第21卷 第3期
2007年09月
实验流体力学
Journal of Experiments in F luid Mech anics
V ol.21,N o.3
Sep.,2007
文章编号:167229897(2007)0320070206
Tubing2transfer2function correction on signal distortion
for unsteady pressure measurementsΞ
Y ANG Hui1,D.B.SI MS2WI LLI AMS2,HE Li2
(1.Aero2engine Numerical Simulation Research Center,Beijing University of Aeronautics and Astronautics,
Beijing100083,China;2.School of Engineering,University of Durham,Durham DH13LE,UK)
Abstract:A method of correcting distortion in the measured unsteady pressures using a tubing system and off2board pressure transducers is described.This technique inv olves the using of the frequency domain correc2 tion with a known Tubing2Trans fer2Function(TTF).The advantage of this method not only corrects the am pli2 tude distortion but als o eliminates the phase shift.The technique is verified in an unsteady surface pressure measurement of a turbomachinery blade flutter test and for wake measurements of a v ortex shedding case.
K ey w ords:unsteady pressure measurement;tubing2trans fer2function correction technique;off2board pressure transducer;turbomachinery blade flutter;unsteady v ortex shedding;wake measurements
杨 慧1，西姆斯2威廉姆斯・戴维2，何 力2
(1.北京航空航天大学航空发动机数值仿真研究中心，北京 100083;2.英国达勒姆大学工程学院，英国达勒姆
DH13LE)
摘要：使用外置压力传感器测量非定常压力会造成非定常测量信号失真。这是由连接外置传感器和测点之间的管道传压系统引成的。阐述了一种修正这种非定常信号失真的方法。从而使得运用外置传感器测量非定常压力成为可能。这种技术使用已知的管传递函数在频域中修正非定常测量信号的失真。同时修正失真信号振幅的变化和相位角的偏移。给出了这种修正技术的运用实例：在叶轮机颤振试验中测量叶片表面非定常压力和在非定常旋涡脱落试验中测量尾迹。 关键词：非定常压力测量；管传递函数修正技术；外置压力传感器；叶轮机叶片颤振；非定常旋涡脱落；尾迹测量
中图分类号:V211.1+5;V211.71 文献标识码:A
0 I ntroduction
In recent years,numerical methods for predicting un2 steady flows through oscillating cascades in turbomachines have been fully developed.In order to validate these codes,systematic,accurate and detailed unsteady pressure experimental data are required.M ost previous measure2 ments are con fined to use miniature high2response pressure transducers buried in blade surfaces (largely on tw o2dimensional sections)from linear
ΞReceived date:2006211209;Revised date:2007201231
Author biography:Y ANG Hui(1970-),female,born in Fuyang city Anhui province.P ostdoctor.Research field:experimental and nu2 merical research in flutter and forced response in turbomachinery.
contour as well as costs,only limited number of unsteady signals can be obtained.Thus,unsteady(static and stag2 nation)pressure field patterns are not identified.These could be used to im prove understanding,and to identify limitations of m odeling and to aid future development of both aeromechanic and unsteady loss) applications.M oreover,with embedded transducers,the m ovement of the blade subjects the transducer to an accel2 eration,for which extensive calibrations and corrections are required.And various installation con figurations have been designed to is olate the miniature pressure transducers from the aerofoil strain and centrifugal loads to im prove the du2 rability.Als o im proved transducer characteristics are de2 sired to diminish tem perature sensitivity.Thus,in order to provide the required spatial res olution of the unsteady flow measurements at blade surfaces various optical measurement techniques(pressure sensitive paints,doppler sens ors,mi2 cromachined fabry2perot pressure sens ors and s o on)were developed.H owever,every method requires a com plicated optical technique and expensive equipm
ent.
These issues can be av oided by using off2board pres2 sure transducers with correction of the tubing distortion.A blade can be instrumented by detailed static pressure tap2 pings,which are connected to off2board pressure transduc2 ers by pneumatic tubing.The tubing system is character2 ized by the tubing length,its internal diameter and the transducer internal v olume.It introduces certain distortion of unsteady signals.In the area of turbomachinery aeroelas2 ticity,this distortion of unsteady signals is generally either neglected because of low frequencies and short tubing le2 ngths[9]or sim ply corrected for phase lag and am plitude at2 tenuation for a certain tubing length[10].In contrast to low reduced frequencies for blade flutter,in the case of forced response higher frequencies ass ociated with higher order m odes can be excited.Even for the low m odes of blade flutter applications,higher flow velocity at m ore realistic conditions requires a higher physical frequency to reach a realistic reduced frequency.I f off2board pressure transduc2 ers are used to measure unsteady signals,these signals will be distorted by the pressure measuring system and a correc2 tion must be performed.In the blade flutter test,a correc2 tion method is used which is m ore generally applicable in that it corrects phase lag and am plitude change for all fre2quencies using a measured Tubing2Trans fer2Function (TTF)for each tube.This approach makes economical use of th
e pressure transducers.F or flow2field measurements, the requirement for miniaturization of pneumatic probes makes the use of off2board transducers particularly attrac2 tive.Traditionally,connecting the off2board pressure trans2 ducers to a Pneumatic probe has been limited to steady2 state measurements only.By using TTF correction it is pos2 sible to use a conventional pneumatic probe to make time2 accurate measurements.
