Multisensor Hot-Wire Anemometry

Transcription

1 Multisensor Hot-Wire Anemometry Presentation at the State Key Laboratory of Multiphase Flow in Power Engineering Xi an Jiaotong University, Xi an, China, A. Romeos, A. Cavo, G. Lemonis December 2008 LABORATORY OF APPLIED THERMODYNAMICS & STATISTICAL MECHANICS MECHANICAL ENGINEERING & AERONAUTICS DEPARTMENT UNIVERSITY OF PATRAS

2 Fundamentals Purpose to measure mean and fluctuating variables in fluid flows (velocity, temperature, etc.) Aim of slide show: to explain how Constant Temperature Anemometer (CTA) can be used to meet this purpose

3 Transducer requirements s Physical Quantity U(t), T(t) Transducer Signal S(t) Ideal transducer Output signal is proportional to magnitude of physical quantity The physical quantity is measured at a point in space The output signal represents the input without frequency distortion Low noise on output signal No interference with physical process Output not influenced by other variables s( t) u( t) Real transducer Static transfer function (calibration curve) Spatial resolution (finite size of measuring volume) Temporal resolution (frequency response) Signal-to-noise ratio Interference effects Multi-variate response t Source DANTEC

4 Anemometer signal output The thermal anemometer provides an analogue output which represents the velocity in a point. A velocity information is thus available anytime. Note that LDA signals occur at random, while PIV signals are timed with the frame grapping of illuminated particles.

5 Principles of operation Consider a thin wire mounted to supports and exposed to a velocity U. When a current is passed through wire, heat is generated (I 2 R w ). In equilibrium, this must be balanced by heat loss (primarily convective) to the surroundings. If velocity changes, convective heat transfer coefficient will change, wire temperature will change and eventually reach a new equilibrium. Velocity U Current I Sensor (thin wire) Sensor dimensions: length ~1 mm diameter ~5 micrometer Wire supports (St.St. needles)

6 Governing equation I Governing Equation: de dt = W H E = thermal energy stored in wire E = C w T s C w = heat capacity of wire W = power generated by Joule heating W = I 2 R w recall R w = R w (T w ) H = heat transferred to surroundings

7 Governing equation II Heat transferred to surroundings H = ( convection to fluid + conduction to supports + radiation to surroundings) Convection Q c = Nu A (T w -T a ) Nu = h d/kf = f (Re, Pr, M, Gr,α ), Re = ρu d/μ Conduction f(t w, l w, k w, T supports ) Radiation f (T w4 - T f4 )

8 Simplified static analysis I For equilibrium conditions the heat storage is zero: de dt = O W = H and the Joule heating W equals the convective heat transfer H Assumptions - Radiation losses small - Conduction to wire supports small - Tw uniform over length of sensor - Velocity impinges normally on wire, and is uniform over its entire length, and also small compared to sonic speed. - Fluid temperature and density constant

9 Simplified static analysis II Static heat transfer: W = H => I 2 Rw = ha(t w -T a ) => I 2 R w = Nu k f/ da(t w -T a ) h = film coefficient of heat transfer A = heat transfer area d = wire diameter kf = heat conductivity of fluid Nu = dimensionless heat transfer coefficient Forced convection regime, i.e. Re >Gr 1/3 (0.02 in air) and Re<140 Nu = A 1 + B 1 Re n = A 2 + B 2 U n I 2 R w2 = E 2 = (T w -T a )(A + B U n ) King s law The voltage drop is used as a measure of velocity.

10 Hot-wire static transfer function Velocity sensitivity (King s law coeff. A = 1.51, B = 0.811, n = 0.43) 2,4 5 E volts 2,2 2 1,8 du/de/u volts^ , U m /s U m /s Output voltage as fct. of velocity Voltage derivative as fct. of velocity

11 Directional response I Probe coordinate system y U α Uz Uy x θ Ux z Velocity vector U is decomposed into normal Ux, tangential Uy and binormal Uz components.

