By Mehak Chopra Indian Institute of Technology Delhi Guide: Dr B. Uensal
Outline Characteristics of an ideal instrument Hot Wire Anemometry Advantages and Drawbacks of Hot Wire Anemometry Principle of Operation Basic Construction of Hot Wire Probe Modes of Operation of Hot Wire Anemometers Governing Equation and Model of HWA Calibration Directional Sensitivity Turbulence Measurement using HWA
Fluid Flow Fluid flow is ubiquitous! e.g processes in our body, Flow around airplanes etc it is essential to measure fluid flow. Most practical flows are turbulent. Hence it is equally important to measure Turbulent Fluctuations. Pitot tube low frequency response Many Methods to measure velocity discussed earlier
Characteristics of an ideal Instrument to measure Velocity Fluctuations Good Signal Sensitivity: Measurable change in output for small changes in velocity High Frequency Response: to accurately follow transients without any time lag Wide velocity range Create minimal flow disturbance Good Spatial Resolution Low in cost High Accuracy Measure velocity component and Detect flow reversal Easy to use
In making measurements, it is not a question of the best instrument but rather which instrument will perform best for the specific application.
Hot Wire Anemometry Intrusive Technique Measurement of instantaneous velocities and temperature at a point in a flow. Hot wire anemometry is an ideal tool for measurement of velocity fluctuations in time domain in turbulent flows Principal tool for basic studies of physics of turbulent flows. Development of realistic turbulence models, HWA necessary to carry out fundamental turbulence studies
Advantages of HWA Good Frequency response: Measurements to several hundred khz possible, 1 MHz also feasible Velocity Measurement: measures magnitude and direction of velocity and velocity fluctuations, Wide velocity range Temperature Measurements Two Phase Flow: Measurements in flows containing continuous turbulent phase and distributed bubbles.
Advantages of HWA Signal to noise ratio : have low noise levels. Resolution of 1 part in 10000 is accomplished Signal Analysis: Output is continuous analogue signal, both time domain and frequency domain analysis can be carried out. Output can also be processed by digital systems. Measurement of turbulent quantities like vorticity, dissipation rate etc.
Drawbacks Intrusive Technique: modification of local flow field High Turbulence Intensity Flows: Errors due to neglecting higher order terms Rectification Error insensitive to reversal of flow direction. Contamination: Deposition of impurities in flow on sensor alter the calibration characteristics and reduce frequency response. Probe breakage and burn out Unable to fully map velocity fields that depend strongly on space coordinates and simultaneously on time. Spatial array of many probes would be required. Fails in hostile environment like combustion
Principle of Operation Based on convective heat transfer from a heated sensing element, possessing temperature coefficient of resistance. Flow Rate varies Convective heat transfer coefficient (h) varies Heat transfer from filament varies Operation of Hot Wire Sensor
Hot Wire Probe Structure of hot wire probe
Characteristics of material used for making sensor High Temperature Coefficient of resistance High Specific Resistance High Mechanical Strength Good Oxidation Resistance Low Thermal Conductivity Availability in small diameters Tungsten : good strength, poor oxidation resistance Platinum: good oxidation resistance, weak Tungsten with thin platinum coating is generally used. At high temperatures Platinum iridium alloys, Platinumrhodium alloys are used.
Wire Dimensions Large aspect ratios i.e l/d where l is the wire length and d is the wire diameter, to minimize conduction losses to supports and have uniform temperature distribution Small diameter are preferred even though they have less strength as: maximizes time response due to low thermal inertia maximize spatial resolution improves signal to noise ratio at high frequencies eliminates output noise
Classification of Hot Wire Probes On the basis of number of sensors: Single Sensor Probe Dual Sensor Probe Triple Sensor Probe ( X probes, Split Fibre probes) Information about magnitude and direction of velocity can be obtained with probes having 2 or more sensors
Modes of Operation of Hot Wire Anemometers Constant Current Constant Temperature Current in the wire is kept constant Variations in wire resistance caused by the flow are measured by monitoring the voltage drop variations across the filament. Temperature hence Resistance of the wire is kept constant by using a servo amplifier The measurable signal when a change in flow velocity occurs is the change in current to be fed to the sensor.
