Comprehensive Rotor Analyses

CFD models of the complexity required to yield the aerodynamic fidelity desired for helicopter rotors will be too expensive in the shorter term for parametric design cal­culations. Yet the hope is that the knowledge obtained using these types of models can be used to guide and inform the construction of more parsimonious models that can be used in an engineering context to design the next generation of quieter, safer, more comfortable helicopters. This fundamental concept is embodied in so-called comprehensive rotor ana­lyses, which attempt to combine together the best available models of aerodynamics, the rotor and airframe structure, rotating blade dynamics, aeroelasticity, etc. into a single com­puter code. The principles of comprehensive code development are reviewed by Johnson (1981a, b). Over the past 40 years several such models have been developed by government research organizations, individual helicopter companies and by universities specializing in helicopter teaching and research.

The aim of the comprehensive analysis is to use the highest levels of modeling capability while still balancing the overall requirements of practicality and computational feasibility for use in parametric helicopter design studies. The objectives are to calculate accurately all of the blade airloads, the rotor trim, the aircraft performance, overall vibration levels, control loads, aeroelastic effects, acoustics, and so on. Notable among the modem comprehensive codes is the CAMRAD (Comprehensive Analysis and Modeling of Rotor Aerodynamics and Dynamics) family that has been developed by Johnson (1981a, b, 1994, 1998). However, a principal difficulty in the comprehensive analysis is that by definition the approach is multidisciplinary and so relies on an ability to couple together often traditionally separate areas of analysis developed by different specialists. This may be difficult for reasons of computational cost or because the models in the separate disciplines are written in different mathematical forms that do not lend themselves readily to interdisciplinary coupling. Yet it

is the better integration of traditionally separate disciplines of helicopter analysis that will ultimately allow better rotor systems and more capable helicopters to be designed.

Currently, the technical capabilities of the comprehensive codes continue to be limited by several factors, including both the understanding of the physical behaviors and the mathematical modeling capabilities in each subdiscipline, as well as the numerical solution methods and the actual techniques used for computer implementation. Unfortunately, there is not always a good balance of disciplines in comprehensive helicopter analyses codes, this being a result of many factors, including the notion by the developers of what is actually considered state-of-the-art in each discipline.

Recently, there has been a bold effort toward integrating CFD into comprehensive rotor analyses – see, for example, Strawn et al. (1989), Kim et al. (1991), Beaumier (1994), Yang et al. (2002), Sitaraman et al. (2003), and Potsdam et al. (2004). The idea is obvious, in that the theoretically higher aerodynamic fidelity of the CFD solution can be used to better predict nonlinear and 3-D phenomena on the blades, including transonic flows and dynamic stall. This approach, however, involves several practical issues, not least of which is the much higher computational cost of the CFD. A significant issue is the actual process of numerically coupling together the CFD solution with the structural dynamic motion of the rotor blades. One approach is to use the loose or “weak” coupling procedure that has been alluded to previously. Here, the inflow angles from the comprehensive rotor analysis (which may involve blade aeroelastic effects using a nonlinear structural dynamic model of the rotor and its blades, and a FVM for the wake) are used as an input boundary condition to the CFD solution. Some information, such as integrated airloads from the CFD solution, is iterated between the two methods. This approach, however, has shown difficulties in achieving proper convergence to periodic conditions. Another approach is called the tight or “strong” coupling procedure, whereby the CFD and structural dynamic solution are coupled in time and solved simultaneously. This approach is computationally more demanding, but for some problems it has shown somewhat more encouraging results.

The development of various types of improved wake models in differential equation form may provide a good bridge between the capabilities of parsimonious models and more complete CFD-based methods. One goal for the future is to develop reduced order aerodynamics models directly from the Navier-Stokes equations, taking into account the need for simplified, fast mathematical realizations in certain applications – such as helicopter flight dynamics and handling qualities where the integration of CFD techniques for modeling the wake is seen as a route to improving the fidelity of the free-flight dynamic model of the helicopter [see Brown & Houston (2000)] but where there is also a particular need for accurate real-time simulation of the dynamic response of the helicopter. These reduced – order models will require extensive validation to assess confidence levels, both against complete solutions and against experimental measurements. This is one reason why the wind tunnel testing of complete helicopters and their subcomponents is essential if better understanding of helicopter aerodynamics and evaluation of predictive capability is ever to be obtained.

