This paper describes an improved model of curved vortex element on the circular arc (CVEC) for rotor wake analysis.As the key of the paper,two approximate formulas are derived by the series of limited terms to replace...This paper describes an improved model of curved vortex element on the circular arc (CVEC) for rotor wake analysis.As the key of the paper,two approximate formulas are derived by the series of limited terms to replace the Legendre incomplete elliptical integrals from the Biot-Savart integration,and the analytical solution of the induced velocity for the CVEC is obtained, which is more efficient in the complex rotor free wake calculation. Furthermore,the approximate formulas with the chosen factors are selected to avoid sigularity and give finite result of the induced velocity on the Vortex line,and an equivalent viscous vortex core radius might be evaluated.As examples, the induced velocity calculations on the vortex ring and two turns of a skew vortex helix are performed, and the comparisons between the circular-arc vortex element and the conventional straightline vortex element (SLVE) are given.It is shown that this curved vortex element model is advantageous over the SLVE model and is suitable for the rotor wake analysis.展开更多
文摘This paper describes an improved model of curved vortex element on the circular arc (CVEC) for rotor wake analysis.As the key of the paper,two approximate formulas are derived by the series of limited terms to replace the Legendre incomplete elliptical integrals from the Biot-Savart integration,and the analytical solution of the induced velocity for the CVEC is obtained, which is more efficient in the complex rotor free wake calculation. Furthermore,the approximate formulas with the chosen factors are selected to avoid sigularity and give finite result of the induced velocity on the Vortex line,and an equivalent viscous vortex core radius might be evaluated.As examples, the induced velocity calculations on the vortex ring and two turns of a skew vortex helix are performed, and the comparisons between the circular-arc vortex element and the conventional straightline vortex element (SLVE) are given.It is shown that this curved vortex element model is advantageous over the SLVE model and is suitable for the rotor wake analysis.
