1. Title Jordanian – German Winter Academy Jordanian – German Winter Academy Amman, 4-11/ Feb. 2006 Amman, 4-11/ Feb. 2006 Hot Wire Anemometry

2. Hot wire anemometry is the most common method used to measure instantaneous fluid velocity. The technique depends on the convective heat loss to the surrounding fluid from an electrically heated sensing element or probe. If only the fluid velocity varies, then the heat loss can be interpreted as a measure of that variable. Hot wire anemometry is the most common method used to measure instantaneous fluid velocity. The technique depends on the convective heat loss to the surrounding fluid from an electrically heated sensing element or probe. If only the fluid velocity varies, then the heat loss can be interpreted as a measure of that variable.

3. Features Features Measures velocities from a few cm/s to supersonic High temporal resolution: fluctuations up to several hundred kHz High spatial resolution: eddies down to 1 mm or less Measures all three velocity components simultaneously Provides instantaneous velocity information Features Measures velocities from a few cm/s to supersonic High temporal resolution: fluctuations up to several hundred kHz High spatial resolution: eddies down to 1 mm or less Measures all three velocity components simultaneously Provides instantaneous velocity information

4. Application : » Aerospace » Automotive » Bio-medical & bio-technology » Combustion diagnostics » Earth science & environmental » Fundamental fluid dynamics » Hydraulics & hydrodynamics » Mixing processes » Process & chemical engineering » Wind engineering » Sprays (atomisation of liquids) : » Aerospace » Automotive » Bio-medical & bio-technology » Combustion diagnostics » Earth science & environmental » Fundamental fluid dynamics » Hydraulics & hydrodynamics » Mixing processes » Process & chemical engineering » Wind engineering » Sprays (atomisation of liquids)AerospaceAutomotiveBio-medical & bio-technologyCombustion diagnosticsEarth science & environmentalFundamental fluid dynamicsHydraulics & hydrodynamicsMixing processesProcess & chemical engineeringWind engineeringSprays (atomisation of liquids)AerospaceAutomotiveBio-medical & bio-technologyCombustion diagnosticsEarth science & environmentalFundamental fluid dynamicsHydraulics & hydrodynamicsMixing processesProcess & chemical engineeringWind engineeringSprays (atomisation of liquids)

5. Principles of operation Consider a thin wire mounted to supports and exposed to a velocity U. 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.

6. Principle f operation

7. Measurement Principles The control circuit for hot wire anemometry is in the form of a Wheatstone bridge consisting of four electrical resistances, one of which is the sensor. When the required amount of current is passed through the sensor, the sensor is heated to the operating temperature, at which point the bridge is balanced. If the flow is increased, the heat transfer rate from the sensor to the ambient fluid will increase, and the sensor will thereby tend to cool. the accompanying drop in the sensor's electrical resistance will upset the balance of the bridge. This unbalance is sensed by the high gain DC amplifier, which will in turn produce a higher voltage and increase the current through the sensor, thereby restoring the sensor to its previously balanced condition. The DC amplifier provides the necessary negative feedback for the control of the constant temperature anemometer. The bridge or amplifier output voltage is, then, an indication of flow velocity. The control circuit for hot wire anemometry is in the form of a Wheatstone bridge consisting of four electrical resistances, one of which is the sensor. When the required amount of current is passed through the sensor, the sensor is heated to the operating temperature, at which point the bridge is balanced. If the flow is increased, the heat transfer rate from the sensor to the ambient fluid will increase, and the sensor will thereby tend to cool. the accompanying drop in the sensor's electrical resistance will upset the balance of the bridge. This unbalance is sensed by the high gain DC amplifier, which will in turn produce a higher voltage and increase the current through the sensor, thereby restoring the sensor to its previously balanced condition. The DC amplifier provides the necessary negative feedback for the control of the constant temperature anemometer. The bridge or amplifier output voltage is, then, an indication of flow velocity.

8. Probes

9. Probe Types 1. Hot film, which is used in regions where a hot wire probe would quickly break such as in water flow measurements. 2. Hot wire. This is the type of hot wire that has been used for such measurements as turbulence levels in wind tunnels, flow patterns around models and blade wakes in radial compressors.

