Lecture # 15: Review for Final Exam

Transcription

1 AerE 311L & AerE343L Lecture Notes Lecture # 15: Revew for Fnal Exam Hu Hu Department of Aerospace Engneerng, Iowa State Unversty Ames, Iowa 50011, U.S.A

2 AerE343L: Dmensonal Analyss and Smltude L Commonly used non- dmensonal parameters: Δp pressure force Euler number, Eu ρv nertal force ρvl nertal force Reynolds number, Re μ vscous force V nertal force Froude Number, Fr lg gravty force V Mach Number, M c Strohal Number, Str Weber Number, We nertal force compressblty force lϖ centrfugal force V nertal force V lρ nertal force σ surface tenson force Smltude: Geometrc smlarty: the model have the same shape as the prototype. Knematc smlarty: condton where the velocty rato s a constant between all correspondng ponts n the flow feld. Dynamc smlarty: Forces whch act on correspondng masses n the model flow and prototype flow are n the same rato through out the entre flow

3 Measurement Uncertantes Error s the dfference between the expermentally-determned value and ts true value; therefore, as error decreases, accuracy s sad to ncrease. A error A measured A true Total error, U,, can be consdered to be composed of two components: a random (precson) component, a systematc (bas) component, We usually don t t know these exactly, so we estmate them wth P and B,, respectvely. E A m A true A E relatve A error true U B + P Repeatablty Reproducblty Precson Error Both Bas and Precson Errors Bas error True value X100 precson error measured value X101 X

4 Copyrght by Dr. Hu Iowa State Unversty. All Rghts Reserved! Measurement Uncertantes Measurement Uncertantes ρ ρ ρ p p p V Bernoull V p p statc total statc total Δ + ) ( ),( 1 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 1 1 ; M j j B B 1 For a large number of samples (N>10) S P ( ) [ ] ( ) N k k N k k X N X X X N S ; 1 1

5 Pressure Measurement Technques Deadweght gauges: Elastc-element gauges: Electrcal Pressure transducers: Wall Pressure measurements Remote connecton Cavty mountng Flush mountng Pressure Measurements nsde Flow Feld:

6 Velocty measurement technques Ptot Statc Probe Advantage: Smple cheap Dsadvantage: averaged velocty only Sngle pont measurements Low measurement accuracy p 0 V p stat ( p 1 + ρv 0 p ρ stat,( Bernoull) )

7 Velocty measurement technques Hotwre Probe Advantage: Hgh accuracy Hgh dynamc response V Flow Feld The rate of whch heat s removed from the sensor s drectly related to the velocty of the flud flowng over the sensor Dsadvantage: Sngle pont measurements Fragle, easy to broke Much more expansve compared wth ptot-statc probe. Current flow through wre dt mc dt w R w q& ( V, T Constant-current anemometry Constant-temperature temperature anemometry w )

8 Partcle Image Velocmetry (PIV) Advantage: Whole flow feld measurements Non-ntrusve measurements Dsadvantage: Low temporal resoluton Very expansve compared wth hotwre anemometers and ptot- statc probes. To seed flud flows wth small tracer partcles (~µm), and assume the tracer partcles movng wth the same velocty as the low flud flows. To measure the dsplacements (ΔL) of the tracer partcles between known tme nterval (Δt). The local velocty of flud flow s calculated by U Δ L/Δt. tt 0 ΔL U ΔL Δt t t 0 +Δt spanwse vortcty (1/s) m/s Y (mm) 0 0 GA(W)-1 arfol shadow regon X (mm) C. Derved Velocty feld A. tt 0 B. tt μs Copyrght by Dr. Hu Iowa Classc State Unversty. -D D PIV All measurement Rghts Reserved!

9 PIV System Setup Partcle tracers: Illumnaton system: Camera: Synchronzer: Host computer: to track the flud movement. to llumnate the flow feld n the nterest regon. to capture the mages of the partcle tracers. the control the tmng of the laser llumnaton and camera acquston. to store the partcle mages and conduct mage processng. seed flow wth tracer partcles Illumnaton system (Laser and optcs) camera Synchronzer Host computer

10 Lamnar Flows and Turbulent Flows u u + u' ; v v + v' w w + w' u 1 0 T t + T t 0 u( x, y, z, t) dt... u' 0; v' 0 w' 0 ( u') t + T o 1 ( u') T t 0 dt > 0; ( v') > 0 ( w') > 0

11 Boundary Layer Flow at y δ, u 0. 99U Dsplacement thckness: y Momentum thckness:

12 AerE343L Lab #1: Pressure Sensor Calbraton and Measurement Uncertanty Analyss Task #1: Pressure Sensor Calbraton experment A pressure sensor Setra pressure transducer wth a range of +/- 5 nho It has two pressure ports: one for total pressure and one for statc s (or reference) pressure. A computer data acquston system to measure the output voltage from the manometer. A manometer of known accuracy Mensor Dgtal Pressure Gage, Model 101, Range of +/- 10 nho A plenum and a hand pump to pressurze t. Tubng to connect pressure sensors and plenum Lab output: Calbraton curve Repeatablty of your results Uncertanty of your measurements tubng Setra pressure transducer (to be calbrated) Mensor Dgtal Pressure Gage A computer A plenum hand pump

