High efficiency and low fuel consumption make the contrarotating open rotor (CROR) system a viable economic and environmentally friendly powerplant for future aircraft. While the potential benefits are well accepted, concerns still exist with respect to the vibrations and noise caused by the aerodynamic interactions of CROR systems. In this paper, emphasis is placed on the detailed analysis of the aerodynamic interactions between the front and aft propellers of a puller CROR configuration. For the first step, unsteady Reynolds-averaged Navier-Stokes (URANS) simulations coupled with dynamic patched grid technology are implemented on the isolated single-rotating propeller (SRP) configuration in various operating conditions in order to test the accuracy and feasibility of the numerical approach. The numerical results are verified by a wind tunnel test, showing good agreements with the experimental data. Subsequently, the URANS approach is applied to the CROR configuration. The numerical results obtained through the URANS approach help to improve the understanding of the complex flow field generated by the CROR configuration, and the comparison of SRP flow field and CROR flow field allows for a detailed analysis of the aerodynamic interactions of the front propeller blade wakes and tip vortices with the aft propeller. The main reason of the aerodynamic interactions is the mutual effects of the blade tip vortices, and the aft propeller reduces the strength of the blade tip vortices of the front propeller. Aerodynamic interactions will lead to the periodic oscillations of the aerodynamic forces, and the frequency of the oscillations is linked to the blade numbers. In addition, a CROR has a larger thrust and power coefficient than that of the SRP configuration in the same operating conditions. The URANS approach coupled with a dynamic patched grid method is tested to be an efficient and accurate tool in the analysis of propeller aerodynamic interactions.

In modern aircrafts, besides supersonic and transonic mainline airliners, regional airliners have the properties of smaller weight and size, lower flight speed and altitude, and good maneuverability; as a result, propeller-driven aircrafts can meet these requirements very well. Due to their shorter take-off distance, larger climbing speed, longer voyage, less fuel consumption, and lower requirements for runways, propeller-driven aircrafts play an important role in both civil and military applications [

The efficiency of the CROR system mainly comes from the reduction of the front propeller slipstream swirl by the impingement of the aft propeller slipstream, which will also lead to the extra axial acceleration of the flow downstream when it passes through the aft propeller; therefore, CROR systems can generate greater thrust [

In recent years, the rapid developments of computer hardware and numerical computation approach have enabled the computational fluid dynamics (CFD) method to become one of the most effective methods to simulate and analyze propeller slipstream flow field [

In this paper, the URANS code coupled with a dynamic patched grid method is first used on an isolated SRP configuration with experiment verification. The same numerical method is applied to an isolated CROR configuration in different operating conditions with the specific focus on analyzing the mechanism of the complex flow field and the aerodynamic interactions between the front propeller and the aft propeller [

An isolated SRP configuration wind tunnel test was conducted in the DNW-LST wind tunnel in Netherland in 2014. The main purpose of the wind tunnel test was to gain access to the thrust and power coefficient as well as the efficiency of the isolated propeller in different rotor speeds under certain blade pitch angles in various operating conditions. The DNW-LST wind tunnel is a low-speed return-flow wind tunnel, which has a 3.0 m (width) × 2.25 m (height) × 8.75 m (length) test section, as shown in Figure ^{th} scale model that consisted of a nonrotating center shaft and a rotor equipped with 6 blades of the same blade geometry at a fixed diameter of ^{th} scale SRP configuration provides a broad scope of database to evaluate the numerical approaches’ ability to predict the aerodynamic performance of the SRP configuration as well as the related CROR configuration. Specific emphasis was placed on the flow conditions of the wind tunnel test in order to accommodate the numerical simulations; the flow speed of the wind tunnel test could be set ranging from 1.5 m/s to 80 m/s, and the flow precision can be controlled in the range of 0.2%. The yaw angle of the horizontal and vertical flow is less than 0.1°, while the turbulence level is controlled between 0.02% and 0.03%. The center shaft was connected to a strut, which was connected to an external balance. In this particular wind tunnel test, attentions were paid to aerodynamic performance by installing a rotated shaft balance inside the faring. Thrust coefficients of different advance ratios are obtained via the rotated shaft balance. The results obtained by the rotated shaft balance were verified through the comparison of the results obtained by the external balance.

Sketch of a wind tunnel.

Isolated single-rotating propeller configuration in the DNW/LST wind tunnel.

The experiment Mach number was set to

Wind tunnel test settings.

