Transcript Lecture18 - Lcgui.net

Measurements in Fluid Mechanics
058:180:001 (ME:5180:0001)
Time & Location: 2:30P - 3:20P MWF 218 MLH
Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
[email protected]
http://lcgui.net
Lecture 18. Thermal anemometry
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Measurement of local flow velocity
Pressure difference methods
- utilize analytical relationships between the local velocity and the static and total pressure
- examples: Pitot-static tube, multi-hole probes
Thermal methods
- compute flow velocity from its relationship to the convective heat transfer from heated elements.
- examples: hot-wire and hot-film anemometers
Frequency-shift methods
- based on the shifting of the frequency of waves scattered by moving particles.
- examples: Laser-Doppler velocimeter, ultralsonic Doppler velocimeter
Marker-tracing methods
- trace the motion of suitable flow markers, optically or by other means.
- examples: Chronophotography, particle image velocimetry (PIV), pulsed-wire anemometry
Mechanical methods
- take advantage of the forces and moments that a moving stream applies on immersed objects.
- examples: vane, cup, and propeller anemometers
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Thermal anemometry
Hot-wire (HW) sensor
- platinum or tungsten wires of 0.8-1.5mm long and 2.5-7.5 m in diameter
- mounted at two ends on thin tapered metallic prongs
- Wollaston wire or gold plated wire to avoid non-uniform temperature distribution
- usable in clean gas flows
Hot-film (HF) sensor
- 0.1-m thick film of platinum or nickel
- on wedge shape support or hollow glass tube etc.
- usable in both gas and liquid flows
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Thermal anemometry
Velocity measurement using HW & HF
Energy balance
Electric resistance
Heat convection coefficient
Flow velocity
I – electric current
RRef – reference resistance
Rw – electric resistance
Aw – surface area
Tf – fluid temperature
vf – fluid velocity
TRef – reference temperature
Tw – wire temperature
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Thermal anemometry
HW & HF measuring system
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Thermal anemometry
Heat-transfer characteristics
Nusselt number:
𝑞 – heat transfer rate
𝑘 – thermal conductivity
General relationship:
𝑅𝑒 = 𝑉𝑑/𝑣 – Reynolds number
𝑃𝑟 = 𝑣/ – Prandtl number
𝐺𝑟 = 𝑔 𝑇𝑤 − 𝑇 𝑑 3 /𝑣 2 – Grashof number
𝐾𝑛 = 𝜆/𝑑 – Kundsen number
𝑀 = 𝑉/𝑐 – Mach number
- Pr disregarded in air flows
𝑎 𝑇 = 𝑇𝑤 − 𝑇 /𝑇 – overheat ratio
- Gr ignored in most cases
- M neglected in incompressible flows (V<100 m/s)
- Kn neglected in continum regime
- conduction effects neglected with 𝑙/𝑑>100
- flow direction perpendicular to HW
Simplified relationship:
- experimentally determined as:
King’s law:
- 𝑛 = 0.5 or between 0.40 and 0.55
- A and B determined with calibration
HW/HF resistance relationship:
𝐸 – voltage output of HW operating circuitry
𝑟 – thermal resistivity coefficient
𝑅𝑟 – reference resistance
𝑇𝑟 – reference temperature
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Thermal anemometry
Constant-current anemometry (CCA)
- Current through sensor is kept Constant
with RS>>RW
- Frequency response improved with
a compensation circuit
- Advantages: simple electric circuit,
high frequency response
- Disadvantages:
difficult to use
output decreases with velocity
risk of probe burnout
Constant-temperature anemometry (CTA)
- Sensor resistance is kept constant
through electronic feedback system
- Advantages:
easy to use
high frequency response
low noise
- Disadvantages: more complex circuit
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Thermal anemometry
Velocity orientation effect
Effective cooling velocity:
Modified by considering tangential component:
- constant k determined by calibration, typical k2 values between 0.05 and 0.20
Prong interference effects
- Prongs and probe body produce interference to heat transfer between flow and HW
Heat conduction effects
- End conduction adds system error when l/d not large enough
Compressibility effects
- King’s law not sufficient for HW when M>0.6
Temperature-variation effects
- Response deviates from calibration relationship because of temperature variation
Others
Thermal anemometry
Multi-sensor probes
Cross-wire (X-wire) anemometer
- Identical sensors inclined exactly 45
- Tow velocity components may be calculated as:
- Calibration required for high accuracy
- Data reduction more complicated when
wires not perpendicular to each other
Three or four sensor probes
- used to measure three velocity components
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Homework
- Read textbook 11.1 on page 249 - 264
- Questions and Problems: 1 on page 284
Hint: The temperature for tungsten to oxidizes can be found in page 250.
- Due on 10/07
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