12 Directional response II Finite wire (l/d~200) response includes yaw and pitch sensitivity: where: U 2 eff(a) = U 2 (cos 2 a + k 2 sin 2 a) θ = 0 U 2 eff(θ ) = U 2 (cos 2 θ +h 2 sin 2 θ ) α = 0 k, h = yaw and pitch factors α, θ = angle between wire normal/wire-prong plane, respectively, and velocity vector General response in 3D flows: U 2 eff = Ux 2 + k 2 Uy 2 + h 2 Uz 2 Ueff is the effective cooling velocity sensed by the wire and deducted from the calibration expression, while U is the velocity component normal to the wire

13 Directional response III Typical directional response for hot-wire probe (From DISA 1971)

14 Directional response IV Yaw and pitch factors k1 and k2 (or k and h) depend on velocity and flow angle (From Joergensen 1971)

15 Probe types I Miniature Wire Probes Platinum-plated tungsten, 5 µm diameter, 1.2 mm length Gold-Plated Probes 3 mm total wire length, 1.25 mm active sensor copper ends, gold-plated Advantages: - accurately defined sensing length - reduced heat dissipation by the prongs - more uniform temperature distribution along wire - less probe interference to the flow field

16 Probe types II For optimal frequency response, the probe should have as small a thermal inertia as possible. Important considerations: Wire length should be as short as possible (spatial resolution; want probe length << eddy size) Aspect ratio (l/d) should be high (to minimise effects of end losses) Wire should resist oxidation until high temperatures (want to operate wire at high T to get good sensitivity, high signal to noise ratio) Temperature coefficient of resistance should be high (for high sensitivity, signal to noise ratio and frequency response) Wires of less than 5 µm diameter cannot be drawn with reliable diameters

17 Probe types III Film Probes Thin metal film (nickel) deposited on quartz body. Thin quartz layer protects metal film against corrosion, wear, physical damage, electrical action Fiber-Film Probes Hybrid - film deposited on a thin wire-like quartz rod (fiber) split fiber-film probes.

18 Probe types IV X-probes for 2D flows 2 sensors perpendicular to each other. Measures within ±45 o. Split-fiber probes for 2D flows 2 film sensors opposite each other on a quartz cylinder. Measures within ±90 o. Tri-axial probes for 3D flows 3 sensors in an orthogonal system. Measures within 70 o cone.

19 Hints to select the right probe Use wire probes whenever possible relatively inexpensive better frequency response can be repaired Use film probes for rough environments more rugged worse frequency response cannot be repaired electrically insulated protected against mechanical and chemical action

20 Modes of anemometer operation Constant Current (CCA) Constant Temperature (CTA)

21 Constant current anemometer CCA Principle: Current through sensor is kept constant Advantages: - High frequency response Disadvantages: - Difficult to use - Output decreases with velocity - Risk of probe burnout

22 Constant Temperature Anemometer CTA I Principle: Sensor resistance is kept constant by servo amplifier Advantages: - Easy to use - High frequency response - Low noise - Accepted standard Disadvantages: - More complex circuit

23 Constant temperature anemometer CTA II 3-channel StreamLine with Triaxial wire probe 55P91

24 Modes of operation, CTA I Wire resistance can be written as: R w = R o (1+ α o (Τ w -Τ o )) R w = wire hot resistance R o = wire resistance at T o α o = temp. coeff. of resistance T w = wire temperature = reference temperature T o Define: OVERHEAT RATIO as: a = (R w -R o )/R o = α o (Τ w -Τ o ) Set DECADE overheat resistor as: RD = (1+a)R w

25 Modes of operation, CTA II The voltage across wire is given by: E 2 = I 2 R w2 = R w (R w - R a )(A 1 + B 1 U n ) or as R w is kept constant by the servoloop: E 2 = A + BU n 2,4 Note following comments to CTA and to CCA: - Response is non-linear: - CCA output decreases - CTA output increases - Sensitivity decreases with increasing U E volts 2,2 2 1,8 1, U m /s CTA output as fct. of U

