CHAPTER 5 AERODYNAMIC DATA AT ONE CLOCKING POSITION
5.3 TIME-RESOLVED PRESSURE ENVELOPES AND FFT’S
The time-resolved pressures data is important in visualizing how the envelope sizes, and FFT magnitudes change in the clocking analysis. They will be presented in two modes: a time domain mode, which will be envelopes, and a frequency based mode that will be power spectrums (FFTs).
The HPV time averaged values with the time-resolved data are shown in combination figures in Figure 5.3 to Figure 5.5. These figures show the envelope maximum and minimum as range bars on the time-averaged data and the small figures show the actual envelope or the power spectrum results. For all these figures, there is no action on the pressure side all the way to the 40% location on the suction surface. Only the last five sensors show any significant variation. The small plots are all 2 blade- passing plots, and the vertical scale is the same for all figures. One can see how the strong peak and valley that are close to each other at the 50% wetted distance location spreads out at the 60% location and then forms into a two-pulse system at the 70% and 90% locations. The same data shown in Figure 5.3 is reproduced as a power spectrum in Figure 5.4, where the FFTs are printed in absolute pressure units (as opposed to
normalized pressure), so that one can get a feel for the absolute size of these fluctuations.
While all the harmonics are clearly visible in the data, the relative importance changes for different locations on the airfoil with the first harmonic being larger than the fundamental at the 50% location. Figure 5.5 shows the same data, but in this case the FFT is
normalized. The red lines (which are hard to see) are the pressure fluctuations
normalized by the inlet total pressure. The blue lines are the data normalized by the local average pressure. The maximum value shown is 7%. What is important to realize is that the fluctuations can represent a significant fraction of the average local pressure.
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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
-100 -50 0 50 100
Tech56 HPV 50% Span Time Averaged Values
Bars Represent Average Max and Min Values During Blade Passing For One Revolution of Data
Average
P Local/P total
% WETTED DISTANCE
-0.1 -0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV21 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing
-0.1 -0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV13 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing -0.1
-0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV22 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing -0.1
-0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV26 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing -0.1
-0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV11 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing
-0.1 -0.05 0 0.05 0.1
0 0.5 1 1.5 2
Passage_press.dat
PV25 (Avg) Unsteady Pressure (PL/Ptotal)
Blade Passing
Pressure side to 40% WD all Flat
Figure 5.3 HPV 50% Time-Averaged Normalized Pressures with Envelopes
64
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
-100 -50 0 50 100
Tech56 HPV 50% Span
FFT's and Time-Average Values for 2 Revolutions All FFT's are in absolute units scaled 0 to 12 KPa Average
P Local/P Total
% WETTED DISTANCE
0 2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run 31 HPV 50% Span PV10: Amp
Amplitude
Frequency
0 2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run31_HPV_120_136.8.FFT_all PV13: Amp
Amplitude
Frequency 0
2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run31_HPV_120_136.8.FFT_all PV22: Amp
Amplitude
Frequency 0
2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run31_HPV_120_136.8.FFT_all PV26: Amp
Amplitude
Frequency 0
2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run31_HPV_120_136.8.FFT_all PV11: Amp
Amplitude
Frequency
0 2 4 6 8 10 12
0 10000 20000 30000 40000 50000
Run31_HPV_120_136.8.FFT_all PV25: Amp
Amplitude
Frequency
Pressure side to 40% WD all Flat
Figure 5.4 HPV 50% Span Time Averages with Absolute FFT's
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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
-100 -50 0 50 100
Tech56 HPV 50% Span
FFT's and Time-Average Values for 2 Revolutions All FFT's are Normalized (Max value shown is 7%) Average
P Local/P Total
% WETTED DISTANCE
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV10: Amp/Ref PV10: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV13: Amp/Ref PV13: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV22: Amp/Ref PV22: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV26: Amp/Ref PV26: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV11: Amp/Ref PV11: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0 10000 20000 30000 40000 50000
Tech56 HPV 50%
Normalized FFT Data Local Amplitude/Inlet Total Presure (Pr)
and Pr/Pr(Avg) PV25: Amp/Ref PV25: Amp/Ref /[Amp/Ref (avg)]
Normalized Amplitude
Frequency
Pressure side to 40% WD all Flat
Figure 5.5 HPV 50% Span with Normalized FFT's
66
Since there is a lot more periodic behavior on the HPB and LPV, the data for these airfoils will be presented a little differently. In Figure 5.6 to Figure 5.12 for the HPB and Figure 5.13 to Figure 5.16 for the LPV, both the normalized FFT and the Ensemble envelopes will be shown. As stated earlier, the red lines are the amplitudes normalized by the total inlet pressure, while the blue lines are the amplitude normalized by the local average pressure. The bars on the envelope figures show the range of data at each position in the passage used to generate the average (don’t forget that this includes some of the error in the passage location since this data is not phase locked, as discussed earlier). The data proceeds from pressure side trailing edge to suction side trailing edge.
To start, Figure 5.8 shows the difference between the pressure side and the suction side of the blade close to the leading edge. On the suction surface the second harmonic
dominates, although both the fundamental and first harmonic is close in size, whereas on the pressure side, the second harmonic is virtually non-existent. While the fundamental and first harmonics are of similar size between the two positions, the effect of not having that second harmonic makes the ensemble shape very different and generates a range of the envelope of about three times less on the pressure side. Moving towards the trailing edge on the pressure side (going towards Figure 5.6), one can see how there is an energy transfer between the higher harmonics and the main frequencies with the second
harmonic growing again in importance at –45%, and then dying off, leaving the
fundamental. While the shape of the envelope changes a little in this area, the range stays fairly constant at about ±0.04.
