Instrumentation. Dr. Hui Hu Dr. Rye Waldman. Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A

Transcription

1 AerE 344 Lecture Notes Lecture # 05: elocimetry Techniques and Instrumentation Dr. Hui Hu Dr. Rye Waldman Department of Aerospace Engineering Iowa State University Ames, Iowa 500, U.S.A Sources/ Further reading: Tropea, Yarin, & Foss, Springer Handbook of Experimental Fluid Mechanics, Part B Ch 5

2 Methods to Measure Local Flow elocity - Mechanical methods: Taking advantage of force and moments that a moving stream applies on immersed objects. ane anemometers Propeller anemometers

3 Methods to Measure Local Flow elocity - Pressure difference methods: Utilize relationship between the local velocity and the static and total pressures (Bernoulli). Pitot-static tubes are instruments that measure both static and stagnation pressures Static pressure taps are located circumferentially around the probe stem and are connected to the reference port of a differential manometer p stat Stagnation pressure tap at the probe tip senses p 0 The differential manometer measures the dynamic pressure, (p 0 p stat ), which allows to the flow velocity at the probe p 0 C p stat ( p ( p 0 0 p stat p,( Bernoulli) ) / stat ) / a. streamlined airfoil b. Flat plate

4 Methods to Measure Local Flow elocity - There are sources of error in the pressure measurement, e.g., probe misalignment, viscosity, compressibility, turbulence, shear, and proximity to boundaries. Errors can be taken care of by an empirical factor: C ( p p ) / 0 stat Special arrangements of the pressure taps (Three-hole, Five-hole, Seven-hole probes) in conjunction with special calibrations are used to measure all velocity components.

5 Methods to Measure Local Flow elocity -3 Thermal methods: (next week s lecture) Compute flow velocity from its relationship between local flow velocity and the convective heat transfer from heated elements. Hot wire anemometers Hot film anemometers

6 Particle-based Flow Diagnostic Techniques Seeded the flow with small particles (~ µm in size) Assumption: the particle tracers move with the same velocity as local flow velocity! Flow velocity f = Particle velocity p Measurement of particle velocity

7 Methods to Measure Local Flow elocity - 4 Frequency-shift methods: Based on the Doppler phenomenon: the frequency shift by moving objects Laser Doppler elocimetry (LD) or Laser Doppler Anemometry (LDA) Phase Doppler Anemometry (PDA) Planar Doppler elocimetry (PD) Interference fringes

8 Doppler Shift The Doppler effect, named after Christian Doppler (an Austrian mathematician and physicist), is the change in frequency and wavelength of a wave as perceived by an observer moving relative to the source. Light from moving objects will appear to have different wavelengths depending on the relative motion of the source and the observer. Observers looking at an object that is moving away from them see light that has a longer wavelength than it had when it was emitted (a red shift), while observers looking at an approaching source see light that is shifted to shorter wavelength (a blue shift).

9 Doppler Shift a. Stationary Sound Source b. Source moving with source < sound c. Source moving with source = sound ( Mach - breaking the sound barrier ) d. Source moving with source > sound (Mach.4 - supersonic)

10 Fundamentals of LD Take the coordinate system to be at rest with respect to the medium, whose speed of light wave is c. There is a source s moving with velocity s and emitting light waves with a frequency f s. There is a detector r moving with velocity r, and the unit vector from s to r is n i.e.,. Then the frequency f r at the detector is found from If c >> s, then the change in frequency depends mostly on the relative velocity of the source and detector. f f f nˆ f f c s r s r s s nˆ eˆ ˆ ˆ ˆ sin( ) r ei f s ( er ei ) r 0 fs c c

11 Fundamentals of LD How to determine doppler shift? Optical heterodyne! Mix the response from two beams on the reciever:

12 Fringe spacing: sin( / ) 4 DT Fringe number : N ; d D f sin( / ) Frequency of the scattering light : T sin( / ) f Frequency shift according to Doppler shift theory: sin( / ) f T e Dual-Beam LD