26 Dynamic response, CCA I Hot-wire Probes: For analysis of wire dynamic response, governing equation includes the term due to thermal energy storage within the wire: W = H + de/dt The equation then becomes a differential equation: I 2 R w = (R w -R a )(A+BU n ) + C w (dt w /dt) or expressing Tw in terms of Rw: I 2 R w = (R w -R a )(A+BU n ) + C w / α o R o dr w /dt C w α o = heat capacity of the wire = temperature coeff. of resistance of the wire

27 Dynamic response, CCA II Hot-wire Probes: The first-order differential equation is characterised by a single time constant τ : τ = C w /(α o R o )(Α+ΒΥ n ) The normalised transfer function can be expressed as: H wire (f) = 1/(1+jf/f cp ) Where f cp is the frequency at which the amplitude damping is 3dB (50% amplitude reduction) and the phase lag is 45 o. Frequency limit can be calculated from the time constant: f cp = 1/2πτ

28 Dynamic response, CCA III Hot-wire Probes: Frequency response of film-probes is mainly determined by the thermal properties of the backing material (substrate). The time constant for film-probes becomes: τ = (R/R0) 2 F 2 ρ s C s k s /(A+BU n ) 2 ρ s = substrate density C s = substrate heat capacity k s = substrate heat conductivity and the normalised transfer function becomes: H film (f) = 1/(1+(jf/f cp ) 0.5 )

29 Dynamic response, CCA IV U 2 U 1 Velocity 3 db 30 Amplitude response and phase lag 6 db/octave Time Resistance R (R 1 -R ) 2 R 2 τ Time Upper frequency limit f = ½ π τ Frequency Dynamic characteristic may be described by the response to - Step change in velocity or - Sinusoidal velocity variation

30 Dynamic response, CCA V The hot-wire response characteristic is specified by: (From P.E. Nielsen and C.G. Rasmussen, 1966) For a 5 µm wire probe in CCA mode τ ~ 0.005s, typically. (Frequency response can be improved by compensation circuit)

31 Dynamic response, CTA I CTA keeps the wire at constant temperature, hence the effect of thermal inertia is greatly reduced: Time constant is reduced to where τ CTA = τ CCA /(2aSRw) a = overheat ratio S = amplifier gain Rw = wire hot resistance Frequency limit: fc defined as -3dB amplitude damping (From Blackwelder 1981)

32 Dynamic response, CTA II Typical frequency response of 5 mm wire probe (Amplitude damping and Phase lag): (From Dantec Dynamics) Phase lag is reduced by frequency dependent gain (-1.2 db/octave)

33 Velocity calibration (Static cal.) Despite extensive work, no universal expression to describe heat transfer from hot wires and films exist. For all actual measurements, direct calibration of the anemometer is necessary.

34 Velocity calibration (Static cal.) II Calibration in gases (example low turbulent free jet): Velocity is determined from isentropic expansion: P o /P = (1+(γ 1)/2Μ 2 ) γ /(γ 1) a 0 = (γ ΡΤ 0 ) 0.5 a = a o /(1+(γ 1)/2Μ 2 ) 0.5 U = Ma

35 Velocity calibration (Static cal.) III Film probes in water - Using a free jet of liquid issuing from the bottom of a container - Towing the probe at a known velocity in still liquid - Using a submerged jet

36 Typical calibration curve Wire probe calibration with curve fit errors E1 v.u Error (%) E1 (v) Error (%) U velocity U velocity (Obtained with Dantec Dynamics 90H01/02)Calibrator) Curve fit (velocity U as function of output voltage E): U = C 0 + C 1 E + C 2 E 2 + C 3 E 3 + C 4 E 4

37 Dynamic calibration/tuning I Direct method Need a flow in which sinusoidal velocity variations of known amplitude are superimposed on a constant mean velocity - Microwave simulation of turbulence (<500 Hz) - Sound field simulation of turbulence (>500 Hz) - Vibrating the probe in a laminar flow (<1000Hz) All methods are difficult and are restricted to low frequencies.