On the suction surface, the story is much different. Here there is a great deal of harmonic energy that dies of by about the 30% location. The frequencies and the envelopes become hard to discern from about 40% to about 70%. After that the main frequencies increase a little and the envelope becomes more defined. This seems to indicate that the influence of the HPV is prevalent over the early part of the blade, and the LPV over a latter part, but that there is an area where there is not much influence (on this machine at the 50% span location!)
67
The LPV data is shown in Figure 5.13 to Figure 5.16. The main frequencies are also apparent on the LPV, and probably the most interesting is that the unsteadiness on the pressure side toward the leading edge can be about the same magnitude as on the HPB. Thus, the relative fraction of the average pressure for each frequency can be relatively high on the LPV.
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0 0.01 0.02 0.03 0.04 0.05
0 10000 20000 30000 40000 50000
PR24: Amp/Ref
PR24: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05
0 10000 20000 30000 40000 50000
PR48: Amp/Ref
PR48: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.04 -0.02 0 0.02 0.04
0 0.5 1 1.5 2
PR24 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.04 -0.02 0 0.02 0.04
0 0.5 1 1.5 2
PR48 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -75% Wetted Distance = -60%
Figure 5.6 HPB 50% Span FFT's and Ensemble Plots (A)
69
0 0.01 0.02 0.03 0.04 0.05 0.06
0 10000 20000 30000 40000 50000
PR23: Amp/Ref
PR23: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05
0 10000 20000 30000 40000 50000
PR22: Amp/Ref
PR22: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.04 -0.02 0 0.02 0.04
0 0.5 1 1.5 2
PR23 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.04 -0.02 0 0.02 0.04
0 0.5 1 1.5 2
PR22 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -45% Wetted Distance = -20%
Figure 5.7 HPB 50% Span FFT's and Ensemble Plots (B)
70
0 0.01 0.02 0.03 0.04 0.05
0 10000 20000 30000 40000 50000
PR46: Amp/Ref
PR46: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
0 10000 20000 30000 40000 50000
PR42: Amp/Ref
PR42: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.04 -0.02 0 0.02 0.04
0 0.5 1 1.5 2
PR46 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
0 0.5 1 1.5 2
PR42 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -10% Wetted Distance = 10%
Figure 5.8 HPB 50% Span FFT's and Ensemble Plots (C)
71
0 0.02 0.04 0.06 0.08 0.1
0 10000 20000 30000 40000 50000
PR18: Amp/Ref
PR18: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.02 0.04 0.06 0.08 0.1
0 10000 20000 30000 40000 50000
PR43: Amp/Ref
PR43: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.12 -0.08 -0.04 0 0.04 0.08 0.12
0 0.5 1 1.5 2
PR18 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.12 -0.08 -0.04 0 0.04 0.08 0.12
0 0.5 1 1.5 2
PR43 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = 20% Wetted Distance = 30%
Figure 5.9 HPB 50% Span FFT's and Ensemble Plots (D)
72
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR19: Amp/Ref
PR19: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR44: Amp/Ref
PR44: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR19 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR44 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = 40% Wetted Distance = 50%
Figure 5.10 HPB 50% Span FFT's and Ensemble Plots (E)
73
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR20: Amp/Ref
PR20: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR45: Amp/Ref
PR45: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR20 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR45 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = 60% Wetted Distance = 70%
Figure 5.11 HPB 50% Span FFT's and Ensemble Plots (F)
74
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR45: Amp/Ref
PR45: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PR21: Amp/Ref
PR21: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR45 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PR21 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = 70% Wetted Distance = 80%
Figure 5.12 HPB 50% Span FFT's and Ensemble Plots (G)
75
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV32: Amp/Ref
PLV32: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.02 0.04 0.06 0.08 0.1
0 10000 20000 30000 40000 50000
PLV31: Amp/Ref
PLV31: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV32 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV31 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -58% Wetted Distance = -26%
Figure 5.13 LPV 50% Span FFT's and Ensemble Plots (A)
76
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV30: Amp/Ref
PLV30: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV29: Amp/Ref
PLV29: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV30 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV29 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -17.3% Wetted Distance = -8.7%
Figure 5.14 LPV 50% Span FFT's and Ensemble Plots (B)
77
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV28: Amp/Ref
PLV28: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV17: Amp/Ref
PLV17: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV28 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV17 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = -0.2% Wetted Distance = 26.7%
Figure 5.15 LPV 50% Span FFT's and Ensemble Plots (C)
78
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV17: Amp/Ref
PLV17: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 10000 20000 30000 40000 50000
PLV18: Amp/Ref
PLV18: Amp/Ref /[Amp/Ref (avg)]
Normalized Peak Amplitude
Frequency
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV17 (Avg)
Unsteady Normalized Pressure
Blade Passing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
0 0.5 1 1.5 2
PLV18 (Avg)
Unsteady Normalized Pressure
Blade Passing
Wetted Distance = 26.7% Wetted Distance = 40%
Figure 5.16 LPV 50% Span FFT's and Ensemble Plots (D)
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It is important to note that the preceding figures that describe the time resolved data can only be created from one run. Similar types of plots are not available when one examines the average condition, as done in the next chapter. What can be done is to look, on average, at indicators of the time resolved data, such as the FFT magnitudes,
frequencies, and envelope sizes, and then compares how these change with clocking as done in the next chapter. Since the clocking effects are small, the figures shown in this section provide a very good review of the shape of the pressure envelopes throughout the machine, for all conditions.