In the present paper,a TTF approach with correction in the frequency domain is described.T ypical trans fer functions are presented and the correction technique is dem onstrated for the tubing system in is olation,for un2 steady surface pressure measurements in a turbomachinery blade flutter test and for wake measurements in a v ortex shedding case.
1 Theory of tubing2transfer2function approach
The TTF approach is based on a technique originally em ployed for wall pressure measurements in wind engineer2 ing by Irwin et al[11].This technique was subsequently ap2 plied for time2accurate measurements of unsteady flow2 fields by using multi2hole probes[12213].T o the authors’knowledge,it is the first use of TTF approach for unsteady surface pressure measurements in turbomachinery aeroelas2 ticity.
In measuring an unsteady pressure,the signal propa2 gates from a pressure tapping or a probe head to an off2 board pressure transducer via a tubing between them.The signal can be am plified by res onance effects at particular frequencies and will be attenuated by viscous effects at higher frequencies.There will als o be a time2lag for the pressure signal to reach the transducer which will result in an increasing phase offset at higher frequencies.This fre2 quency2dependent tubing response can be characterized by a trans fer function.Once the trans fer function of a given tubing system is known,it is possible to correct the mea2 surement for the tubing distortion.This technique requires the system to obey the principal of linear superposition s o that an unsteady signal can be decom posed into multiple frequency com ponents and this has been con firmed.
鹿心社简历17
第3期 Y ANG Hui et al:Tubing2trans fer2function correction on signal distortion for unsteady pressure measurements
T o utilize this approach,the TTF of a measuring sys2 tem must be known in advance.This can be obtained ex2 perimentally.A test signal including a range of frequencies is recorded by a reference pressure transducer directly and by test pressure transducer via a tubing length used for ac2 tual un
steady pressure measurements.Fast F ourier Trans2 forms(FFT)of both the undistorted and distorted signals are performed.The unsteady part of the undistorted pres2 sure p A(t)is written as a F ourier series:
p A(t)=6+∞n=-∞A n e i2nπft(1) The distorted unsteady pressure p B(t)can be described as:
p B(t)=6+∞n=-∞B n e i2nπft(2)
Then the com plex tubing2trans fer2function T
n
(f)is expressed as:
T n(f)=B nΠA n(3)
where A
n
and B n are the com plex F ourier coefficients of the pressure individually.
When aerodynamic measurements are later recorded, the F ourier coefficients of the distorted signal(B′n)are obtained.The known trans fer function(T n(f))is then used to in fer the F ourier coefficients of the signal prior to distortion(A′n):
A′n=
B′n
T n(f)
(4)
Finally,the corrected pressure p′什么是美貌效应
B
(t)is constructed through the corrected A′n:
p′B(t)=6+∞n=-∞A′n e i2nπft(5) Both am plitude and phase distortions are rem oved, the latter being essential in the blade flutter test where multiple simultaneous signals are to be com pared.
2 Implementation issues
A block diagram of the apparatus used in measure2 ments of TTF of a tubing system is presented in Fig. 1.A swept sine wave is generated by a sweep function generator which covers the range of frequencies of interest and this is fed to an audio am plifier and loudspeaker.The loudspeaker produces pressure fluctuations with the roughly same wave
forms as the input v oltage.The loudspeaker is connected to a small cavity via a short rubber tube to is olate mechanical vibrations.A reference pressure transducer is directly
con2 nected to the small cavity and used to record the pressure inside the cavity.A static pressure tapping used in the un2 steady signal measurements is als o connected to the cavity.
A length of plastic tube used to connect the static pressure tapping with the test pressure transducer is as w ould be done for the aerodynamic measurements.
Fig.1 Tubing2T rans fer2Function measurement app aratus
(not to scale)
图1 管传递函数测量设备(非等比例)
Fig.2illustrates the effectiveness of the TTF correc2 tion in reconstructing an original reference signal from a distorted one.The tubing system
of Fig.2was subjected to a100H z saw waveform.Significant phase lag and am pli2 tude attenuation relative to the reference signal is clearly apparent in the uncorrected signal and the increased atten2 uation of higher harm onics alters the waveform shape.“C orrected”signal can be seen to closely match the original reference signal.
