Open AccessAn inconsistency in the actuator disc momentum theory
Author(s) -
van Kuik Gijs A. M.
Publication year - 2004
Publication title -
wind energy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.743
H-Index - 92
eISSN - 1099-1824
pISSN - 1095-4244
DOI - 10.1002/we.104
Subject(s) - momentum (technical analysis) , inviscid flow , mechanics , actuator , physics , constant (computer programming) , classical mechanics , balance (ability) , control theory (sociology) , engineering , computer science , electrical engineering , medicine , control (management) , finance , artificial intelligence , economics , physical medicine and rehabilitation , programming language
The classical momentum theory for actuator discs with a constant normal load Δp addresses only the axial momentum balance. Now the radial balance is also derived, which, in the absence of a radial disc load, leads to the requirement that the integral of the static pressure along the disc centre line must be zero. The axial and radial balances appear to be mutually inconsistent: the axial balance provides the well‐known results, but the radial balance cannot be satisfied. The inconsistency can be removed by assuming that the actuator disc force field is composed of more than the constant normal load Δp. It is shown that the modelling by Lee and Greenberg (Journal of Fluid Mechanics 1984; 145 : 287) of the load and flow of an actuator strip in hover implies the existence of a singular suction force at the edge. Their results deviate, without explanation so far, from the predictions of classical momentum theory. Addition of this edge force to the radial and axial momentum balances provides consistent results. A more general explanation or solution for the inconsistency is not yet are cable. Comparison the present inviscid analysis with a Navier–Stokes calculation by Mikkelsen et al. (Wind Energy 2001; 4 : 121) shows that the integrated pressure along the disc centre line is indeed non‐zero, but that the radial balance is still satisfied. It is not clear why this deviates from the analysis. Copyright © 2004 John Wiley & Sons, Ltd.