The uncertainty of the experimentally-measured momentum coefficient

Abstract

Abstract We quantify the uncertainty of the momentum coefficient, $$C_{\mu}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> , for six different experimental approaches. The approaches vary depending on compressibility effects and on the utilized acquisition equipment to measure the product of the mass flow rate with the jet exit velocity. The uncertainty of the directly-measured variables is propagated into the momentum coefficient using the Taylor expansion method to the first order. All relevant random and systematic uncertainties are meticulously quantified and listed. The analysis reveals unacceptably high uncertainty of the momentum coefficient under certain settings. Practical solutions to minimize the sources of uncertainty are then proposed and analyzed. The proposed improvements on the benchmark example of a Coanda actuator with a high aspect ratio slot reduce the uncertainty of $$C_{\mu}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> significantly but not sufficiently, as it remains at a non-negligible value of $$\approx 11\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>11</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for the best scenario. Finally, a list of practical recommendations and guidelines on how to accurately estimate the momentum coefficient experimentally is provided. Graphic abstract