Short Course: Advanced Flow Diagnostic Techniques for Thermal Fluid Studies

Transcription

1 Short Course: Advanced Flow Diagnostic Techniques for Thermal Fluid Studies Lecture : Shadowgraph, Schlieren; Interferometry; Hotwire Anemometry, LDV and PDV Dr. Hui H Hu Department of Aerospace Engineering Iowa State University Ames, Iowa 50011, U.S.A

2 Shadowgraph, Schlieren and Interferometry

3 Refractive index: Light propagate through media λ n c / v 0 > 1 λ Index of refraction of a material generally increasing slightly with decreasing wavelength of the light. Such phenomena is called dispersion. 1+ K Lρ n 1 K ρ Gas Air He CO H n nm Liquid Water Ethyl alcohol Turpentine Benzene n L c Solid 0 Fused quartz Pyrex glass Crown glass Flint glass Plexiglas Lexan Polystyrene sapphire zircon Diamond 3x10 8 n m / s ~

4 Light Refraction Snell s Law: θ 1 n 1sin θ1 n sin θ n 1 < n Medium 1 Medium θ

5 Example, Refraction in Water Water Surface Pole

6 Index of refraction: λ n c / v 0 > 1 λ Depend on variation of index of refraction in a transparent medium and the resulting effect on a light beam passing through the test section Introduction-1 Shadowgraph systems: are used to indicate the variation of the second derivatives (normal to the light beam) of the index of refraction. Schlieren Systems: are used to indicate the variation of the first directive of the index of refraction shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew Davidhazy ) Interferometry systems: response directly the difference of optical path length,, especially giving the index of reflection field within the flow field. Holographic interferometry image of shock-vortex interaction Schlieren images of the muzzle blast and supersonic bullet from firing a caliber high-powered rifle (by Gary S. Settles )

7 Introduction- Shadowgraph and Schlieren Systems are often used in shock waves and flame phenomena, in which density gradient is quite big. Interfereometry are often used to study a flow in which density gradient are small. While these techniques are mostly used for qualitative flow visualization, they can be used to determine pressure, density or temperature measurements theoretically. These techniques are often used to determine the integrated quantity over the length of light beam. These techniques are usually used for -D D flow without index of refraction or density variations along the beam. shadowgraph image of plumes during solidification process (by Lum Chee) temperature fields and the heat transfer around a heated cylinder Schlieren image

8 Introduction-3 Index of refraction is a function of thermodynamic state (density) for homogeneous medium: Lorenz-Lorentz Lorentz relationship: When n 1, n for gaseous flow: at standard condition, with n o and ρ o, : 1 n ρ n 1 + const When first and second derivative is determined as in Schlieren and shadowgraph apparatus: n 1 n 1 const ρ ρ const n0 1 const ρ 0 ρ n 1 ( n0 1) ρ0 n 1 ρ ρ0 n 1 ρ 1 n ρ ρ0 n y const y y n0 1 y ρ 1 n ρ ρ0 n y const y y n 1 y 0 0

9 Introduction-4 Application of the Schlieren and shadowgraph techniques: Compressible flow with shock waves Natural convective flow density changes density changes Flame and combustion system: density changes Temperature changes inside flows: For low speed flow with heat transfer: P constant ρ P T ρ T ρ P / RT y RT y T y n n0 1 ρ n0 1 ρ T y ρ0 y T ρ0 y T T ρ0 n y n 1 ρ y n y 0 n0 1 ρ T [ ρ T y 0 ρ T + ( ) T y ]

10 Copyright by Dr. Hui Iowa State University. All Rights Reserved! Introduction-5 For reversible, adiabatic process: For reversible, adiabatic process: y n k n P y n y n n P y n n n P y P n n P P const n k P P const P k k k k k 1) ( ) ( 1) ( ) 1 1 ( 1 C C specific heat; k the ratio of is ) ( v p 0 0 ρ ρ ρ ρ

11 Fundamentals of Schlieren System According to definition of index of refraction, the light velocity will be VC o /n. The slope of the wave front of the light: If the angle Δα' is quite small. dy dz C0 ΔZ Δτ n 1 Δ Z ΔZ ΔZ y+δy C0( Δ( ) / Δy) Δτ Δy n Δ Z 1 Δα' n ( Δ( ) / Δy) ΔZ Δy n 1 d( ) dy n 1 dn 1 dn d(ln n) dα' n[ ] dz n [ ] dz ( ) dz dz dz dy n dy n dy dy d y d(ln n) dz dy Parallel lights y λ n c / v 0 > 1 λ Δy Δα' Δ ΔZ Z Z Δα' 1 d( ) n 1 dn 1 dn d(ln n) dα' n[ ] dz n [ ] dz ( ) dz dz dy n dy n dy dy 1 dn n 1 dn α' ( ) dz α' dz n dy dy

