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Characteristics of a hot-wire microsensor for time-dependent wall shear stress measurements

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Abstract

Hot-wire microsensors for the purpose of measuring the instantaneous velocity gradient close to a wall were designed and their characteristics were evaluated. The sensors were made using MEMS (microelectromechanical systems) technology, which permits the fabrication of various microgeometrical configurations with high precision and good repeatability. The design is based on estimates of the heat rates from the sensor wire to the air, through the supports, and to the wall. Several hot-wire configurations were fabricated with wires positioned in the range 50–250 µm from the wall. Requirements for the design and details of the fabrication methodology are outlined. The hot-wire microsensors were calibrated and tested in a flat-plate boundary layer with and without pressure gradients and were found to have good steady-state characteristics. In addition, the developed sensors were used for preliminary studies of transitional phenomena and turbulence, and the sensors were found to have a good time-dependent response as well.

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Abbreviations

a :

diameter (m)

A :

area (m2)

d :

distance to wall (m)

d s :

distance from hot wire to wall and support length (m)

E :

output voltage from anemometer (V)

h :

convective heat transfer coefficient (W/m2 K)

I :

electrical current (A)

k :

thermal conductivity of metal (W/m K)

k a :

thermal conductivity of air (W/m K)

l :

length (m)

Nu :

Nusselt number

P :

perimeter (m)

Q :

heat rate (W)

Q gen :

rate of heat generation by current (W)

Q r :

radiative heat rate (W)

R :

electrical resistance (Ω)

Re :

Reynolds number

S θ :

sensor temperature sensitivity (mV Pa−1)

S τ :

sensor wall shear stress sensitivity (mV °C−1)

T :

temperature (°C)

T ∞ :

temperature of wall and surroundings (°C)

U :

local fluid velocity (m/s)

U ∞ :

velocity outside boundary layer (m/s)

y :

coordinate normal to wall (m)

α 20 :

temperature coefficient of resistivity at 20°C (°C−1)

δ**:

boundary layer displacement thickness (m)

Δτ 0 :

measurement error of wall shear stress (N/m2)

ε :

emissivity

θ :

temperature fluctuation of T ∞ (°C)

ν :

kinematic viscosity of air (m2/s)

ξ :

local coordinate along wire and support (m)

ρ :

density of air (kg/m3)

σ :

Stefan–Boltzmann constant (W/K4m2)

τ 0 :

shear stress at wall (N/m 2 )

τ e :

effective wall shear stress with wall influence (N/m2)

χ :

resistivity (Ω m)

air:

air

s:

sensor support

w:

sensor wire

wall:

wall

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Acknowledgements

M.S. thanks the Chalmers University of Technology for hosting him during his sabbatical when this work was carried out. Thanks are also due to the Swedish Research Council for financial support. Useful comments by two referees are highly acknowledged as well.

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Authors and Affiliations

  1. Thermo and Fluid Dynamics, Chalmers University of Technology, 41296, Göteborg, Sweden

    L. Löfdahl & V. Chernoray

  2. Department of Signals, Sensors and Systems, Microsystem Technology, Royal Institute of Technology, 10044, Stockholm, Sweden

    S. Haasl & G. Stemme

  3. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    M. Sen

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  1. L. Löfdahl
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  2. V. Chernoray
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  3. S. Haasl
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  4. G. Stemme
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  5. M. Sen
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Correspondence to L. Löfdahl.

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Löfdahl, L., Chernoray, V., Haasl, S. et al. Characteristics of a hot-wire microsensor for time-dependent wall shear stress measurements. Exp Fluids 35, 240–251 (2003). https://doi.org/10.1007/s00348-003-0624-y

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  • DOI: https://doi.org/10.1007/s00348-003-0624-y

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