AAE 520 Experimental Aerodynamics HotWire Anemometry Purpose to

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

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

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

AAE 520 Experimental Aerodynamics 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, a ), Re = r U/m Conduction f(Tw , lw , kw, Tsupports) Radiation f(Tw 4 - Tf 4) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Simplified static analysis II Static heat transfer: W =H h A d kf Nu = = = I 2 Rw = h. A(Tw -Ta) I 2 Rw = Nukf/d. A(Tw -Ta) film coefficient of heat transfer area wire diameter heat conductivity of fluid 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 · Ren = A 2+ B 2 · Un I 2 Rw 2 = E 2 = (Tw -Ta)(A + B · Un) “King’s law” The voltage drop is used as a measure of velocity. Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics 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 Voltage derivative as fct. of velocity Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics 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) q =0 U 2 eff(q ) = U 2(cos 2 q +h 2 sin 2 q ) a =0 where: k , h = yaw and pitch factors a , q = angle between wire normal/wire-prong plane, respectively, and velocity vector • General response in 3 D 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 Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Directional response IV • Yaw and pitch factors k 1 and k 2 (or k and h) depend on velocity and flow angle (From Joergensen 1971) Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Probe types I • Miniature Wire Probes Platinum-plated tungsten, 5 mm 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 Purdue University - School of Aeronautics and Astronautics

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

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

AAE 520 Experimental Aerodynamics Probe types IV • X-probes for 2 D flows 2 sensors perpendicular to each other. Measures within ± 45 o. • Split-fiber probes for 2 D flows 2 film sensors opposite each other on a quartz cylinder. Measures within ± 90 o. • Tri-axial probes for 3 D flows 3 sensors in an orthogonal system. Measures within 70 o cone. Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Hints to select the right probe • Use wire probes whenever possible ürelatively inexpensive übetter frequency response ücan be repaired • Use film probes for rough environments ümore rugged üworse frequency response ücannot be repaired üelectrically insulated üprotected against mechanical and chemical action Purdue University - School of Aeronautics and Astronautics

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

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

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

AAE 520 Experimental Aerodynamics Constant temperature anemometer CTA II • 3 -channel Stream. Line with Tri -axial wire probe 55 P 91 Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Modes of operation, CTA I • Wire resistance can be written as: Rw = Ro(1+a o(Tw-To)) Rw Ro ao Tw To • = = = wire hot resistance wire resistance at To temp. coeff. of resistance wire temperature reference temperature Define: “OVERHEAT RATIO” as: a = (Rw-Ro)/Ro = a o(Tw-T 0) • Set “DECADE” overheat resistor as: RD = (1+a)Rw Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics 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 Un) or as Rw is kept constant by the servoloop: E 2 = A + BUn • 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 Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics 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 + d. E/dt The equation then becomes a differential equation: I 2 Rw = (Rw-Ra)(A+BUn) + Cw(d. Tw/dt) or expressing Tw in terms of Rw: I 2 Rw = (Rw-Ra)(A+BUn) + Cw/a o. Ro(d. Rw/dt) Cw = heat capacity of the wire ao = temperature coeff. of resistance of the wire Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Dynamic response, CCA II Hot-wire Probes: The first-order differential equation is characterised by a single time constant t : t = Cw/(ao. Ro(A+BU n) The normalised transfer function can be expressed as: Hwire(f) = 1/(1+jf/fcp) Where fcp is the frequency at which the amplitude damping is 3 d. B (50% amplitude reduction) and the phase lag is 45 o. Frequency limit can be calculated from the time constant: fcp = 1/2 pt Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Dynamic response, CCA III • Hot-wire Probes: Frequency response of film-probes is mainly determined by thermal properties of the backing material (substrate). The time constant for film-probes becomes: t = (R/R 0)2 F 2 rs. Csks/(A+BUn)2 rs = substrate density Cs = substrate heat capacity ks = substrate heat conductivity and the normalised transfer function becomes: Hfilm(f) = 1/(1+(jf/fcp)0. 5) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics 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 t ~ 0. 005 s, typically. (Frequency response can be improved by compensation circuit) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Dynamic response, CTA II • Typical frequency response of 5 mm wire probe (Amplitude damping and Phase lag): (From Dantec MT) Phase lag is reduced by frequency dependent gain (-1. 2 d. B/octave) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Velocity calibration (Static cal. ) II • Calibration in gases (example low turbulent free jet): Velocity is determined from isentropic expansion: Po/P = (1+(g -1)/2 M 2)g a 0 = (g RT 0 )0. 5 a = ao/(1+(g -1)/2 M 2)0. 5 U = Ma Purdue University - School of Aeronautics and Astronautics /(g- -1)