12 Fundamentals of Schlieren System The intensity after the shape razor blade (knife edge) before the experiment I k a a K 0 I 0 The intensity after the deformation due to the variation of the index of refraction Δa Δa I d I k + I k (1 + ) I k ak ak ΔI I d I k Δa contrast I k I k ak d( contrast) f sensitivity : dα a Sensitivity is proportional to f and inversely to a k. K α f ± a K

13 Fundamentals of Schlieren System The intensity after the shape razor blade (knife edge) before the experiment I k a a K 0 I 0 The intensity after the deformation due to the variation of the index of refraction Δa Δa I d I k + I k (1 + ) I k ak ak ΔI I d I k Δa contrast I k I k ak d( contrast) f sensitivity : dα a Sensitivity is proportional to f and inversely to a k. K α f ± a K

14 Fundamentals of Schlieren System

15 Fundamentals of Schlieren System

16 Fundamentals of Schlieren System

17 Fundamentals of Schlieren System For a gas flow with density change: ΔI α f ± I k ak dn ΔI α' dz dy I k ρ ρ 0 n y n0 1 y ΔI f n 1 ± I a k K f dn ± dz a K dy ΔI f n0 1 ± I k ak ρ0 n0 1 dρ L ρ dy 0 dρ dz dy

18 Fundamentals of Schlieren System For a gas flow with constant pressure distribution: ΔI f dn ± dz I a k K dy T T ρ0 n y n0 1 ρ y ΔI f n0 1 ρ dt ± dz I k ak ρ 0 T dy ΔI f n0 1 P dt ± I k ak ρ 0 RT dy ΔI f n0 1 P dt ± L I a ρ RT dy k K 0 dz

19 Fundamentals of Schlieren System For a liquid flow: n is a function of temperature T. dn n T dy T y ΔI f dn f n T ± dz I a dy a k K K T y n T if n 1 const T y ΔI f n T ± L I a T y k K dz

20 Visualization of shock wave in a transonic/supersonic nozzle using Schlieren technique

21 Lab#3: Pressure Measurements in a de Laval Nozzle Tank with compressed air Test section Tap No. Distance downstream of throat (inches) Area (Sq. inches)

22 1st, nd and 3 rd critic conditions nd critical shock is at nozzle exit Flow close to 3 rd critical Over-expanded expanded flow with shock between nozzle exit and throat Under- expanded flow Over- expanded flow 1 st critical shock is almost at the nozzle throat.

23 Alternative Schlieren system A. Setup with one converging and one plane mirror A. Setup with one converging mirror

24 Holographic Schlieren system

25 Shadowgraph technique Δy I sc I0 Δysc Δysc Δy + Z sc dα ΔI I sc I0 Δy 1 I0 I0 Δysc dα dα Z sc Z sc Δysc dy ΔI dα Z sc I0 dy 1 dn since α dz na dy ΔI Z sc d n dz I n dy 0 a Sensitive is proposal to Z sc

26 Shadowgraph technique Experimental setup with one converging mirror Experimental setup without lens or mirror

27 Schlieren vs. Shadowgraph Shadowgraph Displays a mere shadow Shows light ray displacement Contrast level responds to n y No knife edge used Schlieren Displays a focused image Shows ray refraction angle, ε Contrast level responds to n y Knife edge used for cutoff

28 Examples

29 Interferometers Unlike the Schlieren and shadowgraph systems, an interferometer does not depend upon the deflection of a light beam to determine density or index of refraction variation. Interferometers are often used for quantitative measurements

30 Interferometers

31 Coherent light Source Coherent sources... Two sources of light are said to be coherent if the waves emitted from them have the same frequency and are 'phase-linked'; that is, they have a zero or constant phase difference.

