4 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES COMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION Jiri Nozika*, Josef Adame*, Daniel Hanus** *Department of Fluid Dynamis and Power Engineering, **Department of Automotive and Aerospae Engineering Faulty of Mehanial Engineering, Czeh Tehnial University in Prague, Tehnika 4, 66 07 Prague 6, Czeh Republi Keywords: flow speed, temperature, inidene, measurement, thermoouple Abstrat New appliation possibilities of the thermometers for the purpose of the measurements of the mean veloity flow field, whih is the vetor of veloity and its diretion in the spae is desribed. The appliation is based on the diretional harateristi (reovery fator) of the ylindrial shaped termoouple probe and its speifi ourse. The influene of the angle of attak of the gas flow on the measured temperature allows with a very good auray to use a thermoouple probe as an element of the veloimeter probe like a pneumati probe. So that speially adjusted thermoouples with the onfiguration of or elements form the probe that an indiate the veloity of the gas flow and its diretion in the plane or spae eventually. The auray of the measurements inreases with Mah numbers. The simpliity, easy operation and maintenane of those probes destine them for use in an airborne appliation as well as in experimental researh. Some simplified modifiations of suh a probe are suitable as flow diretion indiators as an angle of attak or stall indiator in airraft aerodynamis or as a surge indiator in turbo mahinery. Introdution This paper presents some new appliations for a method of flow speed measurement with help of at least two different thermometers. The prinipals of this method are desribed in the simplest way in []. Further development of the method mentioned led to the design of the probe for indiation of angle of attak - in fat an analogial probe to a three or five hole pneumati one. Basi Theoretial Overview For the purpose of the paper presented let's adopt the following desription of probe behaviour: Temperature probe is desribed by a dimensionless error of the temperature measured, often alled over all reovery fator r, see [], Ti T T0 Ti r = = () p p where T, T 0 and are free stream temperature, total temperature and veloity, p a speifi heat apaity at onstant pressure and T i a temperature indiated by a probe. The predition of the numerial value of r is usually diffiult, and thus an experimental way - the probe alibration - seems to be unavoidable. For this purpose the appliation of the theory of similarity gives the most representative results, r ís then given as a funtion of Reynolds and Mah numbers Re and Ma, Strouhal Sh and Fourier Fo numbers, Poisson number κ, angle of attak - pith and yaw, and some others desribing the influene of heat radiation and ondution, and, of ourse, of a probe geometry.
JIRI NOICKA, JOSEF ADAMEC, DANIEL HANUS Five-hole probe properties should be desribed in a dimensionless way, as well. The following parameters are very useful: Total pressure parameter p0 p Π0 () p p ss Dynami pressure parameter p0 p Πd () p p ss Pith angle parameter p p Π (4) p p ss Yaw angle parameter p4 p Π () p Here p i means the pressure indiated by hole i. p o and p are total and line pressure of the stream and p ss is a mean indiated line pressure, p ss = 0.. (p + p + p 4 + p s ) (6) All parameters Π i are then to be onsidered as funtions of Mah and Reynolds numbers and pith and yaw angles, respetively. Sheeted Thermoouple Probe In the introdution in this paper a method of evaluation of a free stream veloity with help of the data of two different thermometers was mentioned. In [] it has been proved, that a pair of sheeted thermoouples with different angles of attak an reate the simplest ombined total temperature and flow speed probe. The following formulas for flow speed and total temperature, valid for the probe ontaining two perpendiularly fixed K type thermoouples, were derived and experimentally verified: =.97( U) /, U = U - U (7) T t =0.(U +U )+..0-4. =0.(U +U )+0.06. U (8) Here U, are thermoeletri voltages measured by a data aquisition system. The results obtained were based on the results of a single sheeted thermoouple, measured by the author on a great set of sheeted K - type thermoouples p ss by various manufaturers and dimensions, see fig.. It is valid with good auray for 0. < Ma < 0.8 and.0 Re.0 4. 4 More ompliated probes Let's now study the funtion r = r () in fig. in more detail. There are two loal peaks at about zero and 90 deg. inidene. Both extremes are flat. However, between 0 and a 7 deg the funtion has a simple form and an be mathematially expressed as r = 0.786-0.00000., in angular degrees. (9) If the inidene of a thermoouple will be large enough, let's say 60 deg, its signal will vary with a small hange of. Using this effet, we an reate more-thermoouple probes similar to three or five-hole pneumati probes, being able to indiate the diretion of the flow stream as well. r 0,8 0,7 0,6 0 0 60 90 0 Fig. o () Three-thermoouple Probe Three sheeted thermoouples with their relative angle = 60 deg. reate the simplest ombined probe for total temperature, flow speed and pith angle measurement (see fig. ). Thermoouples TC and TC indiate the same temperature T = T, if the probe has just a zero
COMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION inidene. This position an be found rotating the probe around its shaft. The numerial value of an then be read diretly from the sale on a support. The flow speed an be alulated in a similar way as in the ase of the two thermoouple probe. If there is no possibility to rotate the probe, some more ompliated method similar to one developed for a pneumati probe is to be used. The behaviour of this probe from the point of view of the veloity measurement an be desribed by parameters, defined analogialy to the Π - parameters, see eq. () to (6). Ignoring the total temperature measurement, the following two - parameters exist: T Ts = flow speed parameter, (0) T T a = pith parameter, () s here T i are temperatures indiated by TC to TC and T s = 0.. (T + T ). To predit the numerial values of parameters, see (0) and (), we an use the simplified thermoouple angular harateristis (9). If the probe is positioned in the flow stream with an inidene of deg., the angles of attak of the three thermoouples are: TC +, TC, () ΤC, Reovery fators are then: ( + ) r = r = = p r = r ( ) = = p r = r ( ) = = ( + ) 0 = 0.786 0.00000. 0 = 0.786 0.00000,, () ( ) 0 = 0.786 0.00000. p, From () the following expressions an be easily derived: = 0.00000, (4) = 4 a. If we now assume that = 60 deg, we an rewrite (4) as: = 0. () a = 0.066 (6) Both () and (6) seem to be very simple, but it is still neessary to have in mind, this is due to the simplifiation of sheeted thermoouple behavior, using (9). The qualities of a real probe will be in good aordane with () and (6) for small ± 0 deg only. To onfirm () and (6), the probe desribed was alibrated. The results of suh measurements in omparison with diagrams of () and (6) are in fig.. 0, 0-0 -0-0 0 0 0 0 ( ) 6 Five-thermoouple Probe The addition of two more thermoouples as shown in fig. 4 allows us to measure the yaw angle as well. One more - parameter is now - - Fig. Theory
JIRI NOICKA, JOSEF ADAMEC, DANIEL HANUS TC TC TC TC 4 TC Sometimes there is no possibility to hange the probe position at all. We have to operate the probe as a fixed one. Let's assume the probe is plaed into a stream with any pith and yaw angles and. For the sake of simplifiation we an define a ommon spatial angle of attak χ, defined χ + = (8) The angles of attak of thermoouples are now: Fig. 4 defined using the signals of these two additional thermoouples: T4 T = yaw parameter. (7) T T s In ase of a five-thermoouple probe, the mean temperature Ts should be defined as s ( T + T + T T ) T = 0.. + Similar to pneumati five-hole probes, several types of operation are possible as well. One is the simplest way, from the point of view of the data evaluation - the free movable probe. That means it is possible to hange both pith and yaw angles of the probe, whih an then be balaned just into the diretion of the flow. We simply have to find that position, where T = T and T 4 = T. The value of and an be read on the sale of the supporting devie immediately. The simple way of measurement and wiring is unfortunately violated by the very ompliated onstrution of the support. Another possibility is to mount the probe, as it is semi-adjustable. Usually it is quite easy to turn the probe around its shaft. In this ase the position where T = T an be set. Then, using signals of thermoouples TC, 4 and only, yaw angle an be find, when using the probe as the fixed three thermoouple one (see previous setion). 4 χ = +, TC ( ) TC + =, χ + χ = +, (9) TC ( ) TC4 χ + ( + ) 4 TC χ + ( ) Obviously (8) and (9) are valid for small and. The reovery fators are: ( + ) + ) r = 0.786 0., r = 0.786 0. + ), r = 0.786 0. 00000( ) + ), (0) r ( ( ) 4 = 0.786 0. 00000 + +, r ( ( ) = 0.786 0. 00000 +. In the same way as in the previous setion we an now obtain = 0.00000, () = 4, () = 4., () and further for = 60 deg = 0., (4) = 0.066, () = 0.066. (6) These results are based on simplifiations similar to those desribed by (6) and (7), so the probe alibration is unavoidable as well. There is the probe veloity parameter shown 4
COMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION =0 =0 =0 =0 =0 =0 0 Fig. Fig. 6 as a funtion of pith and yaw angles and in fig.. It is obvious there is a good aordane with theoretial values for small, ± deg. only. For greater inidene the value of is dropping. The angular harateristi of a five thermoouple probe an be introdued in the form of the diagram, = f(,), developed for five hole pneumati probes. There is an example of one in fig. 6. A good aordane between theory and experimental data for small and is obvious again. 8 Probe for Measurement of Surge A part of experiments on ompressors - and sometimes the most dangerous one - is the measurement of the unstable part of the harateristis of a ompressor, espeially during so alled surge. The most ompliated problem from the point of view of the data aquisition system is the sudden hange of the flow diretion. Probes designed in a onventional way annot provide suffiient signals during this period. From the other point 7 Some Speial Appliations In previous setions it is desribed how to use several thermoouples for the measurement of veloity and diretion. This allows us to design the flow speed probes independent of pressure measurement, whih an help us hek the results of measurement. Moreover, as shown in [], for higher Mah numbers, Ma > 0., the auray of suh probes an be better than that of the pneumati sensors. From the other point of view, it is possible to design some simplified sensors, based on results desribed above, orresponding to speial kinds of measurement. For the use in turbomahinery the following two speial appliations have been designed. C TC TC Fig. 7 TC TC 4 Pumping
