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Development of a functional relationship between port pressures and flow properties for the calibration and application of multihole probes to highly three-dimensional flows

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Abstract

It is common in the calibration of multihole probes to curve-fit the calibration data in order to determine a relationship between measured port pressures and flow properties. The parameters used in these techniques typically lack a theoretical background. In this article, a functional relationship is developed, based on theoretical considerations, that relates the port pressure directly to the flow properties and details a procedure that enables flow properties to be determined from the measured pressures of the multihole probe. The method is simple, easy to implement and provides a better understanding of the multihole probe operation in a three-dimensional flow.

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Abbreviations

A 1 :

axis aligned with center probe port

a :

position vector of an arbitrary point on the probe

\( {\mathbf{\hat{a}}} \) :

unit vector of a

b i :

vector of functional coefficients for port i

Cp i :

pressure coefficient at port i

i :

subscript of an arbitrary port

j :

data point number

K :

nondimensional pressure constant

m :

total number of probe ports

n :

total number of data points in pitch and yaw for a particular zone

P i :

vector of measured pressures from port i

P :

pressure measured at probe surface

P 1,2..., m :

measured pressure from each of the pressure ports

P s :

static pressure in the freestream

P T :

total pressure of the flow

q :

dynamic pressure of the flow

r :

radius of sphere

R 2 :

coefficient of multiple determination

U :

velocity vector of flow

\( {\mathbf{\hat{U}}} \) :

unit vector of U

U :

magnitude of flow velocity

u :

X -component of flow velocity

V n :

flow component normal to X -direction

v :

Y -component of flow velocity

w :

Z -component of flow velocity

X :

matrix of flow velocity products

X, Y , Z :

axis of coordinate system

Z :

reduced matrix

α :

pitch angle

β :

yaw angle

α ′:

fixed pitch angle

β ′:

fixed yaw angle

ΔP i :

differential measured pressure at port i

ΔP t :

differential measured total pressure

θ :

flow dihedral angle relative to defined coordinates

φ :

flow rotational angle relative to defined coordinates

θ i :

dihedral angle defining position of arbitrary port i

φ i :

rotational angle defining position of arbitrary port i

θ T :

total angle between pressure port and velocity vector

ρ :

density of ambient air

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Acknowledgements

The authors would like to thank the Australian Research Council and Edmonds Pty. Ltd. for funding this research.

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Authors and Affiliations

  1. School of Mechanical and Manufacturing Engineering, The University of New South Wales, 2052, Sydney, Australia

    A. J. Pisasale & N. A. Ahmed

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  1. A. J. Pisasale
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  2. N. A. Ahmed
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Correspondence to A. J. Pisasale.

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Pisasale, A.J., Ahmed, N.A. Development of a functional relationship between port pressures and flow properties for the calibration and application of multihole probes to highly three-dimensional flows. Exp Fluids 36, 422–436 (2004). https://doi.org/10.1007/s00348-003-0740-8

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  • DOI: https://doi.org/10.1007/s00348-003-0740-8

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