Embedded Files
한국항공대학교 항공 모빌리티 및 공력음향학 연구실
Summary
Background
In coaxial rotors, the wakes of the upper and the lower rotors interact actively, which adversely affects the performance. It is possible that the blade/vortex interaction (BVI) phenomenon occurs actively owing to the direct interaction between the lower rotor and the wake of the upper rotor, which is connected to the unique noise characteristics. Therefore, inter-rotor spacing (IRS) is an important design parameter governing the performance of coaxial rotors.
Many difficulties are encountered in the analysis of a complex coaxial rotor flow field by using CFD. General CFD techniques have large numerical dissipation, which means rotor inflow and wake dynamics cannot be predicted properly.
Objective
I propose a novel combination of numerical techniques to achieve high resolution on a simple Cartesian grid system. The truncated vortex tube model for a single rotor, which accurately captures wake geometry and reduces numerical dissipation of the tip vortex, was adopted for coaxial rotors. Moreover, the wave-number-extended finite-volume (WEFV) scheme, a computational aeroacoustics (CAA) technique developed through optimization of dissipation and dispersion errors, was used. These techniques were used simultaneously to discuss the wake dynamics of coaxial rotors for the first time.
Contribution
Develop the high-wake-resolution CFD method for rotorcraft applications
Illustrate the complicated wake dynamics of coaxial rotors as inter-rotor spacing (IRS) conditions
[Wake structure of coaxial rotors]
Method
High-wake-resolution method: Truncated vortex tube model
The first method of the high-wake-resolution method is the truncated vortex tube model. This model is used to assign initial and boundary conditions when predicting the hovering, vertical ascent, and descent flights of a single rotor. This model assumes that the rotor wake is distributed in the form of a tube and then derives the velocity of the boundary by using the Biot–Savart equation according to the vortex distribution of the tube.
Because the vortex tube model appropriately assumes the effect of the actual wake, it generates the flow component at the boundary more accurately. Therefore, it is possible to improve the convergence characteristics by ensuring that the starting vortex effectively escapes the numerical domain and to reduce tip vortex dissipation, which is very beneficial from the viewpoints of tip vortex capturing and predicting rotor inflow accurately on a small numerical domain.
High-wake-resolution method: WEFV CAA scheme
The second method for accurately simulating the wake of a coaxial rotor involved using the WEFV CAA scheme. The WEFV scheme uses the interpolation technique developed to minimize the numerical dissipation and dispersion errors in the smooth region, where flow discontinuity is small. While the general numerical interpolation technique aims to minimize the numerical truncation errors induced by the truncated Taylor series, WEFV interpolation is characterized by the inclusion of an additional condition for minimizing errors in the wavenumber domain.
[Vortex tube model for coaxial rotors]
[Comparison of source-sink and vortex tube model in the analysis of a coaxial rotor]
Results
IRS test: Details of wake structure
For identifying wake asymmetry, tip vortex locations were plotted in three azimuthal planes. Compared to the wake of the lower rotor, the wake of the upper rotor shows a similar trajectory regardless of the azimuth section because wake asymmetry is weak. In each IRS, the lower stable wakes show similar trajectories, but the wake aperiodicity of the lower rotor could be confirmed from the trajectories of the lower unstable wakes. It is a similar result as the coaxial rotor experiment. Especially for IRS 5%D, the lower unstable wakes of all sections are not smoothly developed and exhibit large wake instability, owing to the complex effects of upwash and downwash. For IRS 14%D, the lower unstable wake is more stable than that in the other IRS cases. Therefore, the lower unstable wake is well contracted along the axial direction and takes a similar trajectory in all azimuth sections.
IRS test: Wake instability phenomena
In IRS = 5%D, the vortex pairing and vortex merging phenomena occur. The wakes of both rotors are located close to each other, owing to the small spacing. Up to 6.375 revolutions, pairing of vortices 1 and 2 of the lower rotor proceeds. At 6.625 revolutions, the pairing of vortex a of the upper rotor and vortex 2 of the lower rotor commences. Thereafter, the upper/lower rotor vortex pairing proceeds, including vortex b. At 6.625 revolutions, vortex 2 interacts with the tip vortex of the upper rotor, failing to generate sufficient downwash in vortices 3 and 4 of the upper rotor. Vortices 3 and 4 are considerably closer, and the upwash effect is relatively strong. As a result, vortex merging occurs at 6.875 revolutions. The occurrence of vortex merging near the lower rotor of the coaxial rotor is observed only when IRS = 5%D. It represents a typical wake-instability phenomenon caused by a small IRS value.
[Wake trajectory of the upper and lower rotors in IRS = 5%D]
[Vortex pairing and vortex merging phenomena in IRS = 5%D (numbered vorticies are from the lower rotor, and lettered vorticies are from the upper rotor)]
Conclusion
The proposed high-wake-resolution method consists of the truncated vortex tube model for coaxial rotors and the WEFV CAA scheme. The boundary condition of the truncated vortex tube model is useful for simulating appropriate wake structure in a small computational domain, and the initial condition of that improves the convergence characteristics. The WEFV CAA scheme reduces the numerical dissipation and dispersion errors, making it useful to discuss the wake dynamics. The high wake-resolution method was used to investigate the wake dynamics of a coaxial rotor with three different IRS values.
A coaxial rotor has a periodic thrust coefficient based on the relative positions of both rotors. The sectional Ct of the upper rotor exhibits almost the same distribution as that of a single rotor. Still, the sectional Ct of the lower rotor is affected by the vortex sheet of the upper rotor on the inboard side, and its distribution is similar to that of the equivalent rotor at the tip side. Moreover, the sectional Ct of the lower rotor increases steeply when the wake of the upper rotor impinges directly on the lower rotor. There is a significant correlation between BVI strength and IRS, so the BVI strength of IRS 5%D is almost 1.5 times that of IRS 14%D.
Wake geometries of the upper and lower rotors differ considerably. The wake geometry of the lower rotor varies depending on the relative positions of the two rotors, which induces aperiodicity in the wake dynamics. The differences in miss distance, wake trajectory, and wake instability were compared for various IRS values. The lower unstable wakes could confirm the wake aperiodicity of the lower rotor. This unstable wake is led to the vortex pairing and vortex merging phenomena near the lower rotor. Wake aperiodicity and asymmetry result from the wake-instability phenomena.
Page updated
Google Sites
Report abuse