Basic Circuitry of Constant Current Anemometer Circuit Diagram of Constant Current Anemometer
Basic Circuitry of Constant Temperature Anemometer Velocity Varies Error Voltage (e 2 e 1 ) varies Input Voltage to amplifier varies Change in current i through the sensor Restores the resistance of sensor to original value
CCA vs CTA Compensation of Thermal inertia of the filament is automatically adjusted in CTA as the flow conditions vary. CTA is used the same way as it is calibrated. Calibration is dynamic in this case, while in CCA instrument is calibrated at constant temperature and used in a constant current mode. In constant current mode, wire can be destroyed by burning out if velocity is very small. There is no such danger in CTA In CTA there is no thermal cycling hence long life of probe.
CTA Measuring Chain Basic CTA Measuring Chain
General Hot Wire Equation Where: W power generated by joule heating given by I 2 R w where R w = R w (T w ) Q heat transfer rate to surrounding Q i thermal energy stored in the wire (C w T w ) C w Heat capacity of wire T w Temperature of wire
Q = Q fc + Q nc + Q r + Q c Forced convection term given by h*a*(t w T A ) natural convection term where A is the area of the wire T A is the temperature of the fluid h is the heat transfer coefficient σ is the Stefan Boltzmann constant ε is the emissivity k is the thermal conductivity Radiation to surrounding given by A*σ*ε*(T 4 w T 4 A ) Conduction to prongs given by (k*a*dt/dx)
Heat Transfer due to radiation Performing an energy balance on this differential element, neglecting radiation and self convection we get:
Natural Convection: is effective at very low velocities. It depends on the value of Grashof number Gr ( ) According to Collis and Williams (1959), It can be neglected for hot wire probes with large values of aspect ratio, if Re>Gr 1/3 Radiation: in most hot wire anemometer applications this term is very small and can be neglected
Conduction: Conductive heat transfer takes place towards the prongs resulting in temperature distribution in wire. Temperature Profile in Hot Wire To minimize conductive end losses, wire should be as long as possible and possess low value of thermal conductivity For wires with large aspect ratios (l/d) heat losses by conduction can be neglected.
Forced Convection: plays the main role in heat transferred to the surrounding. It depends upon Nusselt number Where Re = Reynolds number Pr = Prandtl number which accounts for fluid properties. (generally constant) α 1 = angle between free stream flow direction and flow normal to the cylinder Gr = Grashof number which accounts for free convection (buoyancy) effects Ma = Mach number which accounts for compressibility effects γ = C p / C v a t = overheat ratio or temperature loading (T w T a )/ T a 2l/d = accounts for sensors dimension k f /k w = ratio of thermal conductivity of fluid to sensor
Assumption: Flow is incompressible Wire is normal to the flow (α 1 = 0) No effect of free convection and conduction(basically assuming infinitely long wire) Nu = Nu(Re) According to King, for an infinitely (Kings long Law) wire Nu = X + YRe 1/2 Kramers proposed that for 0.01<Re<10000 and 0.71<Pr<1000 and evaluating the fluid properties at T f = (T w + T a )/2, Nu can be given by:
Simple Model for Hot Wire Anemometer Considering only forced convection as the mode of heat exchange and not considering heat storage term: Where T w = Temperature of wire T a = Temperature of fluid As, hence Resistance is a function of temperature:
Simple Model for Hot Wire Anemometer Thus putting the value of Nu (by Kings Law) and expressing resistance as a function of temperature, Hence for finite length hot wire anemometer, In terms of voltage E w, For CTA, as temperature and resistance are constant, )
Dynamic Characteristics Wire not respond instantaneously due to its thermal inertia. Dampen the variation in wire resistance R w and result in flow fluctuation measured smaller than they are. Heat Storage term needs to be accounted in heat balance equation Cw = thermal capacity
Dynamic Characteristics The above differential equation has time constant τ given by Frequency limit is given by Exponential change in resistance of wire with instantaneous rise in velocity
Frequency Response of CTA The servo loop amplifier reduces the time constant and increases the wire frequency limit. where τ w = wire time constant alone and = a = overheat ratio R w = wire resistance S = amplifier gain Amplitude transfer function for velocity fluctuation
Methods to Determine Dynamic Response of CTA A small electronic square wave signal is injected into the bridge and response of anemometer voltage E is observed. Output voltage response to this current signal has the same time constant as the response to the flow velocity signal Square wave test response of CTA
Calibration Probe is exposed to a set of known velocities and output voltage E is recorded. Should be done at low turbulence intensities and constant temperature Pitot static tube is generally used for velocity measurement. Calibration of hot wire sensor using pitot tube Where h is total pressure in height of flowing fluid.
