Lecture # 02: Pressure measurements and Measurement Uncertainties

Transcription

1 AerE 3L & AerE343L Lecture Notes Lecture # 0: Pressure measurements and Measurement Uncertantes Dr. Hu H Hu Deartment of Aerosace Engneerng Iowa State Unversty Ames, Iowa 500, U.S.A

2 Mechancal Pressure Gauges - Deadweght gauges: Hgh accuracy Usually used for the calbraton of other nstruments Alcaton range : 0~08 a weght lunger cylnder um Uncertanty s wthn 0.0% ~0.05% of the readng Calbraton ressure P Flud chamber

3 Mechancal Pressure Gauges - Elastc-element gauges: Contan an elastc elements that deforms under ressure and creates a lnear or angular dslacement The dslacement s ether dslayed on a dal by means of urely mechancal lnkages or transformed to an electrc sgnal that can be dslayed or recorder at wll. They usually used for montorng suly ressure Cross sectonal shae Curved Bourdon tube Twsted Bourdon tueb

4 Electrcal Pressure transducers These devces rovdes an electrc outut sgnal that s lnearly or nonlnearly deendent on the absolute ressure or a ressure dfference. They can be categorzed as: Molecular transducers: Aled ressure or force roduces a change (on the molecular level) of a electrcal roerty of materal. Pezo-electrc electrc materal such as quartz crystal: change n nternal dole moments of the molecules of the crystal when the ressure or force s aled. Parametrcal transducers: The gross electrcal arameter (resstance, nductance, caactance) of an assocate electrcal arameter s altered by aled force. Varable-caactance transducer E

5 Wall Pressure measurements - Makng small orfce (ressure ta) facng the flow. Δ P m P > 0 V, P Machnng small hole could be dffcult d 0.5~3.0mm n ractce l/d 5 ~ 5 s common used l Potental effect on the wall roughness Effects of unsteady shock wave, and shock- boundary-layer nteractons for transonc and suersonc flows: PSP method to be ntroduced later P m d

6 Wall Pressure measurements - For a unsteady flow, the dynamc resonse of a ressure acquston system s a key ssue! Dynamc resonse of the ressure transducers Dynamc resonse of the connecton tubng Remote connecton Dynamc resonse s low Satal resoluton s hgh Cavty mountng Dynamc resonse s good Satal resoluton s hgh V Pressure transducers Connecton tubng V Flush mountng Dynamc resonse s hgh Satal resoluton s low V ressure transducer ressure transducer

7 Pressure Measurements nsde Flow Feld Non-ntrusve technque s unavalable for drect ressure measurements Based on N-S N S equaton to calculate ressure feld usng the measured (PIV) velocty feld. Statc robe: for statc ressure measurements Ptot robe: for total ressure measurements Ptot-statc robe: for statc and total ressures measurements (velocty measurements) Mult-hole robe:

8 AerE343L Lab #: Pressure Sensor Calbraton and Measurement Uncertanty Analyss Task #: Pressure Sensor Calbraton exerment A ressure sensor Setra ressure transducer wth a range of +/- 5 nho It has two ressure orts: one for total ressure and one for statc s (or reference) ressure. A comuter data acquston system to measure the outut voltage from the manometer. A manometer of known accuracy Mensor Dgtal Pressure Gage, Model 0, Range of +/- 0 nho A lenum and a hand um to ressurze t. Tubng to connect ressure sensors and lenum Lab outut: Calbraton curve Reeatablty of your results Uncertanty of your measurements tubng Setra ressure transducer (to be calbrated) Mensor Dgtal Pressure Gage A comuter A lenum hand um

9 Calbraton curves 400 Pressure (Pa) ya+bx max dev:30.4, r a3., b40 Exermental data curve fttng Voltage (V)

10 AerE343L Lab #: Pressure Sensor Calbraton and Measurement Uncertanty Analyss Task #: velocty rofle measurements of Bll James wnd tunnel A Setra manometer to be used wth a Ptot- statc robe. A Ptot-statc robe mounted to a traverse for measurng velocty rofles n the wnd tunnel. A thermometer and barometer for observng ambent lab condtons (for calculatng atmosherc densty). A comuter wth a data acquston system caable of measurng the voltage from your ressure transducer. Lab Outut Velocty rofles across the wnd tunnel test secton. V 0 a. streamlned arfol b. Flat late stat ( + ρv 0 ρ stat,( Bernoull) )

11 Velocty rofle n the Bll James wnd Tunnel 0 Velocty (m/s) Poston (mm)

12 Before you do the Labs Choose ~ member as the Lead Oerators Brng you own flash drve for the data storage. Do not touch other research equments n the wnd tunnel laboratory. Kee the wnd tunnel laboratory clean and organzed.

13 Measurement Uncertantes Accuracy s generally used to ndcate the relatve closeness of agreement between an exermentally-determned value of a quantty and ts true value. Error s the dfference between the exermentally-determned value and ts true value; therefore, as error decreases, accuracy s sad to ncrease. Snce the true value s not known, t s necessary to estmate error, e and that estmate s called an uncertanty, U. Uncertanty estmates are made at some confdence level a a 95% confdence estmate, for examle, means that the true value of the quantty s exected to be wthn the ±U U nterval about the exermentally-determned value 95 tmes out of 00. A error A measured A true E A m A true Whch Case s more accurate measurement? V 0m / s, Measurement error ΔV m / s V t t 00m / s, Measurement error ΔV 5m / s E relatve A A error true

14 Measurement Uncertantes Total error, U,, can be consdered to be comosed of two comonents: a random (recson) comonent, a systematc (bas) comonent, We usually don t t know these exactly, so we estmate them wth P and B, resectvely. U B + P Reeatablty Reroducblty Precson Error Both Bas and Precson Errors Bas error True value X00 recson error measured value X0 X

15 Measurement Uncertantes We almost always are dealng wth a data reducton equaton to get g to our fnal results. In ths case, we must not only deal wth uncertanty n the measured values but uncertanty n the fnal results. A general form looks lke ths: ( X X, X, ) R R,, 3 K X J R s the result determned from J ndeendent varables.

16 Coyrght by Dr. Hu Iowa State Unversty. All Rghts Reserved! Examle ρ ρ ρ V Bernoull V statc total statc total Δ + ) ( ),( R R R P B U + Uncertanty n velocty V: Uncertanty n velocty V: J R J R P X R P B X R B ; M j j B B For a large number of samles (N>0) S P ( ) [ ] ( ) N k k N k k X N X X X N S ;