Abstract
A method of calibrating and extracting velocities from arbitrary geometry triple hot-wire probes has been developed and tested. The three-step procedure involves experimental determination of an accurate cooling law for each wire in the array, use of these models to develop a set of tables relating anemometer output to flow velocity input, and a table look-up procedure to extract the velocities. The functional form for the cooling law can be arbitrarily chosen and these equations are never directly inverted. Solutions are tabulated making use of special variable transformations that separate the dependence on flow angle and velocity magnitude. Errors in the table look-up procedure are commensurate with those in exact inversion techniques. Most of the error arises from accurate determination of the cooling laws. An application to turbulent boundary layer measurements is presented as an example of the use of the method.
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Abbreviations
- d :
-
diameter of hot-wire
- e :
-
voltage
- i :
-
subscript denoting ith hot-wire
- l :
-
length of hot-wire
- u, v, w :
-
orthogonal components of velocity
- Q :
-
estimated cooling velocity
- Q mag :
-
cooling velocity magnitude (Q 21 + Q 22 + Q 23 )1/2
- Q R1:
-
cooling velocity ratio Q 1/Q 3
- Q R2:
-
cooling velocity ratio Q 2/(Q 21 + Q 23 )1/2
- Re d :
-
Reynolds number based on d and U mag
- U :
-
velocity vector
- U b :
-
velocity component normal to a hot-wire and perpendicular to the plane of the wire supports
- U mag :
-
magnitude of velocity vector
- U n :
-
velocity component normal to a hot-wire and in the plane of the wire supports
- U t :
-
velocity component tangential to hot-wire
- δ :
-
99% boundary layer thickness
- ɛ :
-
measure of error
- θ :
-
sweep angle of hot-wire
- ω :
-
angular rotation of hot-wire
- φ,ψ :
-
angles in spherical coordinates describing the flow direction with respect to probe
- Δt :
-
viscous time unit
References
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Gieseke, T.J., Guezennec, Y.G. An experimental approach to the calibration and use of triple hot-wire probes. Experiments in Fluids 14, 305–315 (1993). https://doi.org/10.1007/BF00189488
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DOI: https://doi.org/10.1007/BF00189488