Computational methods have revolutionized the aircraft design process. Prior to the mid sixties aircraft were designed and built largely without the benefit of computational tools. Design information was mostly provided by the results of analytic theory combined with a fair amount of experimentation. Analytic theories continue to provide invaluable insight into the trends present in the variation of the relevant parameters in a design. However, for detailed design work, these theories often lack the necessary accuracy, especially in the presence of non-linearities (transonic flow, large structural deflections, real-life control systems). With the advent of the digital computer and the fast development of the field of numerical analysis, a variety of complex calculation methods have become available to the designer. Advancements in computational methods have pervaded all disciplines: aerodynamics, structures, propulsion, guidance and control, systems integration, multidisciplinary optimization, etc.

The role of computational methods in the aircraft design process is to provide detailed information to facilitate the decisions in the design process at the lowest possible cost and with adequate turnaround (turnaround is the required processing time from the point a piece of information is requested until it is finally available to the designer in a form that allows it to be used). In summary, computational methods ought to:

- Allow the simulation of the behavior complex systems beyond the reach of analytic theory.
- Provide detailed design information in a timely fashion.
- Enhance our understanding of engineering systems by expanding our ability to predict their behavior.
- Provide the ability to perform multidisciplinary design optimization.
- Increase competitivity and lower design/production costs.

Computational methods are nothing but tools in the aircraft designer's toolbox that allow him/her to complete a job. In fact, the aircraft designer is often more interested in the interactions between the disciplines that the methods apply to (aerodynamics, structures, control, propulsion, mission profile) than in the individual methods themselves. This view of the design process is often called multidisciplinary design (one could also term it *multidisciplinary computational design*). Moreover, a designer often wants to find a combination of design choices for all the involved disciplines that produces an overall better airplane. If the computational prediction methods for all disciplines are available to the designer, optimization procedures can be coupled to produce *multidisciplinary design optimization* (MDO) tools. In a nutshell, via a combination of analytic methods and simple computational tools, this is what we will try to accomplish in AA241: an optimum aircraft design for a specifically chosen mission.

The current status of computational methods is such that the use of a certain set of tools has become routine practice at all major aerospace corporations (this includes simple aerodynamic models, linear structural models, and basic control system design). However, a vast amount of work remains to be done in order to make more refined non-linear techniques reach the same routine use status. Moreover, MDO work has been performed using some of the simpler models, but only a few attempts have been made to couple high-fidelity non-linear disciplines to produce optimum designs.

Although computational methods are a wonderful resource to facilitate the process of aircraft design, their misuse can have catastrophic consequences. The following considerations must be always in your mind when you decide to accept as valid the results of a computational procedure:

*A solution is only as good as the model that is being solved*: if you try to solve a problem with high non-linear content using a computational method designed for linear problems your results will make no sense.*The accuracy of a numerical solution depends heavily on the sophistication of the discretization procedure employed and the size of the mesh used*. Lower order methods with underresolved meshes provide solutions where the margin of error is quite large.*The range of validity of the results of a given calculation depends on the model that is at the heart of the procedure*: if you are using an inviscid solution procedure to approximate the behavior of attached flow, but the actual flow is separated, your results will make no sense.*Information overload*. Computational procedures flood the designer with a wealth of information that sometimes is complete nonsense! When analyzing the results provided by a computational method do not concentrate on how beautiful the color pictures are, be sure to apply your knowledge of basic principles, and make sure that the computational results follow the expected trends.

Let's examine the status of the more relevant aerospace disciplines to which computational methods have been applied. These include applied aerodynamics, structural analysis, and control system design.

Computational methods first began to have a significant impact on aerodynamics analysis and design in the period of 1965-75. This decade saw the introduction of panel methods which could solve the linear flow models for arbitrarily complex geometry in both subsonic and supersonic flow. It also saw the appearance of the first satisfactory methods for treating the nonlinear equations of transonic flow, and the development of the hodograph method for the design of shock free supercritical airfoils.

Panel methods are based on the distribution of surface singularities on a given configuration of interest, and have gained wide-spread acceptance throughout the aerospace industry. They have achieved their popularity largely due to the fact that the problems can be easily setup and solutions can be obtained rather quickly on today's desktop computers. The calculation of potential flows around bodies was first realized with the advent of the surface panel methodology originally developed at the Douglas company. During the years, additional capability was added to these surface panel methods. These additions included the use of higher order, more accurate formulations, the introduction of lifting capability, the solution of unsteady flows, and the coupling with various boundary layer formulations.

Panel methods lie at the bottom of the complexity pyramid for the solution of aerodynamic problems. They represent a versatile and useful method to obtain a good approximation to a flow field in a very short time. Panel methods, however, cannot offer accurate solutions for a variety of high-speed non-linear flows of interest to the designer. For these kinds of flows, a more sophisticated model of the flow equations is required. The figure below (due to Pradeep Raj) indicates a hierarchy of models at different levels of simplification which have proved useful in practice. Efficient flight is generally achieved by the use of smooth and streamlined shapes which avoid flow separation and minimize viscous effects, with the consequence that useful predictions can be made using inviscid models. Inviscid calculations with boundary layer corrections can provide quite accurate predictions of lift and drag when the flow remains attached, but iteration between the inviscid outer solution and the inner boundary layer solution becomes increasingly difficult with the onset of separation. Procedures for solving the full viscous equations are likely to be needed for the simulation of arbitrary complex separated flows, which may occur at high angles of attack or with bluff bodies. In order to treat flows at high Reynolds numbers, one is generally forced to estimate turbulent effects by Reynolds averaging of the fluctuating components. This requires the introduction of a turbulence model. As the available computing power increases one may also aspire to large eddy simulation (LES) in which the larger scale eddies are directly calculated, while the influence of turbulence at scales smaller than the mesh interval is represented by a subgrid scale model.