13 Lab#0: Arfol Pressure Dstrbuton Measurements and Calbraton of a Small Wnd Tunnel Y (nches) NACA001 arfol wth 3 pressure tabs X (nches) 0.40 Lft Coeffcent, C l L 1 ρv C l c C L πα Expermental data Drag Coeffcent, C d D 1 ρv C d c Expermental data Angle of Attack (degrees) Angle of Attack (degrees)

14 Lab 3: Arfol Wake Measurements and Hotwre Anemometer Calbraton on y x D CD 1 ρu CD C U ( y) U ( y) ρu [ (1 )] da U U 1 C ρu C U ( y) U ( y) [ (1 )] dy U U y Pressure rake wth 41 total pressure probes (the dstance between the probes dmm) x 80 mm

15 y AerE343L #4: Hot wre measurements n the wake of an arfol Pressure rake wth 41 total pressure probes (the dstance between the probes dmm) x 80 mm Lab#3 Test condtons: Velocty: V15 m/s Angle of attack: AOA0, and 1 deg. Date samplng rate: f1000hz Number of samples: 10,000 (10s n tme) No. of ponts: 0~5 ponts Gap between ponts: ~0. nches Lab#4 Hotwre probe

16 AerE343L Lab#5: Measurements of Boundary Layer over a Flat Plate To conduct velocty profle measurements at 10 downstream locatons. To determne boundary layer thckness and drag coeffcent based on the velocty measurement results. Dsplacement thckness: Momentum thckness: Drag coeffcent: C d θ L Ptot rake Y X

17 AerE343L Lab#6: PIV Measurements of a Flappng Wng 30 Spanwse Vortcty (1000*1/s) Spanwse Vortcty (1000*1/s) Y (mm) 0 Y (mm) X (mm) Flappng frequency: f 60Hz Chord length: C 1.7mm Wng span: L 76.7 mm Flow velocty: V 1.44 m/s X (mm) Flappng frequency: f 60Hz Chord length: C 1.7mm Wng span: L 76.7 mm Flow velocty: V 6.36 m/s

18 AerE311L: The nature of lght Lght as electromagnetc waves. Lght as photons. Color of lght Index of reflecton λ n c / v 0 > 1 λ c 0 3x10 8 m / s

19 Index of refracton: Shadowgraph and Schleren technque λ n c / v 0 > 1 λ Depend on varaton of ndex of refracton n a transparent medum and the resultng effect on a lght beam passng through the test secton Shadowgraph systems: are used to ndcate the varaton of the second dervatves (normal to the lght beam) of the ndex of refracton. shadowgraph depctng the flow generated by a bullet at supersonc speeds. (by Andrew Davdhazy ) Schleren Systems: are used to ndcate the varaton of the frst dervatve of the ndex of refracton Schleren mages of the muzzle blast and supersonc bullet from frng a calber hgh-powered rfle (by Gary S. Settles )

20 Vsualzaton of a Schockwaves usng Schleren technque After turnng on the Supersonc jet Before turnng on the Supersonc jet

21 Schleren vs. Shadowgraph Shadowgraph Dsplays a mere shadow Shows lght ray dsplacement Contrast level responds to No knfe edge used n y Schleren Dsplays a focused mage Shows ray refracton angle, ε Contrast level responds to n y Knfe edge used for cutoff

22 Revew of Quas-1D Nozzle Flow da A ( M 1) du u Throat M1 u ncreasng M<1 M>1 Throat M1 u decreasng M>1 M<1

23 1st, nd and 3 rd crtc condtons st crtc condton P 0 ncreasng 1st crtc condton P 0 ncreasng 3st crtc condton

24 AerE311L Lab#1: Vsualzaton of Shockwaves usng Schleren technque nd crtcal shock s at nozzle ext Flow close to 3 rd crtcal Under- expanded flow Over- expanded flow 1 st crtcal shock s almost at the nozzle throat.

25 AerE311L Lab#: Set Up Schleren and Shadowgraph System to Vsualze a Thermal Plume Pont Source Candle plume

26 AerE311L Lab#3: Pressure Measurements n a de Laval Nozzle Tank wth compressed ar Test secton Tap No. Dstance downstream of throat (nches) Area (Sq. nches)

27 AerE343L: Fnal Exam Open book Four problems (5 ponts each) ~ 30 mnutes

28 AerE311L: Fnal Exam Open book 0 multple-choce problems ~ 15 mnutes