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

AAE 520 Experimental Aerodynamics Typical calibration curve • Wire probe calibration with curve fit errors (Obtained with Dantec 90 H 01/02)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 Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics 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 (<1000 Hz) All methods are difficult and are restricted to low frequencies. Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics 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 (- 3 d. B damping): fc = 1/1. 3 t Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics 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, a ), • 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. ) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Problem Sources Probe contamination II • Drift due to particle contamination in air 5 mm Wire, 70 mm Fiber and 1. 2 mm Steel. Clad 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 Purdue University - School of Aeronautics and Astronautics

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

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

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

AAE 520 Experimental Aerodynamics 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 air! - Use low overheat! Let liquid stand before use! Don’t allow liquid to cascade in (From C. G. Rasmussen 1967) Clean sensor! Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Problem Sources (solved) Stability in Liquid Measurements • Fiber probe operated stable in water - De-ionised water (reduces algae growth) - Filtration (better than 2 mm) - Keeping water temperature constant (within 0. 1 o. C) Purdue University - School of Aeronautics and Astronautics (From Bruun 1996)

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

AAE 520 Experimental Aerodynamics 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 k. Hz Always use stiff and rigid probe mounts. Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics 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·Un) 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 Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Problem Sources Temperature Variations II • Anemometer output depends on both velocity and (From Joergensen and Morot 1998) temperature When ambient temperature increases the velocity is measured too low, if not corrected for. Purdue University - School of Aeronautics and Astronautics

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

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

AAE 520 Experimental Aerodynamics Measurements in 2 D 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: Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Measurements in 2 D Flows II • Directional calibration provides yaw coefficients k 1 and k 2 (Obtained with Dantec 55 P 51 X-probe and 55 H 01/H 02 Calibrator) Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Measurements in 3 D 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. Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Measurements in 3 D 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 55 P 91 and 55 H 01/02 Calibrator) Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Measurement at Varying 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 0. 5 Ecorr = ((Tw- Tref)/(Tw- Tacq)) Eacq. - 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. Purdue University - School of Aeronautics and Astronautics

AAE 520 Experimental Aerodynamics Measurement at Varying 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 Purdue University - School of Aeronautics and Astronautics

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

AAE 520 Experimental Aerodynamics Data acquisition II A/D boards convert analogue signals into digital information (numbers) They have following main characteristics: • Resolution: - Min. 12 bit (~1 -2 m. V depending on range) • Sampling rate: - Min. 100 k. Hz (allows 3 D probes to be sampled with approx. 30 k. Hz per sensor) • Simultaneous sampling: - Recommended (if not sampled simultaneously there will be phase lag between sensors of 2 - and 3 D probes) • External triggering: Recommended (allows sampling to be started by external event) Purdue University - School of Aeronautics and Astronautics

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

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

AAE 520 Experimental Aerodynamics CTA Anemometry Steps needed to get good measurements: • • Get an idea of the flow (velocity range, dimensions, frequency) • • Make a first rough verification of the assumptions about the flow • • Perform the experiment Select right probe and anemometer configuration Select proper A/D board Perform set-up (hardware set-up, velocity calibration, directional calibration) Define experiment (traverse, sampling frequency and number of samples) Reduce the data (moments, spectra, correlations) Evaluate results Recalibrate to make sure that the anemometer/probe has not drifted Purdue University - School of Aeronautics and Astronautics