38 Dynamic calibration/tuning II Indirect method, SINUS TEST Subject the sensor to an electric sine wave which simulates an instantaneous change in velocity and analyse the amplitude response Amplitude (mv rms) db Amplitude (mv rms) db Frequency (Hz) Frequency (Hz) Typical Wire probe response Typical Fiber probe response

39 Dynamic calibration/tuning III Indirect method SQUARE WAVE TEST Subject the sensor to an electric sine wave which simulates an instantaneous change in velocity and analyse the shape of the anemometer output h τ w 0.97 h 1 f c = 1.3 τw t 0.15 h (From Bruun 1995) For a wire probe (1-order probe response): Frequency limit (- 3dB damping): f c = 1/1.3 τ

40 Dynamic calibration Conclusion: Indirect methods are the only ones applicable in practice. Sinus test necessary for determination of frequency limit for fiber and film probes. Square wave test determines frequency limits for wire probes. Time taken by the anemometer to rebalance itself is used as a measure of its frequency response. Square wave test is primarily used for checking dynamic stability of CTA at high velocities. Indirect methods cannot simulate effect of thermal boundary layers around sensor (which reduces the frequency response).

41 Disturbing effects (problem sources) Anemometer system makes use of heat transfer from the probe Qc = Nu A (Tw -Ta) Nu = h d / k f = f (Re, Pr, M, Gr, α ), Anything which changes this heat transfer (other than the flow variable being measured) is a PROBLEM SOURCE! Unsystematic effects (contamination, air bubbles in water, probe vibrations, etc.) Systematic effects (ambient temperature changes, solid wall proximity, eddy shedding from cylindrical sensors etc.)

42 Problem sources Probe contamination I Most common sources: - dust particles - dirt - oil vapours - chemicals Effects: - Change flow sensitivity of sensor (DC drift of calibration curve) - Reduce frequency response Cure: - Clean the sensor - Recalibrate

43 Problem Sources Probe contamination II Drift due to particle contamination in air 5 µm Wire, 70 µm Fiber and 1.2 mm SteelClad Probes (Um-Uact)/Uact*100% w ire fiber steel-clad U (m/s) (From Jorgensen, 1977) Wire and fiber exposed to unfiltered air at 40 m/s in 40 hours Steel Clad probe exposed to outdoor conditions 3 months during winter conditions

44 Problem Sources Probe contamination IV Low Velocity - slight effect of dirt on heat transfer - heat transfer may even increase! - effect of increased surface vs. insulating effect High Velocity - more contact with particles - bigger problem in laminar flow - turbulent flow has cleaning effect Influence of dirt INCREASES as wire diameter DECREASES Deposition of chemicals INCREASES as wire temperature INCREASES * FILTER THE FLOW, CLEAN SENSOR AND RECALIBRATE!

45 Problem Sources Probe contamination III Drift due to particle contamination in water Output voltage decreases with increasing dirt deposit 10 % voltage reduction 1 0,1 0,001 0,01 0,1 1 Dirt thicknes versus sensor diam eter, e/d theory fiber w edge (From Morrow and Kline 1971)

46 Problem Sources Bubbles in Liquids I Drift due to bubbles in water (From C.G.Rasmussen 1967) In liquids, dissolved gases form bubbles on sensor, resulting in: - reduced heat transfer - downward calibration drift

47 Problem Sources Bubbles in Liquids II Effect of bubbling on portion of typical calibration curve e Bubble size depends on - surface tension - overheat ratio - velocity Precautions - Use low overheat! - Let liquid stand before use! - Don t allow liquid to cascade in air! - Clean sensor! cm/sec (From C.G.Rasmussen 1967)

48 Problem Sources (solved) Stability in Liquid Measurements Fiber probe operated stable in water - De-ionised water (reduces algae growth) - Filtration (better than 2 µm) - Keeping water temperature constant (within 0.1 o C) (From Bruun 1996)

49 Problem sources Eddy shedding I Eddy shedding from cylindrical sensors Occurs at Re ~50 (From Eckelmann 1975) Select small sensor diameters/ Low pass filter the signal

50 Problem Sources Eddy shedding II Vibrations from prongs and probe supports: - Probe prongs may vibrate due to eddy shedding from them or due induced vibrations from the surroundings via the probe support. - Prongs have natural frequencies from 8 to 20 khz Always use stiff and rigid probe mounts.