The following items define in more detail the typical approach and limitations of the comprehensive rotor analysis:

1. Aerodynamics: As explained throughout this book, the aerodynamics of the rotor un­derpins all helicopter flight. It is precisely here, though, that many physical problems require further study if overall modeling capabilities are to be improved. An issue with aerodynamic models is that, because of the complexity of the problems found on helicopters, significant empiricism may be needed to obtain useful results. A good example is in the problem of
modeling dynamic stall (Section 9.5) or the modeling of the tip vortices in the rotor wake (Section 10.6.2). Rotor-airframe interactional problems (Section 11.2.5) are also difficult to model without resorting to significant empiricism, and this is an unavoidable artifact of having to represent the powerful effects of viscosity with more parsimonious models that have practical levels of computational efficiency. While there is nothing wrong with empiri­cism, and all models of physical process incorporate empiricism to a lesser or greater extent, unfortunately the temptation is often to use empirical coefficients in a model as “tunable” variables that can be used to make the model match with the measured overall behavior of specific systems – for instance, those used to “validate” the model. This of course leads to many problems when significant departures from the original systems are encountered. The future must see not only efforts to improve empirical modeling and better experiments to better estimate the coefficients that go into these models, but also an effort to reduce em­piricism outright. This is particularly true in regard to wake modeling, where unnecessary pseudo-empiricism, in the form of tuning parameters, has on occasion been used to control or suppress underlying numerical problems with the solution algorithms – often ultimately proving to give completely misleading results in application. The more recent move toward the use of CFD to define the aerodynamics in comprehensive rotor simulations is a positive step toward better defining the operating capabilities of the rotor. However, because of the inherent limitations of CFD alluded to in previous sections, it would seem that there is still a long path to follow before Navier-Stokes CFD based comprehensive rotor analyses will see regular use in the design of new rotors. In the interim, the continued development of the VTM or FVM similar approaches probably offer much better opportunities for inclusion in practical design activities.

2. Structural dynamics: Because rotor blades are relatively long and slender, models based on beam theory can be used. The governing equations (which are partial differen­tial equations) can be reduced to flap and lag bending, torsional displacements and axial extension. The advent of finite-element methods (in space and time) has allowed a lot of adaptability in the representation of rotor blades and hubs. Nonlinear structural and iner­tial effects must be considered in conjunction with the aerodynamic forces and moments. Historically, the complexity of this coupling has hindered development, and most existing theories (but not all) are restricted to small, nonlinear deflections. Finite element meth­ods have also allowed fairly accurate representation of the dynamics of the airframe and airframe components. Coupling of the rotor and airframe dynamics is still not a mature process, however, in part because of the number and type of finite elements required and also because of the extensive computational resources required to model the fully coupled rotor-fuselage dynamics. Nevertheless, such approaches are urgently required because of the need to better predict airframe vibrations.

3. Numerical methods’. In comprehensive codes, the equations governing the behavior in each subdiscipline are solved numerically. In many cases, the numerical methods most

ОШІаН tn AQpb rllCPinlino точг nnf Vo miihiolli; ллптогіКІа ТТіл naiarl fn олкіаіга ргшсіotanmт LJUXIW’V* wv/ wuvil UJLOVl|/lUiV 1UUJ 11V/1 J W lilULUUllj Wlllj^lUll/lVt |.11V liVAX tv UV111V v v wuoiotvuvj, stability and accuracy for all elements of the model poses many demands on the development of satisfactory numerical methods. The generation of robust numerical methods that can be used under a wider range of conditions continues to be a research goal. Complicated mathematical models involving layers of empiricism seem to be a mainstay for many design purposes, but such methods always have a high probability of capturing the unwanted noise that is inherent in the uncertainties in the experimental data used to deduce the empirical models. There is always a need to balance the complexity of the model against the accuracy of the model, whilst aiming to minimize the variability and maximize the intelligibility

of the resulting simulation. It is known that, for complex mathematical models, predictive accuracy increases with increasing modeling complexity up to a point where the cumulative uncertainties in the empirical components of the model begins to increase the noise in the model. Beyond this complexity, predictive accuracy begins to decrease again, the system exhibiting a classic “Ockham’s Hill” – see Gauch (1993). The goal is to balance modeling complexity with predictive fidelity, something that cannot just be achieved through careful, systematic validation studies, but also requires a degree of engineering “common sense.”

4. Software engineering: The various mathematical models of helicopter analysis are implemented as software or “code ” This code must be carefully written, thoroughly tested and well documented. Ideally the code must be modular, so that components can be updated as improved subcomponent models become available – perhaps as a result of an improved understanding of the physics. This ideal is rarely achieved in practice – codes, unfortunately, always seem to become “hard-wired” between subcomponent models and so upgrading can become very difficult. The complexity of the helicopter problem means that documentation too is often complicated and may be difficult even for users with specialized backgrounds to use effectively. This is a serious problem for which there is no easy answer and simply reflects the multidisciplinary but still specialized nature of helicopter design. However, software standardization is a problem that must be continuously addressed if the community is to move forward toward the development of better comprehensive prediction methods for use in helicopter performance, loads, and design.

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