Fig.2 E ffect of TTF correction w ith single hole of a52hole
probe(100H z sa w w ave)
图2 五孔探针单孔的管传递函数的修正效果(100H z锯
形波)
3 Examples
Fig.3shows a typical exam ple of the measured TTF
27实 验 流 体 力 学 (2007)第21卷
for a tubing length (180mm )used in the blade flutter test.In this case a slight am plification can be seen over the fre 2quency range of interest ,indicating a res onant peak at a higher frequency.The phase distortion is m ore significant due to the im portance of the relative phase of unsteady pre 2ssure fluctuations and the vibration of the
blade.
Fig.3 Tubing 2T rans fer 2Function of the measurement
system for the blade flutter test (brass tube ,180mm ×1mm portex tubing and connector)
图3 叶片颤振试验测量系统的管传递函数(铜管,
180mm ×1mm 塑料管和连接头)
Fig.4shows the TTF for a single tube of a 52hole probe used to wake measurements of a blu ff body exhibiting v ortex shedding.Small tube diameters near the probe head and a longer tubing length (1500mm )result in a system in which viscous attenuation dominates over any res onant ef 2fects.
F or measuring unsteady periodic flow 2fields ,probes with TTF correction are combined with the unsteady recon 2struction technique of Sims 2Williams and Dominy
[14]
to ob 2
tain instantaneous flow 2field data.A signal from a station 2ary reference probe and a com plex conv olution in the fre 2quency domain are used to effectively synchronize probe measurements made sequentially.This provides a m ore ro 2bust determination of relative phase than sim ply using trig 2
gered sam pling and makes this technique appropriate even for weakly periodic flow 2fields.Fig.5shows the instanta 2neous v orticity field in the wake of a “G urney Flap ”high
lift device on the trailing edge of an inverted aerofoil (x 2y plane is normal to the height of the G urney flap ).By pro 2ducing a series of these images v ortex shedding can be
clearly observed.
Fig.4 Tubing 2T rans fer 2Function of the measurement
system for the vortex shedding case (52hole probe ,1500mm ×0.75mm portex tubing and connector)
图4 涡脱落试验中测量系统的管传递函数(五孔探
针,1500mm ×0.75mm 塑料管和连接头)
Unlike other methods of unsteady flow 2field measure 2
ments ,the use of a pressure probe allows the observation of static and stagnation pressure as well as velocity.Fig.6il 2lustrates the instantaneous stagnation pressure field corre 2sponding to Fig.5.An issue of interest regarding the un 2derstanding Πinterpretation of unsteady flows is the decou 2pling between instantaneous stagnation pressure (the mea 2sure of loss for steady flow only )and entropy (the measure of loss in general ).This has been observed com putationally for a LP turbine cascade subject to incoming unsteady wak 2es
[15216]
and has been observed com putationally and experi 2
mentally adjacent to the wake of blu ff bodies exhibiting v or 2tex shedding
[17]
.In Fig.6,packets of stagnation pressure
3
7 第3期 Y ANG Hui et al :Tubing 2trans fer 2function correction on signal distortion for unsteady pressure measurements
deficit corresponding to the shed v ortices can be observed but im portantly it is als o possible to see regions where the stagnation pressure coefficient is greater than unity.The frequency of the shedding in this case was approximately 300H z.Further details of this w ork on G urney flap v ortex shedding may be found in Ref.[18]and [19
].
Fig.5 I
nstantaneous non 2dimensional vorticity in the w ake
of a G urney flap (norm alized by chord c )
图5 摆动翼尾迹中的瞬时涡(对弦长c 无量纲化)
Fig.6 I nstantaneous stagnation pressure coefficient in the
w ake of a G urney flap (norm alized by chord)
图6 摆动翼尾迹中的瞬时总压系数(对弦长无量纲化)
T o validate the use of TTF correction for probe mea 2surements the 52hole probe used above was m ounted adja 2cent to a single element hot 2wire probe in the wake of a blu ff body exhibiting v ortex shedding at frequency of 58H z.The agreement between the hot 2wire and the pneumatic probe with TTF correction was similar to the level of agree 2ment between tw o hot 2wire probes at the same spacing in the same flow.Further details can be found in Ref.[17].
The upper limit on the frequency response which can be obtained using TTF correction is restricted both by the level of correction required (which results in a deterioration in signal to noise ratio )and by time required for the flow around the measuring point to develop.F or typical multi 2hole probes used in low 2speed applications these tw o factors both suggest a similar upper limit in the region of 1000H z.
4 Conclusions
A technique of correcting unsteady signal distortion in
the frequency domain is presented and discussed.This method makes efficiently use off 2board pressure transducers in the area of turomachinery aeroelasticity and possibly use multi 2hole probes to conduct time 2accurate measurements in unsteady flow 2flied regions.R eferences
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尾气处理
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(上接第61页)
(4)应用到构型越复杂、气动特性规律越不明确的对象上，此方法应该更能大幅减少实验次数。
纳达尔资料
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第3期 Y ANG Hui et al:Tubing2trans fer2function correction on signal distortion for unsteady pressure measurements
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