Figure 1: Hierarchy of Aerodynamic Models with Corresponding Complexity and Computational Cost.

Computational costs vary drastically with the choice of mathematical model. Panel methods can be effectively used to solve the linear potential flow equation with personal computers (with an Intel 486 microprocessor, for example). Studies of the dependency of the result on mesh refinement have demonstrated that inviscid transonic potential flow or Euler solutions for an airfoil can be accurately calculated on a mesh with 160 cells around the section, and 32 cells normal to the section. Using multigrid techniques 10 to 25 cycles are enough to obtain a converged result. Consequently airfoil calculations can be performed in seconds on a Cray YMP, and can also be performed on 486-class personal computers. Correspondingly accurate three-dimensional inviscid calculations can be performed for a wing on a mesh, say with 192 x 32 x 48 = 294,912 cells, in about 20 minutes on a high-end workstation (SGI R10000), in less than 3 minutes using eight processors, or in 1 or 2 hours on older workstations such as a Hewlett Packard 735 or an IBM 560 model.

Viscous simulations at high Reynolds numbers require vastly greater resources. Careful studies have shown that between 20 and 32 cells in the normal direction to the wall are required for accurate resolution of the boundary layer. In order to maintain reasonable aspect ratio in all the cells in the mesh (for reasons of numerical accuracy and convergence) on the order of 512 cells are necessary in the direction wrapping around the wing, and at least 64 cells are required in the spanwise direction. This leads to over 2 million cells for a minimally resolved viscous wing calculation. Reynolds Averaged Navier-Stokes calculations of this kind can be computed in about 1 hour on a Cray C-90 computer or over 10 hours in a typical high-end workstation. These computations not only require powerful processors; they also need computers with large memory sizes (1-2 Gb for this kind of calculations).

Calculation from VSAERO from Analytical Methods

Hull, keel and bulb arrangement of Whitbread-race sailboat (courtesy of Dr. J. C. Vassberg)

Geometry using the method of images to simulate ground effect (courtesy of Dr. J. C. Vassberg)

Geometry showing surface panelization (courtesy of Dr. J. C. Vassberg)

Pressure color contours and surface streamlines for the underside of the car (courtesy of Dr. J. C. Vassberg)

Unstructured Euler (inviscid) calculation on a generic HSCT (High-Speed-Civil-Transport) configuration. Pressure contours showing Mach cone footprint on vertical and horizontal cutting planes beneath and behind the aircraft.

Airbus A-320 flow solution and unstructured mesh

Parallel computation on an unstructured mesh showing the domain decomposition of 16 processors of a distributed memory computer.

Viscous Calculation on a full configuration Raytheon-Beechcraft Premier business jet. Parallel computation on 32 processors of an Origin2000.

Viscous computation of a full configuration McDonnell Douglas MDXX with optimized wing. Approximate mesh size: 6,000,000 cells. Computation time: 4 hours on 32 processors of an IBM SP2.

Viscous computation of a full configuration McDonnell Douglas MDXX with optimized wing. Approximate mesh size: 6,000,000 cells. Computation time: 4 hours on 32 processors of an IBM SP2. White lines denote mesh boundaries on the multiblock structured mesh.

McDonnell Douglas X2C Blended Wing Body Configuration. Multiblock Mesh.

Detail of viscous mesh for wind tunnel model (notice sting in the rear part of the aircraft) of the Blended Wing Body Configuration. Notice the extreme bunching towards the surface of the airplane in order to resolve the high Reynolds number boundary layer.

Computational methods for structural analysis have reached an even higher level of maturity and several software packages that incorporate this technology are widely used throughout the aerospace industry. These programs are used to perform static and dynamic structural stress analysis in the linear and non-linear regimes, fatigue analysis, heat transfer calculations, etc.

Similarly to computational aerodynamics programs, structural analysis software is composed of numerical methods that solve the discretized structural equations of motion on a suitable mesh that is created from the geometry of the configuration in question. These numerical methods can also be used to optimize the shape of a given structure by repeated application of the analysis procedure with a suitable coupling to an optimization algorithm.

A few links to some of the more popular software packages are included below:

In preliminary aircraft design one is typically more interested in the structural weight and performance of the principal load bearing structures (wing, fuselage, empennage). However, in the detailed design phase, computational structural analysis often includes a very large percentage of the aircraft components and parts that will be subject to static or dynamic loads.

The design of complex linear and non-linear control systems in aircraft has also benefited greatly from the appearance of computational methods. These systems range from components of an aircraft (hydraulic actuators, propulsions systems, fly-by-wire systems) to the control of the speed and attitude of the aircraft itself (autopilots, take-off and landing systems, oscillation damping systems).

Traditionally, control systems for aircraft and aircraft components were designed using linearized models of the plant and classical control theory. Large simplifications of the models were introduced because of the inability to easily handle large numbers of inputs and outputs in the system.

Software packages like MATLAB and SIMULINK, and MATRIXX can routinely simulate the behavior of very large and complex control systems including some limited amount of non-linearities. The figure below shows the interactive design of a control system using SIMULINK.

In this class we would like you to become familiar with a few computational tools so that you have some exposure to common industrial design practices. These computational tools will mainly be used to complement your work in some of the homework assignments. In particular, for aerodynamic design, we will be using the following tools:

- Airfoil design: Panel method with boundary layer coupling
- Airfoil analysis: Two-dimensional Euler solver for transonic flows.
- Wing design and analysis: Three-dimensional full potential flow solver with or without boundary layer coupling.

These tools are meant to assist you in coming up with better aircraft designs, but the bulk of the work will still be done using traditional techniques.