Cases | Mach number | Angle of attack | Rotor speeds | Advance ratio |
---|---|---|---|---|

1 | 0.2 | 0.03° | 2998 rpm | 1.91066 |

2 | 0.2 | 0.03° | 3097 rpm | 1.8462 |

3 | 0.2 | 0.03° | 3198 rpm | 1.78863 |

4 | 0.2 | 0.03° | 3290 rpm | 1.73779 |

The propeller thrust coefficient, power coefficient, and efficiency have the following forms:

The SRP numerical simulations mainly focus on the investigation of the propeller flow field and blade aerodynamics, and the most important aspect is the validation of the URANS approach with the wind tunnel test. For the numerical studies, a configuration for numerical simulations was approximated as closely to the wind tunnel test model as possible. Modifications were made to the numerical simulation configuration to ensure that there was no adverse impact on the performance of the propeller as well as the flow field in their direct vicinity. The length of the center shaft was chosen to be

SRP numerical configuration and geometric layout.

Side view

Front view

The accuracy and reliability of solutions obtained by means of CFD have close ties to the density and quality of the computational grids used. A dynamic patched grid method has the primary advantage that the grids of each subdomain can be generated separately without concerning the topology relations among adjacent blocks. One-to-one correspondence of grid points is not required on the two sides of the patched surfaces, and fluxes are interpolated near the patched surfaces in the process of computation; therefore, the flow information of adjacent subdomains is coupled and exchanged. For the numerical simulation described here, the baseline SRP configuration grids have one computational domain and one rotating domain. The computational domain, which is also called far-field, is a cylindrical region that has

Computational domain encompassing the SRP configuration.

The entire grids are included in the computational domain. Except the grids in the rotating domain, the other grids in the computational domain remain static. The rotating domain is a cylindrical region that contains the propeller, and the grids are generated in the cylindrical region, while fluxes are interpolated through the cylinder surfaces, which are patched surfaces, between the grids in the computational domains and rotating domain. The sketch map of the patched grid approach is shown in Figure

Sketch of a dynamic patched grid method of the SRP.

The block-structured grids of this SRP configuration have been created with the software ANSYS ICEM CFD. The whole computational grids consist of two parts: the blocks around the rotating propeller and the outer blocks around the static center shaft. Attentions should be paid to the grid generation of the blade passages to make sure that each of the blade passages is created as equal as possible to allow for a reliable spatial resolution for the blades of the propeller. Refined grids are applied in the boundary layer and propeller slipstream region to improve blade wake and tip vortex resolution. The surface grid of the SRP configuration is shown in Figure

Block-structured grids of an isolated SRP.

Surface gird

Far-field section grid

For the simulations described here, URANS calculations are applied to the isolated SRP configuration in order to testify the feasibility and accuracy of this numerical method, spatial discretization of the convective fluxes is done using a third-order upstream MUSCL scheme, and the viscous fluxes are discretized with central differences. A Spalart–Allmaras (SA) model is chosen as the turbulence model. A fully implicit LU-SGS method with subiteration in pseudotime is implemented as a time-marching method, and the well-established dual-time approach is used to enhance the precision of time discretization. In the course of the URANS simulations, the time step size is set equivalent to a propeller rotation of

The comparison of the SRP wind tunnel test and URANS approach in terms of thrust coefficient

Comparison of propeller performance between the wind tunnel test and URANS simulations.

Thrust coefficient

Power coefficient

Efficiency

The detailed results of the wind tunnel test and numerical simulations are listed in Table

Detailed results of the wind tunnel test and URANS numerical simulations.

Cases | Relative error, % | Relative error, % | ||
---|---|---|---|---|

1 | 0.191/0.197 | 3.14 | 0.423/0.441 | 4.26 |

2 | 0.209/0.215 | 2.87 | 0.449/0.469 | 4.45 |

3 | 0.224/0.231 | 3.13 | 0.470/0.493 | 4.89 |

4 | 0.237/0.244 | 2.95 | 0.487/0.513 | 5.34 |

In order to demonstrate the capability of previously used URANS simulations in the analysis of aerodynamic phenomena and interactions of a CROR, an isolated 6 × 6 puller CROR configuration is put forward built on the isolated SRP configuration mentioned above by installing another propeller of the same blade geometry and blade numbers behind the propeller of the SRP configuration, as shown in Figure

CROR numerical configuration and geometric layout.