32 Interference of two coherence light waves Amplitude of a plate light wave in a homogeneous medium can be expressed as : π A A0 sin ( ct z) λ therefore : π π wave1: A1 A01 sin( ct Z0) λ λ π π wave : A A01 sin( ct Z0 Δ) λ λ if A0 A01 A0 then : AT A1 + A π π π π A0 [sin( ct Z0) + sin( ct Z0 Δ)] λ λ λ λ Δ π π Δ A0 cos sin( ct Z0 ) λ λ Therefore, the intensity of the combined wave (which is proportional to the square of the peak amplitude)will be : Δ I ~ 4A0 cos

33 Interference of light waves Thomas Young (1801)

34 Interferometers The ppticle path length along a light beam is defined as : PL ndz or C0 1 dz PL dz C λ 0 λ Therefore, the difference between path 1and path : ΔPL PL PL ndz ndz 0 1 path 1 path 1 dz dz ( 1 1 ) λ path 0 λ path λ The phase difference between the two wave will be : dz dz Δ π ( path 1 path 1 ) λ λ or Δ ΔPL π λ

35 Interferometers 1 ε ( n nref ) dz λ 0 n 1 Acording Glasdstone - Dale equation : ρ Const const ε ( ρ ρref ) dz λ 0 if only varies over a length L, then, the fringe shift will be : n nref ε L λ0 for gaseous flows const ε ( ρ ρref ) L λ0 or λ0ε λ0ε ρ0 ρ ρref const L n 1 L o for temepature measurements in gaseous flows λ0ε 1 T Tref L dn / DT

36 Examples

37 Examples

38 Methods for Local Flow Velocity Measurements

39 Methods to Measure Local Flow Velocity - 1 Mechanical methods: Taking advantage of force and moments that a moving stream applies on immersed objects. Vane anemometers Propeller anemometers

40 Methods to Measure Local Flow Velocity - Pressure difference methods: Utilize analytical relationship between the local velocity and the static and total pressures The tubes sensing static and stagnation pressures are usually combined into one instrument known as Pitotstatic tube. Pressure taps sensing static pressure (also the reference pressure for this measurement) are placed radially on the probe stem and then combined into one tube leading to the differential manometer (p stat ). The pressure tap located at the probe tip senses the stagnation pressure (p 0 ). Use of the two measured pressures in the Bernoulli equation allows to determine one component of the flow velocity at the probe location. Special arrangements of the pressure taps (Threehole, Five-hole, seven-hole Pitot) in conjunction with special calibrations are used two measure all velocity components. It is difficult to measure stagnation pressure in real, due to friction. The measured stagnation pressure is always less than the actual one. This is taken care of by an empirical factor C. a. streamlined airfoil ( p b. Flat plate ( p 1 + ρv ) / ρ p V V 0 C p stat 0 0 p stat p stat,( Bernoulli) ) / ρ

41 Methods to Measure Local Flow Velocity -3 Thermal methods: Compute flow velocity from its relationship between local flow velocity v and the convective heat transfer from heated elements. Hot wire anemometers Hot film anemometers

42 Methods to Measure Local Flow Velocity - 4 Frequency-shift methods: Based on the Doppler phenomenon, namely the shift of the frequency of waves scattered by moving particles. Laser Doppler Velocimetry(LDV) ) or Laser Doppler Anemometry (LDV) Planar Doppler Velocimetry (PDV) or Planar Doppler Anemometry (PDA) Interference fringes

43 Methods to Measure Local Flow Velocity - 5 Marker tracing methods: Trace the motion of suitable flow makers, optically or by other means to derive local flow velocity. Particle Imaging Velocimetry (PIV) Particle Tracking Velocimetry (PTV) Molecular Tagging Velocimetry (MTV) tt 0 PIV image pair tt 0 +4 ms 0.03 m/s Temperature ( O C) tt 0 tt 0 +5ms MTV&T image pair Corresponding flow velocity field

44 Hotwire Anemometry

45 Thermal anemometers: Technical Fundamentals -1 Measure the local flow velocity through its relationship to the convective cooling of electrically heated metallic sensors. Hot wire anemometers: for clean air or other gas flows Hot film anemometers: for liquid or some gas flows

46 How a Hot wire Sensor Works The electric current (i) flowing through the wire generates heat (i R w ) Flow Field V In equilibrium, this must be balanced by heat lost (primarily convective) to the surroundings. Electric current, i, through wire

47 Technical Fundamentals - Heat transfer characteristics: Convection (nature convection, forced convection or mixed convection depending on Richardson numbers) Conduction to the supporting prong Radiation: <0.1%, is negligible. q& Nu πlk( Tw T ) Nu(Re, Pr, Gr, M, Kn, a T, l / d, θ ) Hot wire T w θ Fluid flow r V,T T w > T ρud Re ; μ 3 gα( Tw T ) d Gr ; ν λ 1 Kn πc p / cv d Tw T at T M Re ν Pr γ V M c prongs