51 Problem Sources Temperature Variations I Fluctuating fluid temperature Heat transfer from the probe is proportional to the temperature difference between fluid and sensor. E 2 = (T w -T a )(A + B U n ) As T a varies: - heat transfer changes - fluid properties change Air measurements: - limited effect at high overheat ratio - changes in fluid properties are small Liquid measurements effected more, because of: - lower overheats - stronger effects of T change on fluid properties

52 Problem Sources Temperature Variations II Anemometer output depends on both velocity and temperature Hot-wire calibrations at diff. temperatures Relative velocity error for 1C temp. increase 2,4 2,3 2,2 2,1 2,0 1,9 1,8 1,7 1,6 1, T=20 T=25 T=30 T=35 T=40-1,5-1,7-1,9-2,1-2,3-2,5-2, Tdiff=10 C (From Joergensen and Morot1998) When ambient temperature increases the velocity is measured too low, if not corrected for.

53 Problem Sources Temperature Variations III Film probe calibrated at different temperatures

54 Problem Sources Temperature Variations IV To deal with temperature variations: - Keep the wire temperature fixed (no overheat adjustment), measure the temperature along and correct anemometer voltage prior to conversion - Keep the overheat constant either manually, or automatically using a second compensating sensor. - Calibrate over the range of expected temperature and monitor simultaneously velocity and temperature fluctuations.

55 Measurements in 2D Flows I X-ARRAY PROBES (measures within ±45 o with respect to probe axis): Velocity decomposition into the (U,V) probe coordinate system U = U1 cosα 1 + U2 cosα 2 V = U1 sinα 1 - U2 sinα 2 where U 1 and U 2 in wire coordinate system are found by solving: U cal12 (1+k 2 1 ) (cos(90 - α 1 )) 2 = k 2 1 U1 2 + U2 2 U cal22 (1+k 2 2 ) (cos(90 - α 2 )) 2 = U1 2 + k 2 2 U2 2

56 Measurements in 2D Flows II Directional calibration provides yaw coefficients k 1 and k Uc1,Uc2 vs. Angle K1,K2 vs. Angle Uc1,Uc2 K1,K Angle (deg) Angle (deg) (Obtained with Dantec Dynamics 55P51 X-probe and 55H01/H02 Calibrator)

57 Measurements in 3D Flows I TRIAXIAL PROBES (measures within 70 o cone around probe axis): z 3 35 x 55 Probe stem

58 Measurements in 3D Flows II Velocity decomposition into the (U,V,W) probe coordinate system U = U 1 cos U 2 cos U 3 cos54.74 V = -U 1 cos45 - U 2 cos135 + U 3 cos90 W = -U 1 cos U 2 cos U 3 cos35.26 where U 1, U 2 and U 3 in wire coordinate system are found by solving: U 1cal2 (1+k 1 2 +h 1 2 ) cos = k12 U U h 12 U 3 2 U 2cal2 (1+k 2 2 +h 2 2 ) cos = h 22 U k 22 U U 3 2 U 3cal2 (1+k 3 2 +h 3 2 ) cos = U h 32 U k 32 U 3 2 left hand sides are effective cooling velocities. Yaw and pitch coefficients are determined by directional calibration.

