Trans. Japan Soc. Aero. Space Sci. Vol. 52, No. 177, pp. 168–179, 2009 Aerodynamic Characteristic Analysis of Multi-Rotors Using a Modified Free-Wake Method By Jaewon LEE,1Þ Kwanjung YEE2Þ and Sejong OH2Þ 1ÞResearch Institute of Mechanical Technology, Pusan National University, Busan, Korea 2ÞDepartment of Aerospace Engineering, Pusan National University, Busan, Korea (Received November 23rd, 2008) Much research is in progress to develop a next-generation rotor system for various aircrafts, including unmanned aerial vehicles (UAV) with multi-rotor systems, such as coaxial and tandem rotors. Development and design of such systems requires accurate estimation of rotor performance. The most serious problem encountered during analysis is wake prediction, because wake-wake and wake-rotor interactions make the problem very complex. This study analyzes the aerodynamic characteristics based on the free-wake method, which is both efficient and effective for predicting wake. This code is modified to include the effect of complex planforms as well as thickness by using an unsteady 3D panel method. A time-marching free-wake model is implemented based on the source-doublet panel method that assigns panels to the surface and analyzes them. The numerical wake instability, the most critical problem for analysis, is resolved by adopting slow start-up and by including viscous effects. Also, the instability due to wake interference in tandem rotor analysis is resolved by configuring the initial shapes of the multi-rotor wake as that of a single rotor wake trajectory. The developed code is verified by comparing with previous experimental data for coaxial and tandem rotors. Key Words: Multi Rotor, Time-Marching Free-Wake, Unsteady Panel Method, Wake Instability Nomenclature 1. Introduction c: blade chord An anti-torque system is redundant in a multi-rotor heli- Cd: rotor overlap area copter, such as one with tandem or coaxial rotors. The sub- Cp: pressure coefficient stantial advantage of a multi-rotor system stems from the Cp0 : incompressible pressure coefficient elimination of the tail rotor, which usually consumes an CP: rotor power coefficient additional 5% to 10% of the main rotor’s power. On the CT: rotor thrust coefficient other hand, the mechanical complexity and associated para- d: horizontal distance between rotors sitic drag are believed to be major disadvantages, which D: diameter of rotor disk have made this configuration relatively unpopular so far. H: vertical separation between rotors However, the absence of a tail rotor allows lowers the num- M: mach number ber of helicopter accidents associated with the tail rotor, and rc: vortex core radius enables a more compact configuration than conventional R: radius of blade helicopters. Hence, due to its compact size and lift ability, Re: Reynolds number the multi-rotor system is seem as a viable alternative in t: maximum airfoil thickness UAV or micro-air vehicle (MAV) design.1) In response to vrel: relative velocity increasing needs for compact multi-purpose UAVs, the dual V: velocity rotor system has been chosen in this work. As shown in À : circulation Coleman’s comprehensive review2) of experimental and : induced power factor analytical studies of coaxial rotors, studies during the : doublet 1990s relied heavily on experiments, with a few theoretical : collective pitch angle analyses. Moreover, there is still a long unresolved issue : source about whether or not the coaxial rotor configuration is more rotor: rotor solidity efficient than the conventional rotor system. Detailed aero- È: velocity potential dynamic characteristics, such as wake structures and inter- : azimuth angle rotor interactions, have never been fully understood for wake: wake age coaxial rotor configurations. However, recent advances in computational techniques have enabled modeling of such complex aerodynamics with good confidence. Leishman and Ananthan3) established the Blade Element Momentum Theory (BEMT) for a coaxial Ó 2009 The Japan Society for Aeronautical and Space Sciences Nov. 2009 J. LEE et al.: Aerodynamic Characteristic Analysis of Multi-Rotors Using a Modified Free-Wake Method 169 rotor and solved the local air loads over the upper and lower intends to develop a code for analysis of a multi-rotor UAV rotors. The BEMT does not require the assumptions for the system based on the vortex wake method. The developed induced power factor () and induced power interference method favors analysis of complex wakes generated by factor (int), which are essential for the simple momentum rotors, and also includes the effects of rotor thickness. The theory. Validation of BEMT with Harrington’s experi- current study considers an unsteady source-doublet panel ments4) has shown good agreement. With the limited test method coupled with a time-marching free-wake model. data available, Leishman and Ananthan3) have compared In the single-rotor case, the concept of a finite-thickness- the spanwise airloads of BEMT for a coaxial rotor with bladed rotor was presented by Ahmed and Vidjaja,9) who the results of a Free-Vortex