Transcript Lecture23 - 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 23. Wall shear stress measurement
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Wall shear stress measurement
F
Surface force
- acts across an internal or external surface element
- decomposed in to two perpendicular components
normal component: (Fn)
tangential (or shear) component: (Fs)
Fs
A
Stress - force per unit area () SI unit: pascal (Pa=1N/m2)
Normal stress:
n=Fn/A
Shear stress:
s=Fs/A
Wall shear stress
𝑈
- for Newtonian fluids related to velocity derivative normal to the wall as
 – fluid viscosity
𝑦 – normal direction to the wall
𝑈 – tangential velocity at the wall
- measured velocity distribution in laminar boundary layer can be used to determine 𝜏𝑤
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Wall shear stress measurement
Measurement in turbulent boundary layers
Friction velocity:
Dimensionless
mean velocity:
Viscous length: 𝜈/𝑢𝜏
Dimensionless distance
from the wall:
In viscous (or laminar) sub-layer, i.e. 0 ≤ 𝑦 + < 5~7:
𝑢+ = 𝑦 +
- mean velocity measurements in viscous layer can be used to determine mean 𝜏𝑤
- high uncertainty because of very thin viscous layer
In inertial (or logarithmic) sub-layer, i.e. 𝑦 + ≥ 30:
𝜅– von Karman constant (0.39)
Buffer zone, i.e. 5~7 < 𝑦 + < 30: velocity described with interpolation expression
General expression of velocity distribution in turbulent boundary layer:
𝑢+ = 𝐴 log 𝑦 + + 𝐵
with typical values of 𝐴 =
ln10
≈ 5.9, 𝐵 ≈ 5.0
𝜅
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Wall shear stress measurement
Measurement in turbulent boundary layers
Estimating 𝑢𝜏 with Clauser chart
𝑢+ = 𝐴 log 𝑦 + + 𝐵
𝐴 ≈ 5.9, 𝐵 ≈ 5.0
𝑈
𝑦𝑈 𝑢𝜏
= 𝐴 log
+𝐵
𝑢𝜏
𝜈 𝑈
= 𝐴 log
𝑦𝑈
𝑢𝜏
+ 𝐴 log + 𝐵
𝜈
𝑈
Step 1. determine 𝑦𝑈/𝜈 with measured mean velocity 𝑈 at position 𝑦 and viscosity 
Step 2. determine 𝑈/𝑢𝜏 according to the chart
Step 3. calculate 𝑢𝜏
Step 4. compute wall shear stress with 𝜌𝑢𝜏 2
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Wall shear stress measurement
Estimates from pressure differences
Wall shear stress in fully developed flow in circular pipes
D – pipe diameter
𝑑𝑝/𝑑𝑥 – streamwise wall-pressure gradient
Preston tubes
- Pitot tube of external tube diameter 𝑑 resting on the wall
- Dimensionless parameters:
- Calibration expressions:
for
for
for
for
- Uncertainty: 1.0%  1.5%
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Wall shear stress measurement
Estimates from pressure differences
Santon gauge
- thin blade attached to the wall within the viscous sublayear
- partially blocking the opening of a static-pressure tap
- difference between pressure in blocked tap and local static pressure determines 𝜏𝑤 with calibration
- typical uncertainty: 3%
Sublayer fence
- thin blade partitions wall tap into upstream and downstream halves.
- tip of the blade extends slightly into flow within viscous sublayear
- pressure difference between two halves of the tap linearly related to 𝜏𝑤
- higher sensitivity than Stanton gauge
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Wall shear stress measurement
Floating-element balance
- floating-element mounted in wall cavity with clearance around it
- it may move laterally under influence of wall shear stress
- shear force measured
- shear stress calculated with shear force & surface area
Thermal techniques
- measure local flow velocity in viscous sublayer that is proportional to wall shear stress
Flush-mounted hot-films
- metallic film sensors mounted flush on the wall
- heated by constant-temperature anemometer circuit
- empirical expression of the response:
𝐸 – output voltage
𝑇𝑤 – film temperature
𝑇𝑓 – fluid temperature
- high frequency response to capture unsteady phenomena
Hot-wire sensors on or close to the wall
Infrared thermography
- laser beam used to heat a spot on the wall
- infrared camera used to record temperature time history
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Wall shear stress measurement
Optical techniques
Laser Doppler technique
- laser beam passed through twin slits
- interference fringes created in
flow boundary layer with spacing:
- Doppler frequency measured
with photodetectoor:
- wall shear stress determined as
Oil-film interferometry
- oil film thickness related to wall shear stress
- oil film thickness measured with interferometry
 - phase shift
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Homework
- Read textbook 14.1-14.6 on page 328 - 341
- Questions and Problems: 1 on page 342
- Due on 10/21
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