Side view

Front view

In the investigation of a CROR, the grid generation approach placed primary emphasis on the adequate resolution of the flow phenomena that played a significant role in the interactions between the front and aft propellers. Thus, the main effort goes into obtaining high-quality and high-resolution propeller grids to address requirements for good aerodynamic analysis results, which are a significant aspect for the design of a high efficient CROR system. The surface grid and section grid of the CROR configuration are shown in Figure

Block-structured grids of an isolated CROR.

Surface gird

Far-field section grid

In the investigation of the CROR configuration, all the numerical settings are aligned with the settings implemented in the SRP simulations. The CROR flow field is obtained after 12 full propeller revolutions, and the simulations are considered converged if the periodic fluctuations of the blade loadings for the 4 test cases show no obvious changes. The settings of CROR numerical simulation are listed in Table

CROR numerical settings.

Cases | Mach number | Angle of attack | Rotor speeds | Advance ratio |
---|---|---|---|---|

1 | 0.2 | 0.03° | 2998/2998 rpm | 1.91066 |

2 | 0.2 | 0.03° | 3097/3097 rpm | 1.8462 |

3 | 0.2 | 0.03° | 3198/3198 rpm | 1.78863 |

4 | 0.2 | 0.03° | 3290/3290 rpm | 1.73779 |

The isosurfaces of the

Slipstream flow field;

SRP flow field

CROR flow field

In order to investigate and analyze the vortex systems in depth, instantaneous value of the vorticity magnitude of the cross section is plotted, as shown in Figure

Cross section vorticity magnitude;

Vorticity magnitude of the SRP at longitudinal position

Vorticity magnitude of the CROR at longitudinal position

The blade tip vortex development of SRP and CROR configurations is plotted in terms of vorticity magnitude at axial positions of

Blade tip vortex development at axial positions of

Blade tip vortex development of the SRP

Blade tip vortex development of the CROR

Comparison of SRP and CROR thrust coefficient during one full rotation;

Unsteady thrust coefficients are plotted in order to analyze the aerodynamic interactions between the two propellers, as shown in Figure

Figure

Slipstream acceleration effect;

SRP cross section Mach number distribution

SRP time-averaged slipstream velocity

CROR cross section Mach number distribution

CROR time-averaged slipstream velocity

In the numerical investigation of SRP and CROR configurations, the figures of velocity profiles are plotted in terms of time-averaged slipstream-normalized velocity components of one complete revolution. Figures

Time-averaged slipstream-normalized velocity profiles;

SRP velocity component

CROR velocity component

SRP velocity component

CROR velocity component

Figure

Figure

Figure

Comparison of CROR and SRP performance.

Thrust coefficient

Power coefficient

Efficiency

An analysis of aerodynamic interactions was conducted for a 6 × 6 puller CROR configuration by using a dynamic patched grid method-based URANS numerical simulation approach. The URANS approach has been applied to an isolated SRP configuration with wind tunnel test verification, and this numerical approach is validated to be an efficient and accurate tool in the investigation of propeller slipstream and aerodynamic characteristics. The results obtained through the URANS approach help to improve the understanding of the CROR slipstream flow field and aerodynamic interactions between the two propellers.

The isocontours of vorticity magnitude characterize the vortex system of CROR slipstream flow field, which shows the complex interaction of the front propeller blade wakes and tip vortices with the aft propeller. The mutual interactions between the two propellers result in unsteady periodic blade loading oscillations during one full rotation. Due to the equal diameter and rotational speed of the two propellers, the frequency of blade loading oscillations depends on the blade numbers. The instantaneous contours of vorticity magnitude of the CROR blade tip vortex development reveal the vortex dissipation caused by the aerodynamic interactions. Time-averaged three-component velocity profiles at certain axial positions have been analyzed, and the results show that the freestream is accelerated twice when it passes through the two propellers. With the slipstream developing downstream, the diameter of the slipstream will decrease until the completion of the contraction. The upstream front propeller blade wakes play a dominant role in the interaction with the aft propeller, and these wakes are then ingested by the wakes of the aft propeller and have a strong impact on the vortex system. Generally, a CROR will produce much larger thrust than that of a SRP under the same circumstances, and the higher the rotational speed is, the greater the power consumption will be.

The data of the SRP propeller wind tunnel test used to support the findings of this investigation has not been made available because it involves commercial secrets.

The authors declare that no conflict of interest regarding the publication of this paper.

This study is supported by the State Key Development Program for Basic Research of China (no. 2015CB755800).