# A time-resolved hot-wire shear stress probe for turbulent flow: use of laminar flow calibration

- 143 Downloads
- 18 Citations

## Abstract

A specially-designed rotating rig for producing near Couette flow was used in the calibration of a marginally elevated hot-wire shear stress probe. The probe was then used for measurements in both the turbulent boundary layer and pipe flows. Results showed that the mean wall shear stress can be accurately predicted and the near wall statistical quantities of intensity, skewness and flatness of shear stress fluctuations concurred well with previous works, thereby supporting the notion of a time-resolved shear stress probe for turbulent flows.

### Keywords

Boundary Layer Shear Stress Fluid Dynamics Laminar Flow Wall Shear Stress### List of Symbols

*A*Calibration constant in Eq. (4)

*B*Calibration constant in Eq. (4)

*F*Flatness of the shear stress (or velocity) fluctuations

*n*Calibration constant in Eq. (4)

*r*radial coordinate

*Re*_{s}Reynolds number ( ≡

*ωδ*^{2}/*v*)*S*Skewness of the shear stress (or velocity) fluctuations

*u*streamwise velocity

- ū
mean streamwise velocity

*u*_{τ}mean shear velocity,\((\overline {\mathbf{\tau }} / \rho )^{0.5} \)

*y*^{+}height in wall units,

*u*_{τ}y/v*z*vertical coordinate

### Greek symbols

*δ*Gap between the top rotating disk and the bottom stationary disk

*ɛ*dimensionless coordinate,

*z/δ**v*kinematic viscosity

*ϱ*density

*τ*wall shear stress

- τ
mean wall shear stress

*μ*dynamic viscosity

*ω*angular velocity of the top rotating disk

### Subscript

- rms
root-mean-square

*m*independently measured quantities

## Preview

Unable to display preview. Download preview PDF.

### References

**Ajagu CO**;**Libby PA**;**LaRue JC**(1982) Modified gauge for time-resolved skin friction measurements. Rev Sci Instrum 53: 1920–1926CrossRefGoogle Scholar**Alfredsson PH**;**Johansson AV**;**Haritonidis JH**;**Eckelmann H**(1988) The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys Fluids 31: 1026–1033CrossRefGoogle Scholar**Aoyagi M; Takehana N; Masuda S; Ariga I**(1985) In Proceedings of the Int. Symp. FLUCOME-85. Fluid Control and Measurement 2: 863–868 (ed. Harada M), TokyoGoogle Scholar**Brown GL**;**Davey RF**(1971) The calibration of hot films for skin friction measurement. Rev Sci Instrum 42: 1729–1731Google Scholar**Castro P**;**Dianat M**(1985) The measurement of fluctuating skin friction with a pulsed wire wall probe. In Proceedings of the Fifth Symposium on Turbulent Shear Flows, (ed. Durst F; Launder BE; Schmidt FW; Whitelaw JH). Cornell University, IthacaGoogle Scholar**Champagne FH**;**Sleicher CA**;**Wehrmann OH**(1967) Turbulence measurements with inclined hot-wires. J Fluid Mech 28: 153–175Google Scholar**Chew YT**;**Ha SM**(1988) The directional sensitivities of crossed and triple hot-wires probes. J Phys E Sci Instrum 21: 613–620Google Scholar**Chew YT**;**Shi S**(1993) Wall proximity influence on hot-wire measurements. In Near-Wall Turbulent Flows (ed. So RMC; Speziale CG; Launder BE). Tempe, Arizona, U.S.A.Google Scholar**Collins DC**;**Williams MJ**(1959) Two dimensional convection from heated wires at low Reynolds number. J Fluid Mech 6: 375–384Google Scholar**Corino ER**;**Brodkey R**(1969) A visual investigation of the wall region in turbulent flow. J Fluid Mech 37: 1–30CrossRefGoogle Scholar**Karlsson RL; Johansson TG**(1988) LDV measurements of higher order moments of velocity fluctuations in a turbulent boundary layer. In Third Int. Symp. on Applications of Laser Anemometry to Fluid Mech. (ed. Adrian RJ; Asanuma T; Durao DFG; Durst F; Whitelaw JH). Lisbon, PortugalGoogle Scholar**Ligrani PM**;**Bradshaw P**(1987) Spatial resolution and measurements of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp Fluids 5: 407–417CrossRefGoogle Scholar**Kim J**;**Moin P**;**Moser R**(1987) Turbulent statistics in fully developed channel flows at low Reynolds number. J Fluid Mech 177: 133–166Google Scholar**Mitchell JE**;**Hanratty TJ**(1966) A study of turbulence at a wall using an electrochemical wall shear-stress meter. J Fluid Mech 26: 199–221CrossRefGoogle Scholar**Popovich AT**(1969) Statistical analysis of fluid flow fluctuations in the viscous layer near a solid wall. Ind Eng Chem Fundamental 8: 609–614Google Scholar**Spence DA**;**Brown GL**(1968) Heat transfer to a quadratic shear profile. J Fluid Mech 33: 753–773CrossRefGoogle Scholar**Stewartson K**(1953) Flow between two rotating coaxial disks. Proc Cambridge Phil Soc 49: 333–341MATHMathSciNetGoogle Scholar**Wagner PM**(1991) The use of near-wall hot-wire probes for time resolved skin friction measurements. Advances in Turbulences 3: 524–529Google Scholar**Willmarth WW**;**Lu SS**(1972) Structure of the Reynolds stress near the wall. J Fluid Mech 55: 65–92CrossRefGoogle Scholar