JIRI NOICKA, JOSEF ADAMEC, DANIEL HANUS of view, speial probes for indiation of phenomenon mentioned often have muh worse parameters in a stable regime. There is a simple solution to this problem shown in fig. 7. Thermoouples TC and TC reate a two thermoouple probe and serve as a ommon flow speed measurement. TC is in this situation in the weak past this probe, its signal is similar to that one provided by TC. During the surge yles the flow reverses, TC indiates now the highest temperature. If higher range of angles indiated should be ensured, some additional thermoouple ould be installed, as shown on the fig. 9. For further data evaluation only three 9. Airborne Appliations Obviously probes shown on fig. and 4 were designed as an option to pneumati three or five hole probes. They are thus suitable for the aerodynami researh of flow fields during experiments in wind tunnels of similar failities. Moreover, after simple hanges in respetive position of the thermoouple used speial probes useful for appliation in airraft ontrol systems an be derived. Fig. 8 The simplest onfiguration of a probe designated for airraft speed, angle of attak and yaw angle indiation is shown on the fig. 8. The probe is pratially idential with that shown on the fig. 4; entirely the thermoouples are fixed parallel to the shaft axis. The shaft ensures the thermoouples are plaed far in the unaffeted flow, i.e. in front of the leading edge of the wing or nose of the fuselage. In this ase, the stiffness and reliability of the probe would be preferred to a minimization of their dimensions, so that thermoouples of mm diameter would be preferred. Fig. 9 of them would be preferred. As a basi one that with the highest indiated temperature should be hosen, supplied with two other having relative position to this one of ± 60 deg. For the installation in the airraft fuselage the integration of more temperature sensors into one ombined probe need not to be aeptable solution. Even in suh ase the idea desribed ould be applied. The individual thermometers ould be, for example, built into the surfae of the nose of the fuselage, as shown on the fig. 0. The indiated temperature of any of them is than affeted by the veloity distribution on the fuselage. The data evaluation proeeds in a similar manner as desribed, the numerial values of oeffiients in () to () should be determined experimentally by the alibration. Obviously, the shape of the fuselage nose and the position of individual thermometers will be determining in this ase. 0 Auray of the method The error of the measured veloity of the flow depends on the parameters of the flow, that is veloity, or Mah Number respetively and on the other side on the used measurement 6
COMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION omparison with the pneumati ones at very high subsoni veloities of the fluid flow and at Mah Numbers around ause onsiderably smaller problems. Referenes [] Nožička, J. Unonventional Probe for Flow Speed and Temperature Measurement Pro FLUCOME'94, ONERA CERT, Toulouse, Frane, pp. -7, 994. [] Nožička, J.: Calibration of a Temperature Probe with respet to the Influene of Heat Condution and Radiation, Pro 9th International Conferene on Thermal Engineering and Thermogrammetry. Budapest, Hungary 99. Fig. 0 instrumentation. At the prototype of the veloimeter probe we have used thermoouples Haereus, whih have been alibrated on the very aurate alibrating devie in the measurement department of the CKD Praha Company. For the measurements of the flow parameters using new probe very aurate instrumentation has been used, like measuring entral with range of 0. Volt and auray 0.0% and seven-digit voltmeter, so that the measured tension of the thermometers were indiated in mirovolts. The auray of the measurements of the veloity at the veloity about 00 meters per seond is omparable to Prandtl (or Pitot stati) pneumati probe, that is %, while using simple two-thermoouple probe. At lower veloity the auray dereases, but at higher veloities, for instane at 0 meters per seond the error is only % and over 00meters per seond under 0.%. The use of the probe at Mah Numbers around is without problem. The auray of the measurement of the angle of attak of the flow is about ±0.º at angle of attak in the range ±º. At higher angles the error inreases to about ±.0º. The probes with or thermoouples measure the veloity and the angle of attak with similar auray at smaller angles of attak. At greater angles of attak the sensitivity of the probes dereases and therefore the errors grow. At angle of attak 0º is error approximately double of simple twothermoouple probe. In general it is possible to say that new probes are muh better in Aknowledgements This researh was supported by the Czeh Ministry of eduation, Sports and Youth, by grant No J04/98:00009. 7