Calibration curve is plotted between Hot Wire Voltage and Velocity. Typical Calibration curve is nonlinear and sensitivity decreases as velocity increases. As constants A, B and n can be determined by regression analysis Calibration
Directional Sensitivity of Hot wire probes For an infinitely long sensor, heat transfer varies with the cosine of angle between the velocity and the wire normal and Velocity along the sensor has no cooling effect. For a finite length sensor, a directional sensitivity factor k (yaw factor) is introduced, which describes prong interference. For 3 dimensional flows, pitch factor h is introduce Effective cooling velocity is given by:
Directional Sensitivity of Hot wire probes E 2 = A + B(U eff ) n
Determination of Direction To determine direction using a single wire probe, Rotate the probe in the flow. The orientation which gives maximum current is the direction of flow
Turbulence Measurements Instantaneous velocity in turbulent flow can be expressed as: u(t) = ū + u (t) where ū is the mean velocity and u is the fluctuating component. Mean velocity is given by : Time average of fluctuating component is zero
Turbulence Measurements However, the second moment of turbulent fluctuations or variance <(u ) 2 > is not zero and is a measure of intensity of fluctuations Standard deviation of velocity (σ) or u rms is square root of variance. Turbulence Intensity =
Turbulence Measurements Velocity Sensitivity is given ( ) Thus fluctuating component of velocity is related to fluctuating voltage e : e = u Hence if calibration constants are known, fluctuation in velocity can be calculated by fluctuation in voltage
Filtering and Signal Dynamic Range Voltage fluctuations may be very small compared to mean voltage. Difficult for ADC to measure both average and fluctuating components. Anemometer output is sent to a high pass filter which eliminates mean value <E> of voltage Output of high pass filter is sent to an oscilloscope inorder to observe peak peak fluctuations and set the amplifier gain.
Grid Generated Turbulence Mesh size (M) = one side of the open square of grid. Many methods to generate turbulence for experimentation. Square mesh grid is placed in the cross section to generate turbulence Grid generated turbulence is homogenous and isotropic Used with HWA to provide data for development of turbulence models e.g. to evaluate theory for the decay of turbulence.
High contraction ratio anomaly of axisymmetric contraction of grid generated turbulence [1] Experiments reported anomalous increase in second order moments of longitudinal velocity fluctuations in measuring properties of axisymmetric strained turbulence This anomaly was resolved by removing the experimental inaccuracies and gave results in agreement with direct numerical simulations and turbulence theory Studies were carried in a wind tunnel in which there was grid generated turbulence and hot wire probes were used
References 1. Özgür Ertunç and Franz Durst, On the high contraction ratio anomaly of axisymmetric contraction of grid generated turbulence, PHYSICS OF FLUIDS 20, 025103 2008 2. Bruun H.H, Hot Wire Anemometry Principal and Signal Analysis, Oxford University Press 3. Perry A.E, Hot Wire Anemometry, Oxford Science Publication 4. Smol yakov A.V. and Tkachenko V.M., The Measurement of Turbulent Fluctuations, Springer Verlag Berlin Heidelberg 1983 5. Goldstein R.J, Fluid Mechanics Measurement, Hemisphere Publishing 6. Jorgensen F.E(2002), How to measure turbulence with hot wire anemometers a practical guide 7. Tropea C et al, Springer Handbook of Experimental Fluid Mechanics Springer
Compressibility Effects For high velocity flows, compressibility effects become significant. Need to consider Mach number Ma and C p Knudsen number (Kn) is important parameter for low density flows and is given by: where λ = molecular mean free path In this case Nu = Nu(Re, Kn)
Hot Film Probes Platinum or nickel film are deposited on thermally insulating substrate like quartz. Used in liquid flows and high temperature ultrasonic gas flows due to their sturdy construction
Turbulent Flows Most practical flows are turbulent. Contribute significantly to transport of momentum, heat and mass. A complex, unpredictable and random process. Responsible for most fluid friction losses. Rational design of airplanes, ships, turbines etc have to consider turbulence. Hence it is equally important to measure Turbulent Fluctuations
Measurement of Integral Properties Diagram of Pitot Tube Instruments like Pitot tubes, venturimeters Only measure integral properties like mean velocity. Differential pressure meters Low frequency response Do not respond to fluctuations in velocity, hence unable to measure turbulence.
Methods To Measure Turbulence Fluctuations Hot Wire Anemometry Laser Doppler Anemometry Particle Imaging Velocimetry Flow Visualization Acoustic Anemometry Thermal Markers Discharge Anemometry
Computational Fluid Dynamics Turbulence modeling is an important issue in CFD Measurements are made as a supplement to computer modeling These methods provide high quality experimental flow data for validation of existing computer codes containing turbulence models