48 Technical Fundamentals -3 Following King s s Law (1915), According to Collis and Willams (1959): Nu ( Re Nu 0.48 Re 0.51 )( )(1 + a T ) 1 n m Nu ( A + B Re )(1 + at ) , a T ) 0.17, for for 44 < Re < < Re < 44 For a given sensor and fixed overheat ratio, The above equation can transfer as the relationship between the voltage output, E, of the hot-wire operation circuit and the flow velocity R T w w E T R A + Wire temperature cannot be measured directly, but can be estimated ed from its relationship to the wire resistance, R w, directly measured by the operating bridge. For metallic wires: r BV r n [ 1+ a ( T T r w ar : thermal resistivit y coefficien T : reference temepature t )]

49 Technical Fundamentals - 4 Flow Field V The hot wire is electrically heated. If velocity changes for a unsteady flow, convective heat transfer changes, wire temperature will change and eventually reach a new equilibrium. Current flow through wire The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor

50 Technical Fundamentals - 5 For a sensor placed in a unsteady flow, the unsteady energy equation will become: mc dt dt w i R w q& ( V, T m : the mass of the sensor c : specifich heat of the sensor q& : convective heat flux q& q& ( V, The above equation has three unknowns: i, T w (or R w ) and V To render this equation solvable, one must keep with the electric c current, i, or the sensor temperature (T( w ) constant, which can be achieved with the use of suitable electric circuits. The corresponding methods are known as: (1). Constant Current Anemometry (). Constant Temperature Anemometry w ) T w )

51 Constant-current anemometry R s >> R w R s E Voltage follower C E c i E E o o /( R / R s s + Rw) const The voltage output will be E i R w E o R w sensor R c Compensation circuit R c. The unsteady energy equation is highly-nonlinear. When linearized in the vicinity of an operation point, namely at a particular flow speed, V op, and sensor temperature, T wop, it leads to the following first-order differential equation: dtw τ w + ( Tw Twop ) KT ( V Vop ) dt a time constant, which is proportional to the overheat ratio, and a a static sensitivity, τ w : Since voltage, E, is proportional to, Rw relationship will be: τ w : Rw, which, in turn, is linearly related to Tw,, the linearized E-V de τ w + ( E Eop ) K( V Vop ) dt is usually ~ 1ms for thin hot-wire and ~ 10 ms for slim cylindrical hot-film. For flow with variable velocity or temperature, overheat ratio will vary as well. Flow low speed flow, it may result in burnout,, for high-speed flow, sensitivity is low KT

52 Constant-temperature temperature anemometry (CTA) Electric current through the sensor is adjustable continuously through an electric feedback system, and in response to the changes in convective cooling, to make the temperature of the hot wire keep in constant. nt. The unsteady energy equation becomes steady equation. Dynamic response of the anemometer is the same as its static response with a wide frequency range. mc dt dt w i R q& ( V, T ) i R q& ( V w w w ) 0

53 Constant-temperature temperature anemometry (CTA) R R R 1 E sw E offset E B Rd R w sensor R sw E w - + Differential amplifier E Constant temperature circuit Sensor, Rw,, comprises one leg of the Wheatstone bridge. An adjustable decade resistor array, Rd, compress opposite leg of the bridge. The bridge ratio R /R 1 is fixed, and R /R 1 10~0 to make sure to supply most of the available power to the sensor. The two midpoints of the bridge are connected the input of a high-gain, gain, low noise differential amplifier, whose out put is fed back to the top of the bridge. If R /R d R 1 /R w, then E B -E w 0, the amplifier output will be zero. If R d is increased to a value R d, the resulting bridge imbalance will generate an input imbalance e to the amplifier. The amplifier will create some current through both legs of the bridge. The additional current through the hot wire will create additional joule heating, which tend to increase its temperature and thus its resistance, until the resistance increasing sufficiently y to balance the bridge once more.

