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Accurate Turbine Inertia Measurement

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Abstract

High fidelity power measurements in free wheel devices require accurate inertia measurements. To evaluate the turbine efficiency, a new experimental technique to measure the momentum of inertia has been developed at the von Karman Institute (VKI). This experimental methodology allows the determination of the inertia of complex shape bodies without being dismounted from their rotating housing.

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Abbreviations

\( \overline{x} \) :

Mean level \( \overline{x} = {\sum\nolimits_{i = 1}^{i = N} {{x_{i} } \mathord{\left/ {\vphantom {{x_{i} } N}} \right. \kern-\nulldelimiterspace} N} } \)

ρ :

Density (kg m−3)

μ :

Friction coefficient

ΔE :

change of energy (J)

a 2 a 1 a 0 :

Quadratic law coefficients \( {\left[ {a_{2} \times x^{2} + a_{1} \times x + a_{0} } \right]} \)

b 2 b 1 b 0 :

Quadratic law coefficients \( {\left[ {b_{2} \times x^{2} + b_{1} \times x + b_{0} } \right]} \)

C n :

C normalization constant, n power coefficient power law (C × x n)

f s :

Sampling frequency (Hz)

g :

gravitational acceleration (m/s2)

I :

Momentum of inertia (kg m2)

l :

Length of the suspended wires (m)

m :

mass (kg)

N :

Number of tests

R, r :

Radius (m)

\( r^{2}_{{\text{q}}} \) :

Correlation coefficient of a quadratic fit

t :

Time (s), period of oscillation (s)

α:

Rotational acceleration (rad/s2)

θ :

Angular position (rad)

σ :

Standard deviation \( {\sqrt {{\sum\nolimits_{i = 1}^{i = N} {{{\left( {x_{i} - \overline{x} } \right)}^{2} } \mathord{\left/ {\vphantom {{{\left( {x_{i} - \overline{x} } \right)}^{2} } {{\left( {N - 1} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {N - 1} \right)}}} }} } \)

τ :

Torque (N × m)

\( \tau _{{\text{F}}} \) :

Friction torque (N × m)

ω :

Rotational speed (rad/s)

References

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Acknowledgements

Special thanks to Eugenio Fortugno for his assistance in some of the preliminary measurement campaigns. The authors would like to acknowledge the encouragement of Charles Haldeman to write this paper.

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Authors and Affiliations

  1. Turbomachinery and Propulsion Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640, Sint Genesius Rode, Belgium

    G. Paniagua & T. Yasa

Authors
  1. G. Paniagua
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  2. T. Yasa
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Corresponding author

Correspondence to G. Paniagua.

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Paniagua, G., Yasa, T. Accurate Turbine Inertia Measurement. Exp Mech 47, 693–700 (2007). https://doi.org/10.1007/s11340-006-9031-7

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  • DOI: https://doi.org/10.1007/s11340-006-9031-7

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