Method (FVM).5) Although dif- used a source/sink distribution over the blade surface and ferences were evident when compared in detail, the agree- a doublet distribution over the camber surface inside the ment between BEMT and FVM was found to be reasonable. blade. However this study used source and doublet distribu- Based on 2D theory, BEMT has the remarkable advantage tions over the blade surface. To improve the calculation of very low computational cost, while it has limitations in efficiency for wake-induced velocity, the doublet panel with analyzing flight regimes such as forward flight, for which constant strength representing the wake is replaced by an 3D effects are important. One research that used full equivalent vortex trapezoid. An important issue regarding 3D theory, was by Bagai and Leishman5) for analysis of codes using a time-marching free-wake model is resolution multi-rotors using the potential theory-based vortex wake of wake instability in hover. This paper focuses on resolving method with pseudo-implicit predictor-corrector method. this, issue and the interaction of rotor wakes. The Karman- Another study by Wachspress and Quackenbush6) used the Tsien compressibility correction is applied in order to cor- constant vorticity contour method. Although these studies rect the compressibility effect over the calculated pressure have proved successful and computationally efficient, the coefficient. The Table-lookup method, which is usually used methods use a vortex lattice description of the blade and supplementary in codes that do not account for viscous cannot predict thickness effects. Moreover, complex config- effects, is used for estimating power of the rotor system. urations of blades with variations in the sectional airfoil For UAVs or model rotors, due to the difference in the have rarely been considered. Due to the relative motion of Reynolds numbers between the analysis and the tables for the rotors, multi-rotor analysis using Navier-Stokes (NS) 2D airfoil aerodynamic data, the Reynolds number scaling based methods requires a complicated grid topology and law is used to estimate rotor power. involves significant difficulties in pre- and post-processing. Validation of results for multi-rotor configurations from One instance of a multi-rotor study using a NS-based developed code has been carried out by comparison with method was by Kim and Brown,7) who numerically ana- available experimental data.4,10) The trajectory of the tip lyzed the performance of a coaxial rotor in hover, steady for- wake in the present method is compared with the experi- ward, and level flight conditions, using a Vorticity Transport mental data of Nagashima,11) and Brown.7) The effects of Model (VTM) based on a time-dependent computational the tandem rotor vertical separation (H=D) and horizontal solution of the vorticity conservation form of the NS equa- distance (d=D) are investigated thoroughly. tion. The simulation results provided a detailed analysis of the differences in performance and the wake behavior of 2. Numerical Analysis the single and coaxial rotor systems. Another application of an NS-based method to a coaxial rotor was by Ruzicka To account for the effect of thickness and the complex and Strawn.8) They described efforts at modeling coaxial platform, this work uses a source-doublet panel method, rotor aerodynamics using the Reynolds-averaged, Navier- which is usually used in fuselage or full aircraft analysis Stokes (RANS) solver Overflow 2. The VTM, which is of fixed-wing aircraft. In addition, this work uses a time- formulated assuming incompressibility, is a partial CFD marching free-wake model, which is excellent in reproduc- scheme with NS for the near blade region, but RANS is a ing rotor wake. The problem in applying the time-marching fully viscous CFD scheme. When using a convection algo- free-wake model is wake instability. The following sections rithm and an adaptive-grid system, VTM was more efficient describe the solution to this problem, as well as the numer- than regular CFD analysis using the NS equation. However, ical method used in the multi rotor analysis code. it is still computationally inefficient compared to potential 2.1. Source-doublet panel method theory based panel methods. If flow is considered to be incompressible and irrota- Vortex wake methods represent less diffusive numerical tional, the continuity equation reduces to the Laplace equa- schemes that accurately reproduce the wake and are more tion. The general solution of the Laplace equation is given efficient than NS codes. They are still used widely for heli- as a sum of sources () and doublets (), distributed over copter aerodynamic analysis. However, as mentioned previ- the body surface and its wakes: Z ously for the Vortex Lattice Methods (VLM), which repre- À1 1 1 sent a blade as vortex lattices, the existing vortex wake È ¼ À n^ r ds 4 body r r methods also have limitations in accounting for rotor com- Z 1 1 plexity, including thickness variation and airfoil change by þ n^ r ds þ È1 ð1Þ location, such as found in UH-60 rotor blades.