54 Various effects and error source Velocity orientation effects: Effective cooling velocity V eff V cosθ. In reality, flow velocity tangential to the sensor would result in cooling. V eff V (cos θ + k sin θ ) 1/ Typical values of K are 0.05 and 0.0. Hot wire T w θ Fluid flow r V,T T w > T prongs

55 Various effects and error source Prong interference effects: Interference of the prongs and the probe body may produce additional complications of the heat transfer characteristics. For example a stream in binormal direction will produce higher cooling than a stream with the same velocity magnitude but in the normal direction. In reality,v eff (V N + K V T + h V B ) 1/ V N, V T and V B are the normal tangitail and binormal velocity components. Typically, h 1.1~1. To minimize the effect, it usually use long and thin prongs. Tapered prongs are also recommended. Hot wire T w prongs θ Fluid flow r V,T T w > T

56 Various effects and error source Heat conduction effects: Previous analysis is based on -D assumption with l/d. In reality, the effect of end conduct may effect the accuracy of the measurement results Cold length, l c 0.5*d ((K w /K)(1+a R )/Nu) 1/ K w is thermal conductivity of the sensor K is thermal conductivity of the fluid a R is overheat ratio Effect of the sensor length l/l c A recent study has demonstrate that end conduction effects are expected to decrease significantly as the Reynolds number increasing Hot wire T w prongs θ Fluid flow r V,T T w > T

57 Various effects and error source Compressibility effects: The velocity and temperature fields around the sensor become quite complicated when M>0.6. V ρ T0 For M 1. S S S V ρ T 0 S V S ρ Hot wire T w θ Fluid flow r V,T T w > T Modified King s s law for compressible flow: E A + n 0.55 B( ρv ) n prongs

58 Various effects and error source Temperature variation effects: Calibration at Temperature T1. Correlation is needed if real measurements will be conducted at Temperature T. When the flow temperature varies from position to position or contain turbulent fluctuations, corrections is much more complicated. It requires simultaneous flow temperature measurements. Sv is increasing with overheat ratio a T. At extremely low a T, a thermal anemometer is totally insensitive to velocity variations, and becomes a resistance thermometer. The sensor is called cold wire. Hot wire T w θ Fluid flow r V,T T w > T prongs

59 Various effects and error source Composition effects: Composition of flow may affect the convective heat transfer from a thermal anemometer in as much as it affect the heat conductivity of surrounding fluid. It requires simultaneous measurements of fluid species concentration. Hot wire T w θ Fluid flow r V,T T w > T prongs

60 Various effects and error source Reverse flow and high-turbulence effects: thermal anemometer could not resolve velocity orientation. Forward flow can not be identified from reversing flow In highly turbulent flow (turbulent intensity >5%), reverse flow will occurr statistically some time, therefore, using thermal anemometer for the flow velocity measurement may result quite large measurement uncertainty. Pulsed Hot wire concept Hot wire T w θ Fluid flow r V,T T w > T prongs

61 Multi-sensor probes Cross-wire (X-wire) design: V V eff A eff B V V 1 ( V ( V ( V ( V 1 1 eff A eff A + V V + V V ) ) eff B eff B ) ) V V 1 V r V V V eff-b V 1 V eff-a V 1

62 Multi-sensor probes Three sensor design Four sensor design:

63 Commonly-used Sensor Material Requirements for the sensor material: Good thermal properties Good mechanical strength Commonly-used sensor materials: Tungsten: High thermal resistivity, sufficient mechanical strength and high h melting temperature. However, it oxidized at about 350 o C. Platium: excellent thermal resistivity low mechanical strength. Platinum alloy: Platinum with 0% iridium, 10 rohdium and 10% tangsten Improved mechcanical strength. Slightly reduced thermal resistivity compared with pure platinum

64 Diameter of hot wires L 0.8 ~ 1.5 mm D ~ 5 μm m for conventional applications D ~ 10 μm m for high-speed applications D ~ μm m for low speed applications Prongs: usually tapered to be d d 1mm

65 Laser Doppler Velocimetry (LDV) and Planar Doppler Velocimetry (PDA)

66 Techniques for Flow Velocity Measurements Intrusive techniques Pitot-static probe hotwire, hot film etc... Flow velocity measurement techniques Non-intrusive techniques particle-based techniques molecule-based techniques Laser Doppler Velocimetry (LDV) Planar Doppler Velocimetry (PDV) Particle Image Velocimetry (PIV) etc Laser Induced Fluorescence (LIF) Molecular Tagging Velocimetry (MTV) etc

67 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 V f Particle velocity V p Measurement of particle velocity

68 Laser Doppler Velocimetry (LDV) Laser Doppler velocimetry (LDV, also known as laser Doppler anemometry, or LDA) is a technique for measuring the direction and speed of fluids like air and water. In its simplest form, LDV crosses two beams of collimated, monochromatic laser light in the flow of the fluid being measured. A microscopic pattern of bright and dark stripes forms in the intersection volume. Small particles in the flow pass through this pattern and reflect t light towards a detector, with a characteristic frequency indicating, via the Doppler effect,, the velocity of the particle passing through the probe volume. Interference fringes

69 Doppler Shift The Doppler effect, named after Christian Doppler (an Austrian mathematician and physicist ),) is the change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the waves. 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).