59 Measurements in 3D Flows III U, V and W measured by Triaxial probe, when rotated around its axis. Inclination between flow and probe axis is 20 o. Velocity component, m/s Roll angle. Umeas Vmeas Wmeas Res,meas Uact 0,15 Vact 0,10 Wact 0,05 Res,act 0,00 Meas. - Act. vel., m/s -0,05-0,10-0, Up-Uact Vp-Vact Wp-Wact Roll angle (Obtained with Dantec Dynamics Tri-axial probe 55P91 and 55H01/02 Calibrator)

60 Recommended temperature correction: Keep sensor temperature constant, measure temperature and correct voltages or calibration constants. I) Output Voltage is corrected before conversion into velocity - This gives under-compensation of approx. 0.4%/C in velocity. Improved correction: Measurement at Varying Temperature Temperature Correction I E corr = ((T w - T ref )/(T w - T acq )) 0.5 E acq. E corr = ((T w - T ref )/(T w - T acq )) 0.5(1±m) E acq. Selecting proper m (m= 0.2 typically for wire probe at a = 0.8) improves compensation to better than ±0.05%/C.

61 Measurement at Varying Temperature Temperature Correction II Temperature correction in liquids may require correction of power law constants A and B: A corr = (((T w -T o )/(T w -T acq )) (1±m) (k f0 /k f1 ) (Pr f0 /Pr f1 ) 0.2 A 0 B corr = ((T w -T o )/(T w -T acq )) (1±m) (k f0 /k f1 ) (Pr f0 /Pr f1 ) 0.33 (µ f1 /µ f0 )n (ρ f0 /ρ f1 ) n B 0 In this case the voltage is not corrected

62 Data acquisition I Data acquisition, conversion and reduction: Requires digital processing based on - Selection of proper A/D board - Signal conditioning - Proper sampling rate and number of samples

63 Data acquisition II A/D boards convert analogue signals into digital information (numbers) They have following main characteristics: Resolution: - Min. 12 bit (~1-2 mv depending on range) Sampling rate: - Min. 100 khz (allows 3D probes to be sampled with ~30 khz /sensor) Simultaneous sampling: - Recommended (if not sampled simultaneously there will be phase lag between sensors of 2- and 3D probes) External triggering: Recommended (allows sampling to be started by external event)

64 Data acquisition III Signal Conditioning of anemometer output Anemometer Offset Amplifier E G E(1) E(t)-E off G(E(t)-E off ) t t t Increases the AC part of the anemometer output and improves resolution: E G (t) = G(E(t) - E off ) (From Bruun 1995) Allows filtering of anemometer - Low pass filtering is recommended - High pass filtering may cause phase distortion of the signal

65 Data acquisition IV Sample rate and number of samples Time domain statistics (spectra) require sampling 2 times the highest frequency in the flow Amplitude domain statistics (moments) require uncorrelated samples. Sampling interval min. 2 times integral time scale. Number of samples shall be sufficient to provide stable statistics (often several thousand samples are required) Proper choice requires some knowledge about the flow aforehand It is recommended to try to make autocorrelation and power spectra at first as basis for the choice

66 CTA Anemometry Steps needed to get good measurements: Get an idea of the flow (velocity range, dimensions, frequency) Select right probe and anemometer configuration Select proper A/D board Perform set-up (hardware set-up, velocity calibration, directional calibration) Make a first rough verification of the assumptions about the flow Define experiment (traverse, sampling frequency and number of samples) Perform the experiment Reduce the data (moments, spectra, correlations) Evaluate results Recalibrate to make sure that the anemometer/probe has not drifted

67 Multisensor Hot Wire Anemometry Y Z X A D α B I h h C I Kovasznay type probe Vukoslavčević & Wallace, 1981 β β Foss, V x u γ y v y z 90 o 90 o x o 1 1 mm mm Eckelmann et al., y x wall h 5 z 6 y Kim, 1989 h h h

68 Multisensor Hot Wire Anemometry Wallace, Vukoslavčević & Balint 1991 Wallace, Ong & Balint (1993) Tsinober, Kit & Dracos 1992 Tsinober, Kit & Dracos (1992) Wire 5 1 x 2 x 2 1 =1.23 mm Wire 3 Wire 2 Wire 4 Wire 1 Wire 7 Wire 6 2 β 4, U 1 7 x 1 3, 8 β x 3 Wire 9 Wire Lemonis & Dracos (1995) Honkan & =1.44 mm Andreopoulos (1997) Antonia et al., 1998)