10. Hot wire sensor

11. Hot film sensor

12. Probe selection For optimal frequency response, the probe should have as small a thermal inertia as possible. For optimal frequency response, the probe should have as small a thermal inertia as possible. Wire length should be as short as possible (spatial resolution; want probe length << eddy size) Wire length should be as short as possible (spatial resolution; want probe length << eddy size) Aspect ratio (l/d) should be high (to minimize effects of end losses) Aspect ratio (l/d) should be high (to minimize 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) 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) 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 Wires of less than 5 µm diameter cannot be drawn with reliable diameters

13. Modes of anemometer operation Constant Current (CCA) Constant Temperature (CTA)

14. 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

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

16. 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 = I² Rw recall Rw = Rw(Tw) H = heat transferred to surroundings

17. Governing equation II Heat transferred to surroundings ( convection to fluid H = sum off + conduction to supports + radiation to surroundings) Convectio Qc = Nu · A · (Tw -Ta) Nu = h ·d/kf = f (Re, Pr, M, Gr,α), Re = ρU/μ Conduction f(Tw, lw, kw, Tsupports) Radiationf(Tw- Tf)

18. 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

19. Simplified static analysis II Static heat transfer : W=H I²Rw = hA(Tw -Ta) I²Rw = Nu kf/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 = A1 + B1 · Reⁿ= A2+ B2 · Uⁿ I²Rw² = E² = (Tw -Ta)(A + B · Uⁿ) “King’s law” The voltage drop is used as a measure of velocity.

20. Heat transfer from Probe Convective heat transfer Q from a wire is a function of the velocity U, the wire over-temperature Tw -T0 and the physical properties of the fluid. The basic relation between Q and U for a wire placed normal to the flow was suggested by L.V. King (1914). In its simplest form it reads: Convective heat transfer Q from a wire is a function of the velocity U, the wire over-temperature Tw -T0 and the physical properties of the fluid. The basic relation between Q and U for a wire placed normal to the flow was suggested by L.V. King (1914). In its simplest form it reads: where Aw is the wire surface area and h the heat transfer coefficient, which are merged into the calibration constants A and B. where Aw is the wire surface area and h the heat transfer coefficient, which are merged into the calibration constants A and B.

21. 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 velocity

22. HOT WIRE CALIBRATION The hot wire responds according to King’s Law: The hot wire responds according to King’s Law: where E is the voltage across the wire, u is the velocity of the flow normal to the wire and A, B, where E is the voltage across the wire, u is the velocity of the flow normal to the wire and A, B, and n are constants. You may assume n =0.5, this is common for hot-wire probes. A can be and n are constants. You may assume n =0.5, this is common for hot-wire probes. A can be found by measuring the voltage on the hot wire with no flow, i.e. for u = 0, A = E2. Make sure found by measuring the voltage on the hot wire with no flow, i.e. for u = 0, A = E2. Make sure there is no flow, any small draft is significant. The HWLAB software operating in calibration there is no flow, any small draft is significant. The HWLAB software operating in calibration mode will give you a voltage.) Once you know A, you can measure the wire voltage for a known mode will give you a voltage.) Once you know A, you can measure the wire voltage for a known flow velocity and then determine B from King’s law, i.e. B=2E2-A7 u0.45. flow velocity and then determine B from King’s law, i.e. B=2E2-A7 u0.45.

23. Calibration curve

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

25. Problem Sources Probe contamination II Drift due to particle contamination in air 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

26. Problem Sources Probe contamination III Drift due to particle contamination in water Drift due to particle contamination in water Output voltage decreases with increasing dirt deposit (From Morrow and Kline 1971)

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

28. Problem Sources Bubbles in Liquids I Drift due to bubbles in water 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)

29. Problem Sources Bubbles in Liquids II Effect of bubbling on Effect of bubbling on portion of typical calibration curve Bubble size depends on Bubble size depends on - surface tension - overheat ratio - velocity Precautions Precautions - Use low overheat! - Let liquid stand before use! - Don’t allow liquid to cascade in air! - Clean sensor! (From C.G.Rasmussen 1967)

30. Problem Sources (solved) Stability in Liquid Measurements Fiber probe operated stable in water 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)

31. 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)

32. 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.

33. 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

34. 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)

35. Problem Sources Temperature Variations III Film probe calibrated at different temperatures

36. 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.

37. 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:

38. Measurements in 2D Flows II Directional calibration provides yaw coefficients k 1 and k 2 (Obtained with Dantec Dynamics’ 55P51 X-probe and 55H01/H02 Calibrator)

39. Measurements in 3D Flows I TRIAXIAL PROBES (measures within 70 o cone around probe axis):

40. 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.

41. 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 Dynamics’ Tri-axial probe 55P91 and 55H01/02 Calibrator)

42. 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.

43. 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

44. 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

45. 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:

46. Data acquisition III 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

47. 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

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