70 Doppler Shift a. Stationary Sound Source b. Source moving with Vsource < Vsound c. Source moving with Vsource Vsound ( Mach 1 - breaking the sound barrier ) d. Source moving with Vsource > Vsound (Mach supersonic)

71 Doppler Shift For waves that travel through a medium (sound, ultrasound, etc...) the relationship between observed frequency f f and emitted frequency f is given by: where v is the speed of waves in the medium v s is the velocity of the source For waves that travel at the speed of light, such as laser light, the relationship between observed frequency f f and emitted frequency is given by: Because the detected frequency increases for objects moving toward the observer, the object's velocity must be subtracted when motion is moving toward the observer. (This is because the source's velocity is in the denominator.) Conversely, detected frequency decreases when the object moves away, and so the object's velocity is added when the motion is away.

72 Fundamentals of LDV 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 V s and emitting light waves with a frequency f s. There is a detector r moving with velocity V 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>>v s, then the change in frequency depends mostly on the relative velocity of the source and detector. Δf f s fr fs f s r r Vr Vs nˆ c r ˆ ˆ ˆ ˆ V n er ei Δf Vs (ˆ er ei ) V 0 r fs c φ φ Vφ sin( ) f Vφ sin( ) Δf fλ λ φ φ sin( ) c

73 Fundamentals of LDV By using a laser bean of wavelength λ488nm (Argon-Ion laser), the maximum Doppler shift from a particle moving with a velocity of V would be: V1.0m/s Δf 4.1 MHz V10.0m/s Δf 41 MHz V100.0m/s Δf 410 MHz V1000m/s Δf 4100 MHz However, since C m/s, λ488nm, then, fc/ λ MHz. the Doppler shift in frequency is very small compared with the frequency of the source laser light. In practice, it is always quit difficult to measure the Doppler shift of frequency accurately for low- speed flows by measuring the received total frequency directly. Δf V φ φ sin( ) f Vφ sin( fλ λ φ ) Dual-beam LDV technique was developed to measure the relative frequency change due to the Doppler shift other than the total frequency.

74 Fundamentals of Dual-Beam LDV If the intensity of each scattered beam collected by the photo detector varies sinusoidal, A sin π ( f i + Δf ) t, i i 1,. Then, the optical mixing of these beams on the photoditector (heterodyning process) produces an output voltage E that is proportional to the squire of the combined light intensity. E ~ { A1 sin π ( f + Δf1) t + A sin π ( f + Δf ) t} A1 sin π ( f + Δf1) t + A sin π ( f + Δf) t + A1 A[sin π ( f + Δf1) t][sin π ( f + Δf1) t] A1 sin π ( f + Δf1) t + A sin π ( f + Δf) t + A1 A[cos π ( Δf1 Δf) t] cos π ( f + Δf1 + Δf) t] A1 sin π ( f + Δf1) t + A sin π ( f + Δf) t cos π ( f + Δf1 + Δf) t] + A1 A[cos π ( Δf1 Δf) t] high frequency low frequency If we define, Δf 1 Δf f ' then : E ~ a + bsin π f ' t r r r r r r V ( es 1 ei 1) V ( es ei ) f ' Δf1 Δf r r λ λ Since ei 1 ei, then r r r θ sin( ) V ( ei ei 1) f ' Vθ λ λ λ Vθ f ' θ sin( ) The above equation is independent of observation angle!