69 Multisensor Hot Wire Anemometry

70 Multisensor Hot Wire Anemometry u ic, + uid, uib, u i uib, uie, 2 2 uib, ( uic, + uid, ) A = = = x x x 2 x u u u A = x x i id, ic, 3 3 u 1 i u A = x U t A i A

71 ( α,β ) E =f U, w Calibration 1 m n 1 m n w w = w ijk i 1 j 2 k 3 i= 0 j=0 k=0 ( ) ( ) ( ) E P b B x B x B x, w=1-4, ( ) ( ) 1 i i Β (x) = x 1 x 1 1 i i Bernstein E 3 (volt) m n 1 m n 1 = 1 ijk i 1 j 2 j 3 i=0 j=0 k=0 ( ) ( ) ( ) E b B x B x B x, 1 m n 1 m n 4 = 4 ijk i 1 j 2 j 3 i=0 j=0 k=0 ( ) ( ) ( ) E b B x B x B x.

72 Calibration

73 Rectangular jet

74 Rectangular jet X Y Z

75 Rectangular jet U / U C 1,0 AR=6 x/d=11 X-wire AR=6 x/d=11 12-wire AR=5 x/d=12.6 Quinn (1992) AR=10 x/d=12.6 Quinn (1992) 0,8 0,6 0,4 0,2 0,0 0,0 0,5 1,0 1,5 2,0 2,5 y / y c Ω z y c / U C 1,2 1,0 0,8 0,6 0,4 0,2 0,0-0,2 0,0 0,5 1,0 1,5 2,0-0,2 2,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 1,0 2,5 2,0 1,5 1,0 0,5 0,0 x/d=3 x/d=1-0,5 0,0 0,5 1,0 1,5 2,0 2,5 y/y c Ω z = V x U y 1,0 0,8 0,6 0,4 0,2 0,0 0,8 0,6 0,4 0,2 0,0 differetiating U(y) 12 vorticity mean PIV vorticity mean y/y c x/d=11 x/d=6-0,2 0,0 0,5 1,0 1,5 2,0 2,5

76 Rectangular jet w'/u 0 v'/u 0 u'/u 0 0,25 0,20 0,15 0,10 0,05 0,25 0,20 0,15 0,10 0,05 0,25 0,20 0,15 0,10 0,05 x/d=1 x/d=3 x/d=6 x/d=11 0,00 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 0,00 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 0,00 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 y/y c ω'z D/U 0 ω'y D/U 0 ω'x D/U ,0 0,5 1,0 1, ,0 0,5 1,0 1, x/d=1 x/d=3 x/d=6 x/d=11 0 0,0 0,5 1,0 1,5 y/y c

77 Rectangular jet <u i ω 2 j > / u' i (ω' j )2 <u i ω 2 j > / u' i (ω' j )2 0,8 x/d=3 0,4 0,0-0,4 <uω 2 > x <uω 2 > y <uω 2 > z 0,2 x/d=11 0,0-0,2-0,4-0,8-0,6 0,0 0,4 0,8 1,2 1,6 0,0 0,4 0,8 1,2 1,6 0,4 0,2 0,3 0,2 x/d=1 0,0 0,1-0,2 0,0-0,1-0,4-0,2-0,3-0,6 x/d=6-0,4-0,8 0,0 0,4 0,8 1,2 1,6 0,0 0,4 0,8 1,2 1,6 y/y c y/y c uωω i i

78 Co-rotating tip vortices

79 Co-rotating tip vortices Ακροφύσιο εισόδου κωδωνόσχημης μορφής Θάλαμος καθησυχασμού z y x Θάλαμος μετρήσεων Διάταξη διαφορικής πτέρυγας Ακροφύσιο Boerger Διαχύτης και ανεμιστήρας

80

81 Mean streamwise velocity Mean streamwise vorticity RMS of streamwise velocity RMS of streamwise vorticity

82 Topology + + Saddle point Diverging separatrix + + Converging separatrix

83 Thanks!