1. 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 lichuan-gui@uiowa.edu http://lcgui.net

2. 2 Lecture 23. Wall shear stress measurement

3. 3 Wall shear stress measurement Surface force - acts across an internal or external surface element - decomposed in to two perpendicular components normal component: (F n ) tangential (or shear) component: (F s ) F FsFs A - force per unit area (  ) SI unit: pascal (Pa=1N/m 2 ) Shear stress:  n =F n /A  s =F s /A Normal stress: Stress Wall shear stress - for Newtonian fluids related to velocity derivative normal to the wall as  – fluid viscosity

4. 4 Wall shear stress measurement Measurement in turbulent boundary layers Friction velocity: Dimensionless mean velocity: Viscous length: Dimensionless distance from the wall: - high uncertainty because of very thin viscous layer General expression of velocity distribution in turbulent boundary layer:

5. 5 Wall shear stress measurement Measurement in turbulent boundary layers

6. 6 Wall shear stress measurement Estimates from pressure differences Wall shear stress in fully developed flow in circular pipes D – pipe diameter Preston tubes - Dimensionless parameters: - Calibration expressions: for - Uncertainty: 1.0%  1.5%

7. 7 Sublayer fence - thin blade partitions wall tap into upstream and downstream halves. 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 - typical uncertainty: 3% - tip of the blade extends slightly into flow within viscous sublayear - higher sensitivity than Stanton gauge

8. 8 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 - empirical expression of the response: - heated by constant-temperature anemometer circuit - 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

9. 9 Wall shear stress measurement Optical techniques - laser beam passed through twin slits Laser Doppler technique - 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

10. 10 Homework - Questions and Problems: 1 on page 342 - Read textbook 14.1-14.6 on page 328 - 341 - Due on 10/21