LIN Xian-wu, LAN Wei-yao, LI Zhi-bin, LI He. The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis[J]. Applied Mathematics and Mechanics, 2016, 37(6): 551-566. doi: 10.3879/j.issn.1000-0887.2016.06.001
Citation: LIN Xian-wu, LAN Wei-yao, LI Zhi-bin, LI He. The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis[J]. Applied Mathematics and Mechanics, 2016, 37(6): 551-566. doi: 10.3879/j.issn.1000-0887.2016.06.001

The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis

doi: 10.3879/j.issn.1000-0887.2016.06.001
Funds:  The National Natural Science Foundation of China(11072028;61273199)
  • Received Date: 2016-01-27
  • Rev Recd Date: 2016-04-15
  • Publish Date: 2016-06-15
  • To tackle the calculation problem on steady and unsteady hydrodynamic force coefficients of a moving body in viscous incompressible flow, a method for calculating hydrodynamic force coefficients in viscous flow was proposed based on the quasi-equilibrium hypothesis and the vorticity aerodynamics. Firstly, the concept of time-varying flow systems was defined, and its relationship with the space volume was clarified. Then, the momentum transport equation and the fluid momentum theorem for time-varying flow systems were developed respectively, so as to provide a basis for the further discussion. Secondly, the fluid momentum theorem was applied to a flow system enclosed in the boundary composed of the body surface and the outer fixed surface with an infinite radius, and the fluid dynamic force was related to the change of the total fluid momentum. Thirdly, the quasi-equilibrium hypothesis was proposed and the total fluid momentum was expressed as a function of the body velocity and angular velocity. At last, this function was determined with the CFD technology and the method for calculating the fluid dynamic force coefficients in viscous flow was established. The study also show that the variation of the flow system should be considered during the derivation of the fluid momentum, and consequently an additional steady fluid dynamic force would come forth. This additional steady force can be proved to be zero for the body in linear uniform motion in the ideal flow, which is in accordance with d’Alembert’s paradox and Lamb’s result. However, in the case of viscous flow, this additional steady force is not necessarily to be zero, which is in accordance with the experimental results.
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