Evaluation of Lift Formulas Applied to Low-Reynolds-Number Unsteady Flows Shizhao Wang, ∗ Xing Zhang, † and Guowei He‡ Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China and

Different lift decompositions into the elemental terms are compared based on direct numerical simulations of a flapping flat plate anda flapping rectangularwing at low-Reynolds-number flows.The simple lift formula is givenas a useful approximate form that has the vortex force and local acceleration terms. The accuracy of the simple lift formula in lift estimation is quantitatively evaluated in comparisonwith the general force formulas based on the fully resolved two- and three-dimensional unsteady velocity fields and the planar velocity fields at several spanwise locations in simulated particle-image-velocimetry measurements. In addition, the mathematical connections between the different force formulas are discussed. Nomenclatures A = heaving amplitude, m AR = wing aspect ratio Cl = lift coefficient c = wing chord, m F = aerodynamic force, N Fz = lift, N f = flapping frequency, s−1 l = Lamb vector, m · s−2 p = pressure, Pa Q = second invariant of velocity gradient tensor, s−2 q = dynamic pressure, Pa Re = Reynolds number S = wing area, m