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 Lecture 23. Wall shear stress measurement 2 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 (ïī) SI unit: pascal (Pa=1N/m2) Normal stress: ïīn=Fn/A Shear stress: ïīs=Fs/A Wall shear stress ð - for Newtonian fluids related to velocity derivative normal to the wall as ï – fluid viscosity ðĶ – normal direction to the wall ð – tangential velocity at the wall - measured velocity distribution in laminar boundary layer can be used to determine ððĪ 3 Wall shear stress measurement Measurement in turbulent boundary layers Friction velocity: Dimensionless mean velocity: Viscous length: ð/ðĒð Dimensionless distance from the wall: In viscous (or laminar) sub-layer, i.e. 0 ≤ ðĶ + < 5~7: ðĒ+ = ðĶ + - mean velocity measurements in viscous layer can be used to determine mean ððĪ - high uncertainty because of very thin viscous layer In inertial (or logarithmic) sub-layer, i.e. ðĶ + ≥ 30: ð – von Karman constant (ïŧ0.39) Buffer zone, i.e. 5~7 < ðĶ + < 30: velocity described with interpolation expression General expression of velocity distribution in turbulent boundary layer: ðĒ+ = ðī log ðĶ + + ðĩ with typical values of ðī = ln10 ≈ 5.9, ðĩ ≈ 5.0 ð 4 Wall shear stress measurement Measurement in turbulent boundary layers Estimating ðĒð with Clauser chart ðĒ+ = ðī log ðĶ + + ðĩ ðī ≈ 5.9, ðĩ ≈ 5.0 ð ðĶð ðĒð = ðī log +ðĩ ðĒð ð ð = ðī log ðĶð ðĒð + ðī log + ðĩ ð ð Step 1. determine ðĶð/ð with measured mean velocity ð at position ðĶ and viscosity ïŪ Step 2. determine ð/ðĒð according to the chart Step 3. calculate ðĒð Step 4. compute wall shear stress with ððĒð 2 5 Wall shear stress measurement Estimates from pressure differences Wall shear stress in fully developed flow in circular pipes D – pipe diameter ðð/ððĨ – streamwise wall-pressure gradient Preston tubes - Pitot tube of external tube diameter ð resting on the wall - Dimensionless parameters: - Calibration expressions: for for for for - Uncertainty: 1.0% ïū 1.5% 6 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 ððĪ 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 ððĪ - higher sensitivity than Stanton gauge 7 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: ðļ – output voltage ððĪ – film temperature ðð – 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 8 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 ïĶ - phase shift 9 Homework - Read textbook 14.1-14.6 on page 328 - 341 - Questions and Problems: 1 on page 342 - Due on 10/21 10