1. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Hot-Wire Anemometry Purpose: to measure mean and fluctuating velocities in fluid flows http://www.dantecmt.com/ www.tsi.com/

2. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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. Principles of operation If velocity changes, convective heat transfer coefficient will change, wire temperature will change and eventually reach a new equilibrium.

3. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Governing equation I Governing Equation: E = thermal energy stored in wire E = CwTs Cw = heat capacity of wire W = power generated by Joule heating W = I 2 Rw recall Rw = Rw(Tw) H = heat transferred to surroundings

4. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Governing equation II Heat transferred to surroundings ( convection to fluid + conduction to supports + radiation to surroundings) Convection Qc = Nu · A · (Tw -Ta) Nu = h ·d/kf = f (Re, Pr, M, Gr,  ), Re =  U/  Conduction f(T w, l w, k w, T supports ) Radiationf(T w 4 - T f 4 )

5. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Simplified static analysis I For equilibrium conditions the heat storage is zero: 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

6. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Simplified static analysis II Static heat transfer: W=H I 2 Rw = hA(Tw -Ta) I 2 Rw = Nukf/dA(Tw -Ta) 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 Rw 2 = E 2 = (Tw -Ta)(A + B · U n ) “King’s law” The voltage drop is used as a measure of velocity.

7. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Hot-wire static transfer function Velocity sensitivity (King’s law coeff. A = 1.51, B = 0.811, n = 0.43) Output voltage as fct. of velocityVoltage derivative as fct. of velocity

8. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Directional response I Velocity vector U is decomposed into normal Ux, tangential Uy and binormal Uz components. Probe coordinate system

9. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Directional response II Finite wire (l/d~200) response includes yaw and pitch sensitivity: U 2 eff(a) = U 2 (cos 2 a + k 2 sin 2 a)  = 0 U 2 eff(  ) = U 2 (cos 2  +h 2 sin 2  )  = 0 where: k, h = yaw and pitch factors ,  = 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

10. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Directional response III Typical directional response for hot-wire probe (From DISA 1971)

11. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Directional response IV Yaw and pitch factors k1 and k2 (or k and h) depend on velocity and flow angle (From Joergensen 1971)

12. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Probe types I Miniature Wire Probes Platinum-plated tungsten, 5  m 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

13. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

14. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.”

15. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.

16. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

17. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Modes of anemometer operation Constant Current (CCA) Constant Temperature (CTA)

18. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

19. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

20. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Constant temperature anemometer CTA II 3-channel StreamLine with Tri-axial wire probe 55P91

21. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Modes of operation, CTA I Wire resistance can be written as: Rw = Ro(1+  Rw =wire hot resistance Ro = wire resistance at To  = temp.coeff. of resistance Tw = wire temperature To = reference temperature Define: “OVERHEAT RATIO” as: a = (Rw-Ro)/Ro =  Set “DECADE” overheat resistor as: RD = (1+a)Rw

22. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Modes of operation, CTA II The voltage across wire is given by: E 2 = I 2 Rw 2 = Rw(Rw - Ra)(A 1 + B 1 U n ) or as Rw is kept constant by the servoloop: E 2 = A + BU n Note following comments to CTA and to CCA: -Response is non-linear: - CCA output decreases - CTA output increases -Sensitivity decreases with increasing U CTA output as fct. of U

23. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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 Rw = (Rw-Ra)(A+BU n ) + Cw(dTw/dt) or expressing Tw in terms of Rw: I 2 Rw = (Rw-Ra)(A+BU n ) + Cw/  Cw = heat capacity of the wire  = temperature coeff. of resistance of the wire

24. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Dynamic response, CCA II Hot-wire Probes: The first-order differential equation is characterised by a single time constant  :  = Cw/(  n ) The normalised transfer function can be expressed as: Hwire(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 = 1/2 

25. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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:  = (R/R0) 2 F 2  s C s k s /(A+BU n ) 2  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 )

26. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Dynamic response, CCA IV Dynamic characteristic may be described by the response to - Step change in velocity or - Sinusoidal velocity variation

27. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Dynamic response, CCA V The hot-wire response characteristic is specified by: For a 5 µm wire probe in CCA mode  ~ 0.005s, typically. (Frequency response can be improved by compensation circuit) (From P.E. Nielsen and C.G. Rasmussen, 1966)

28. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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  CTA =  CCA /(2aSRw) where a = overheat ratio S = amplifier gain Rw = wire hot resistance Frequency limit: fc defined as -3dB amplitude damping (From Blackwelder 1981)

29. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Dynamic response, CTA II Typical frequency response of 5 mm wire probe (Amplitude damping and Phase lag): Phase lag is reduced by frequency dependent gain (-1.2 dB/octave) (From Dantec MT)

30. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.

31. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Velocity calibration (Static cal.) II Calibration in gases (example low turbulent free jet): Velocity is determined from isentropic expansion: P o /P = (1+(  2 )  a 0 = (  0 ) 0.5 a = a o /(1+(  2 ) 0.5 U = Ma

32. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

33. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Typical calibration curve Wire probe calibration with curve fit errors 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 (Obtained with Dantec 90H01/02)Calibrator)

34. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.

35. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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. Typical Wire probe responseTypical Fiber probe response

36. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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 (From Bruun 1995) For a wire probe (1-order probe response): Frequency limit (- 3dB damping): f c = 1/1.3 

37. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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).

38. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Disturbing effects (problem sources) Anemometer system makes use of heat transfer from the probe Qc = Nu · A · (Tw -Ta) Nu = h · d/kf = f (Re, Pr, M, Gr,  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.)

39. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

40. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Probe contamination II Drift due to particle contamination in air 5  m Wire, 70  m Fiber and 1.2 mm SteelClad Probes (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

41. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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!

42. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Probe contamination III Drift due to particle contamination in water Output voltage decreases with increasing dirt deposit (From Morrow and Kline 1971)

43. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Bubbles in Liquids I Drift due to bubbles in water In liquids, dissolved gases form bubbles on sensor, resulting in: - reduced heat transfer - downward calibration drift (From C.G.Rasmussen 1967)

44. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Bubbles in Liquids II Effect of bubbling on portion of typical calibration curve 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! (From C.G.Rasmussen 1967)

45. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources (solved) Stability in Liquid Measurements Fiber probe operated stable in water - De-ionised water (reduces algae growth) - Filtration (better than 2  m) - Keeping water temperature constant (within 0.1 o C) (From Bruun 1996)

46. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem sources Eddy shedding I Eddy shedding from cylindrical sensors Occurs at Re ~50 Select small sensor diameters/ Low pass filter the signal (From Eckelmann 1975)

47. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.

48. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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 = (Tw-Ta)(A + B·U n ) As Ta 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

49. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Temperature Variations II Anemometer output depends on both velocity and temperature When ambient temperature increases the velocity is measured too low, if not corrected for. (From Joergensen and Morot1998)

50. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Problem Sources Temperature Variations III Film probe calibrated at different temperatures

51. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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.

52. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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 where U 1 and U 2 in wire coordinate system are found by solving:

53. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Measurements in 2D Flows II Directional calibration provides yaw coefficients k 1 and k 2 (Obtained with Dantec 55P51 X-probe and 55H01/H02 Calibrator)

54. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Measurements in 3D Flows I TRIAXIAL PROBES (measures within 70 o cone around probe axis):

55. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Measurements in 3D Flows II Velocity decomposition into the (U,V,W) probe coordinate system where U 1, U 2 and U 3 in wire coordinate system are found by solving: left hand sides are effective cooling velocities. Yaw and pitch coefficients are determined by directional calibration.

56. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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. (Obtained with Dantec Tri-axial probe 55P91 and 55H01/02 Calibrator)

57. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Measurement at Varying Temperature Temperature Correction I 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: Selecting proper m (m= 0.2 typically for wire probe at a = 0.8) improves compensation to better than ±0.05%/C. E corr = ((T w - T ref )/(T w - T acq )) 0.5 E acq.

58. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Measurement at Varying Temperature Temperature Correction II Temperature correction in liquids may require correction of power law constants A and B: In this case the voltage is not corrected

59. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

60. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Data acquisition II Resolution: - Min. 12 bit (~1-2 mV depending on range) Sampling rate: - Min. 100 kHz (allows 3D probes to be sampled with approx. 30 kHz per 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) A/D boards convert analogue signals into digital information (numbers) They have following main characteristics:

61. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics Data acquisition III Signal Conditioning of anemometer output Increases the AC part of the anemometer output and improves resolution: E G (t) = G(E(t) - E off ) Allows filtering of anemometer - Low pass filtering is recommended - High pass filtering may cause phase distortion of the signal (From Bruun 1995)

62. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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

63. AAE 520 Experimental Aerodynamics Purdue University - School of Aeronautics and Astronautics 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