Different lift decompositions into the elemental terms are compared based on direct numerical simulations of a flapping flat plate and a flapping rectangular wing at low-Reynolds-number flows. The simple lift formula is given as 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 comparison with 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.

This work was supported by the National Natural Science Foundation of China under project numbers 10872201, 11232011, 11302238, and 11372331, and the National Basic Research Program of China (973 Program) under project number 2013CB834100 (nonlinear science). We would like to acknowledge the support from the National Supercomputer Center in Tianjin. We would like to thank Jiezhi Wu of Peking University and the University of Tennessee Space Institute for his detailed constructive comments. Tianshu Liu would like to acknowledge the hospitality received at State Key Laboratory of Nonlinear Mechanics during his visit where he accomplished this work. The simulations were performed on TianHe-1.

Wang SZ,Zhang X,He GW,et al. Evaluation of Lift Formulas Applied to Low-Reynolds-Number Unsteady Flows[J]. AIAA JOURNAL,2015-01,53(1):161-175.