75 Generated Fringes for the Dual-Beam LDV Fring spacing : δ λ θ sin( / ) V Fring number : 4 DT N ; π de D f sin( θ / ) T T Frequency of the scattering light : V sin( θ / ) f V δ λ V T Frequency shift according to Doppler shift theory : sin( θ / ) f V λ

76 Fundamentals of Dual-Beam LDV Width : heigth : length : Volume : 4 ft λ d fe π d e d fe h cos( θ / ) d fe l sin( θ / ) 3 π d fe Volume 6sin( θ / ) cos( θ / )

77 Beam Expander of a Dual-Beam LDV A beam expander is a commonly used LDV accessory, whose function is to reduce the size of the measuring volume. This improves the spatial resolution of velocity measurement while also improving the amplitude resolution as a result of increased light power density within the measuring volume. A beam expander consists of a diverging lens and a converging lens, in addition to the transmitting lens. The beam expansion ratio: E x d ex /d e D Tx / D T 1 Ex ft θ x sin [ sin( θ / )] ftx f is the focal length of the transmitting lens Tx if ftx f 1 4 ftλ then :dfex d fe Ex π dex 4 DT 4 DTx Fringe Numbers : N ; π de π dex The fringe number within the measurement volume is remain unaffected. The fringe spacing will reduced by a factor of Ex, The measurement volume reduced by a factor ~Ex 4 The SNR is also increased! Width : heigth : length : Volume : 4 ft λ d fe π d e d fe h cos( θ / ) d fe l sin( θ / ) 3 π d fe Volume 6sin( θ / ) cos( θ / )

78 Doppler Signal Frequency of the burst signal V sin( θ / ) f δ fλ λ V V sin( θ / ) V a. Typical Doppler Signal of single particle V T b. Typical Doppler Signal of single particle with pedestal removed b. Typical Doppler Signal of multiple particle with pedestal removed The pedestal is due to the intensity of the laser beam is usually has a Gauss G Distribution. The scattering signal is depending on the size and reflective index of the particle and the its position in the measuring volume. Burst intensity: the number of the particles crossing the measuring volume

79 Frequency Shift Frequency of the burst signal V sin( θ / ) f δ fλ λ V V sin( θ / ) V The relationship between the frequency shift and the velocity is equally valid for both senses of direction of velocity. Bragg cell is used to remove this ambiguity. The frequency shift obtained by the Bragg cell makes the fringe pattern move at a constant velocity. Particles which are not moving will generate a signal of the shift frequency f shift. The velocities Vp and V shift will generate signal frequencies f p and V shift respectively. V T f f V then : V V p measured + f V + V particle measured p V shift shift shift

80 Doppler Signal Processing The signal is usually band pass filtered to remove the pedestal and high-frequency noise. A unit named as signal processor is used to determine the Doppler frequency. The signal processor includes: Burst analyzer: : FFT to get the power spectrum, then determine the Doppler frequency. Frequency counters: : count on the number of zero crossings of the filtered bursts. Determine the particle velocity as the ratio between the fringe space over the averaged time between the two zero crossing. Frequency trackers: : used for high particle density case. They contain an electric oscillator, which scans a frequency range and locks at the Doppler frequency, providing an analogue output proportional to it. Advantage is to provide analgue output, but has only limited dynamic range and need for heavy seeding. Photo correlators: : detect the emission of individual photons and correlated them with respect to their times of arrival to computer the time delay for peak correlation. Their advantage over other processor is that they can operate with very low light intensity and noisy signal. But their frequency range is limited, and quit time consuming. V fλ sin( θ / )

81 Errors and uncertainty in LDV measurements Fringe divergence uncertainty: if the beams do not intersect at their waists, the fringes will not be parallel planes. Velocity bias: due to many particles with different velocity passing the measuring volume. U m 1 + U u U V Directional bias: due to the small angle between the particle velocity and fringe direction. V T

82 Fiber Optical Probe of LDV system

83 -component LDV systems Dual-beam laser setup only can measure one component of the velocity with its direction normal to the fringe planes. V Two-color LDV system can be used for - components of flow velocity measurements. Ar-ion Laser beams Blue (488nm) Yellow (514.5 nm) V T -component LDV

84 3-component LDV systems Dual-beam laser setup only can measure one component of the velocity with its direction normal to the fringe planes. V Two-color LDV system can be used for - components of flow velocity measurements. Ar-ion Laser beams Blue (488nm) Yellow (514.5 nm) Purple (476.4nm) V T 3-component LDV

85 Phase Doppler Particle Analyzers/PDPA Systems As particles pass through the probe volume, they scatter light from the beams and create an interference fringe pattern. A receiving lens at an off-axis collection angle projects part of this fringe pattern onto detectors, which produce a 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. PDPA system

86 Theoretical Model for PDPA Measurements S. V. Sankar,, B. J. Weber, D. Y. Kamemoto,, and W. D. Bachalo, APPLIED OPTICS, Vol. 30, No. 33 / 0, S. A. Schaub,, A. A. Naqwi,, and F. L. Harding, Copyright APPLIED by Dr. OPTICS, Hui Hu Iowa 37, State University. All Rights Reserved! No. 3., 1998.

