## Computational Methods for Helicopter Aerodynamics[49]

The ability to design rotorcraft with confidence requires a new order of aerodynamic predictive technology that is both true to the basic flow physics and readily usable by industry.

F. X. Caradonna (1990)

Introduction

This chapter reviews computational methods that have been applied or are being applied to the analysis of various problems in helicopter aerodynamics. The intention is not to review the details of such methods and their associated numerical algorithms per se, but to give a general overview of the underlying principles of the various approaches along with a summary of their capabilities and limitations for the various helicopter problems alluded to in previous chapters. The approaches are described with ample reference to original methodologies and results, as appropriate. A range of methods is covered in this chapter, from classical thin airfoil theory and surface singularity potential flow methods, to advanced computational methods that solve numerically the vorticity transport, Euler and Navier-Stokes equations. Several examples of the application of advanced aerodynamic methods to helicopter problems are also shown and discussed, with suggestions for areas of new research where appropriate.

While historically the helicopter industry has relied extensively on more parsimonious aerodynamic methods such as various forms of “momentum theory” combined with significant empiricism for helicopter design work, this is fast changing. See Gessow (1985) for a good historical review of helicopter predictive methodologies through 1980. Since then, rapid advances in computer technology (both in terms of speed and memory) have allowed much more ambitious numerical methods to be used in helicopter aerodynamics, and this has spawned a great deal of new fundamental work, both in fluid flow modeling and in algorithmic development. Aerodynamic problems that were once considered intractable, or were relegated to the fastest super-computers, are now solvable on desktop workstations. The tremendous recent advances in computer capabilities have played a large part in motivating and accelerating the development of more complete computational techniques for helicopter aerodynamic analysis, including vortex methods. This has helped to improve the rigor of the overall analysis and even to remove some of the more sweeping levels of empiricism – an important factor especially when new helicopters begin to depart from legacy designs.

It is the modeling of the rotor wake and its effects on the rotor and airframe that proves key to solving ultimately many of the outstanding problems in predicting helicopter performance

and improving helicopter design. The ability to better predict and understand rotor wake related problems continues to challenge the helicopter analyst, however, and it is here that further research must be focused. Advances in computer power have made possible the better integration of traditionally separate disciplines of helicopter analysis and will ultimately allow better rotor systems and more capable helicopters to be designed. Yet, bigger problems and more ambitious numerical techniques continue to push the limits of computer resources, with the ultimate (albeit elusive) goal of predicting the behavior of an entire helicopter in an arbitrary flight condition. Yet there is still much work to be undertaken before predictive models can be improved to the level that the aerodynamics of a new helicopter can be adequately predicted before its first flight.

Over the past two decades, advances have been made in the understanding of problems in helicopter aerodynamics using so-called computational fluid dynamics or CFD. Here, finite-difference or finite-volume approximations to the governing flow equations are used to model, from first principles, the complex flow field about the helicopter rotor and its airframe. The general field of helicopter CFD is reviewed by Caradonna (1990), Landgrebe (1988,1994), McCroskey (1995), and Conlisk (2002). These works contain many references documenting past, present, and potentially future capabilities of CFD as it might be applied to helicopter problems. The choice of which governing equations to use affects the level of physics captured by the CFD scheme, as well as the computational effort and time taken to solve the problem. Furthermore, the choice of numerical method affects accuracy, stability, and cost. To some, the development of CFD by itself is held out to be the “Holy Grail” for the helicopter aerodynamicist, yet this is a very misleading perspective because CFD has its limitations. These limitations include grid dependent solutions, numerical issues, the ability to model turbulence, and so on. CFD methods must also be validated against measurements if they are to realize the high predictive confidence levels needed for design work. Therefore, CFD does not, by itself, hold the answer to all the various aerodynamic problems on helicopters. The real answer lies in the successful integration of advanced forms of aerodynamic analysis into other disciplines of engineering analysis. It is also unwise for other approaches to be abandoned in the shorter term while “CFD” matures to an accepted level of capability, given that this could still be decades off.