Abstract
We quantify the uncertainty of the momentum coefficient, C_{mu}, 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} significantly but not sufficiently, as it remains at a non-negligible value of approx 11% 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
Highlights
The momentum coefficient, C, is the most common metric to quantify the blowing intensity of fluidic actuators (Cattafesta and Sheplak 2011; Kumar and Alvi 2006; Radespiel et al 2016), such as fluidic oscillators (Viets 1975; Raman et al 1993), tangential blowing (Pastoor et al 2008) and Coanda actuators (El Sayed et al 2017)
Where ṁ is the mass flow rate, Vj, Pj, and Sj are the jet exit velocity, pressure, and area, respectively, Pa is the pressure near the jet exit, the subscript ∞ denotes freestream conditions, and Sref is a reference area typically defined for airfoils as Sref = c, where c is the chord length and is the span
The large uncertainty is a result of a compounded effect of high uncertainty magnification factors (UMF) and high uncertainty of the jet exit measurements
Summary
The momentum coefficient, C , is the most common metric to quantify the blowing intensity of fluidic actuators (Cattafesta and Sheplak 2011; Kumar and Alvi 2006; Radespiel et al 2016), such as fluidic oscillators (Viets 1975; Raman et al 1993), tangential blowing (Pastoor et al 2008) and Coanda actuators (El Sayed et al 2017). Due to its importance in quantifying the blowing intensity, and correspondingly the actuation effectiveness, and due to its small value (typically O(10−3) − O(10−2) ) compared to other aerodynamic coefficients such as the lift (typically O(10−1) ), it is critical to accurately estimate C. This issue is exasperated when reporting aerodynamic benefits, such as the lift gain ratio ΔCl∕C , where small errors in estimating C will yield large uncertainties in the actuation gains
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