cotri
commented
2 years ago Hi Nina,
Apologies for the lack of clarity in the expressions used in the BEMT code. I understand your frustration, this could have been easily avoided had I included the references from which the formulas are taken in the first place.
TL;DR The main book that you can follow step by step on how C_T and C_P are derived is:
[1] D. R. Greatix, «The Propeller», in Powered Flight: The Engineering of Aerospace Propulsion, London: Springer-Verlag, 2012, p. 63-76.If you just want the "final" C_T and C_P expressions (and not the whole derivation process for the Blade Element Momentum Theory*) take a look at Equations 3.47, 3.51, 3.53 and 3.54 to 3.57.
Finally, a tip loss correction factor, F, is directly applied to the force and power coefficients in the code.
Please note that the code uses T and F to denote thrust and tip loss correction factor respectively, while [1] uses F for the propeller thrust instead (and does not implement any correction factor in the cited equations).
(*) I use "Blade Element Momentum Theory" or just "BEMT", though, the book's author calls it "Momentum-Blade Element Theory".
Other references regarding the BEM Theory that I also used in my thesis are:
[2] R. S. Merrill, «Nonlinear Aerodynamic Corrections to Blade Element Momentum Model with Validatiosn Experiments», M.S. Thesis. Luga, Utah: Department of Mechanical and Aerospace Engineering, Utah State University, 2011.
[3] M. H. McCrink and J. W. Gregory, «Blade Element Momentum Modeling of Low-Re Small UAS Electric Propulsion Systems», in 33rd AIAA Applied Aerodynamics Conference, Dallas, TX, 2015.
[4] B. Li et al., «Validation of an actuator disk model for numerical simulation of propeller», Proc IMechE Part G: J Aerospace Engineering, vol. 0, p. 1-10, 2014.
[5] M. K. Rwigema, «Propeller Blade Element Momentum Theory», in 27th Congress of International Council of the Aeronautical Sciences, Niza, 2010.
[6] J. Morgado et al., «Validation of New Formulations for Propeller Analysis», Journal of Propulsion and Power, vol. 31, p. 467-477, 2015.
[7] J. Leishman, «Blade Element Momentum Theory (BEMT)», in Principles of Helicopter Aerodynamics, New York: Cambridge University Press, 2006, p. 125-135.Hope this solves all your doubts and sorry for the late response,
Best regards.
On Tue, May 24, 2022, 22:36 ninamoello @.***> wrote:
Hello, I am also interested in the reference book/article. I don't get where do the C_T and C_P computations come from. Why do you divide them by 8? Thanks in advance.
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ninamoello
Please add reference to the book, from which BENT formulas were taken. Different author use different formulation.