87 Phase Doppler Particle Analyzers/PDPA Systems For proper performance, there must be a high probability of having only one particle in the sample volume at one time.. Current phase-doppler instruments are designed with a sample volume that is larger than the largest particle to be measured. Phase-Doppler systems are relatively complex instrumentation and a high level of experience is required to obtain accurate results. The phase-doppler instrument only provides reliable data for spherical droplets.. Irregular droplets or particles yield irregular light-scattering patterns and are not measured reliably with the phase-doppler instrument, especially when observed very close to the tip of a pneumatic nebulizer. In practice, the instrument rejects a high percentage of the irregular particles, but some false readings are included. photomultiplier tubes PDPA system

88 PDPA Measurement Results

89 Advantages and disadvantages of LDV technique Advantages: Non-intrusive High resolution High accuracy Wide dynamic range for velocity measurements Disadvantages Single point measurements Expansive in instrumentation

90 Planar Doppler Velocimetry (PDV) or Doppler Global Velocimetry (DGV) technique Planar Doppler Velocimetry (PDV) or Doppler Global Velocimetry (DGV) is capable of determining instantaneous, three-dimensional velocity vectors of moving particles or solid material in a laser light sheet everywhere in the field of view.

91 PDV or DGV technique PDV or DGV relies on light scattering (single exposure) by clouds of Particles (high concentration) carried by the flow, rather than the imaging of each individual particle. it has the ability to generate velocity vector field information more quickly than LDV, and over a plane of larger area. Each pixel within the sensor array could yield a potential velocity vector, therefore, a mega pixels imaging camera would potentially output a million velocity vectors at video rate. V LDV V T

92 PDV or DGV technique In DGV,, the velocity information is obtained by means of an optical & spectroscopic frequency converter (a pre-selected linear spectral line optical transfer function), known as an absorption line filter (ALF), that transforms the Doppler shifted frequency of light scattered by the particles in the flow to image intensity variations in the imaging plane. Once this transformation is completed, the converted Doppler signal intensity map can then be processed by light intensity detectors (CCD camera) and computers to obtain a velocity map of the flow of interest. To eliminate the problem of both scattering signal and illumination ion intensity variations spatially in the measurement window, the Doppler signal intensity y map is normalized by a reference intensity map from the same view of the flow. Δf f r f V φ φ sin( ) f Vφ sin( fλ λ φ ) Io Ix iodine vapor cell: Absorption line filter

93 PDV or DGV technique Δf f r f V φ φ sin( ) f Vφ sin( fλ λ φ ) Io Ix iodine vapor cell: Absorption line filter

94 PDV or DGV technique

95 PDV or DGV technique PDV measurements in a supersonic jet Δf f r f V φ φ sin( ) f Vφ sin( fλ λ φ )

96 Multi component PDV or DGV technique Δf f r f V φ φ sin( ) f Vφ sin( fλ λ φ )

97 Advantages and disadvantages of PDV/GDV technique Advantages: PDV is well suited for high-speed flow measurements where concerns about particle seeding make PIV impractical. Although PDV requires particles to scatter light, individual particles do not need to be imaged thus allowing the use of much smaller seed particles and making the measurements less sensitive to particle seed density. For example, in some unheated supersonic flow facilities it is possible p to use condensation of a vapor, such as water, acetone or ethanol, to produce seed particles p in the flow. In addition, PDV has an inherently higher resolution than PIV as smaller image subregions can be used to determine the velocity. Disadvantages The main weakness of PDV is the complex optical set up required to get accurate measurements (position registration, etc..). For each component of velocity, two images (signal and reference) ) are required, which typically necessitates two cameras. To obtain all three components of velocity, therefore, requires the simultaneous use of up to six cameras. In addition, the laser used for the measurements must be narrow linewidth,, which is typically performed by injection seeding of the laser cavity. Even with seeding, the laser frequency can fluctuate with time and must be monitored. These introduce additional complexity to the experimental set-up. PDV systems, although used in many laboratories, are not yet commercially available and can be quite expensive (equipment, data processing, experience, labor, etc.) if built from scratch.

98 Thank you for your time! Questions?