13 -component LD systems Dual-beam laser setup only can measure one component of the velocity with its direction normal to the fringe planes. Two-color LD system can be used for - components of flow velocity measurements. Ar-Ion Laser Blue (488nm) Yellow (54.5 nm) T -component LD

14 Phase Doppler Particle Analyzers/PDPA Systems The intensity of the incident ray is partly reflected and refracted. The intensity ratio is given by the Fresnel coefficients and depends on the incident angle, polarization and relative refractive index. The scattering angle is given by Snell s law. The phase is given by the optical path length of the ray. Most of the intensity is contained in the first three scattering modes. 3rd order Reflection Incident ray 6th order n p > n m n m n p - - st order refraction 8th order 4th order 5th order - 7th order nd order - refraction

15 Phase Doppler Particle Analyzers/PDPA Systems Phase Doppler anemometers take advantage that the phase difference between burst signals observed at different angles depends on particle size. A receiving lens at an off-axis angle observes the Doppler burst signal with a frequency proportional to the particle velocity. The phase shift between the Doppler burst signals from the different detectors is proportional to the size of the spherical particles. 3rd order Reflection Incident ray st order - - refraction 8th order 4th order 5th order - nd order - refraction 6th order n p n m n p > n m 7th order PDPA system

16 Y (mm) Particle-based techniques: Particle Image elocimetry (PI) To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows. To measure the displacements (L) of the tracer particles between known time interval (t). The local velocity of fluid flow is calculated by U= L/t. L t= t 0 +t t=t 0 L U t spanwise vorticity (/s) m/s GA(W)- airfoil shadow region -60 A. t=t 0 B. t=t 0 +0 s C. Derived elocity field X (mm)

17 Methods to Measure Local Flow elocity - 5 Marker tracing methods: Trace the motion of suitable flow makers, optically or by other means to derive local flow velocity. Particle Imaging elocimetry (PI) Particle Tracking elocimetry (PT) Molecular Tagging elocimetry (MT) t=t 0 PI image pair t=t 0 +4 ms 0.03 m/s Temperature ( O C) t=t 0 t=t 0 +5ms MT&T image pair Corresponding flow velocity field

18 Stereoscopic PI Measurements of a Wing-Tip ortex (Funded by AFOSR) Y pixel Y pixel X Laser Sheet Z Camera Camera Stereo PI technique X/C= Re C 5,000; 5.0 deg X/C = X pixel Displacement vectors in left camera X pixel Displacement vectors in right camera X/C=.0 CFD simulation results

19 Lab#04 Measurements of Pressure Distributions around a Circular Cylinder Flow Around a Circular Cylinder uniform flow + a -D doublet = flow around a circular cylinder Stagnation points Pressure coefficient on the surface of cylinder R r sin ( ) r R r cos ( ) r R r cos ( ) r R sin ( ) r

20 Lab#04 Measurements of Pressure Distributions around a Circular Cylinder At the surface of the cylinder, According to Bernoulli s equation Pressure coefficient distribution on the surface of the circular cylinder will be: sin 0 a r r P P P P 4sin ) sin ( P P C p R P Incoming flow X Y Angle, Deg. Cp

21 Pressure Distribution around a Circular Cylinder Numerical results for the velocity magnitude and pressure distributions over a circular cylinder using FlowLab (h=35.8 m/s, Re=.89E+05)

22 Lab#04 Measurements of Pressure Distributions around a Circular Cylinder Y P Incoming flow R X

23 cp --> Lab#04 Measurements of Pressure Distributions around a Circular Cylinder Cp distribution around a cylinder EFD CFD AFD theta (rad ) --> Cp distributions over a circular cylinder

24 Required Results for the Lab Report Formal lab report format: Make a table showing all the time-averaged data you obtained for all the cases you tested. Show all the calculation steps leading up to the final answer. Plot pressure coefficient (C p ) distributions on the cylinder from for all the cases you tested. Comment on the characteristics of the pressure distribution compared with the theoretical predictions. Calculate the drag coefficients (C d ) of the circular cylinder for all the cases you tested. Plot the drag coefficients (C d ) of the circular cylinder as a function of at the Reynolds numbers.