range, they are relatively few (otherwise the standard deviation would be much larger).
The reason the standard deviation tracks the envelope so well can be seen by modeling the periodic pattern as a sine wave of amplitude “A” and mean value of 0. The definition of the standard deviation we have for one period
STD= N
N– 1 nS= 1N Asin i 2 fiA NN– 1nS= 1N sin 2i fiA NN– 1p
that for large N comes out to a value of STD = 1.7A.
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Now for an actual envelope one would have a value of A. The physics are more complicated for the turbine case since there are several different amplitudes that make up the passage plot, but the rough calculation shown above shows that one would expect the standard deviation to track the envelope well, and experimentally it does. If one has already calculated the envelopes, there is no need for this operation. But during the data acquisition part of the experiment, this trick can be used to estimate the periodic
envelopes with very little knowledge other than just a time window large enough to generate some reasonable statistics. This is often used as a sanity check on the pre- experiment predictions.