Fundamentals of Flight by Shevell, Richard S. What Makes Airplanes Fly? Aerodynamics for Naval Aviators by Hurt, H. Principles of Aeroelasticity by Bisplinghoff, Raymond L. Missile Aerodynamics by Nielsen, Jack N. Combustion Aerodynamics by Beer, James M. Aerodynamics for Engineers by Bertin, John J. Aerodynamics for Engineers 4th Edition by John J.

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This explains the emphasis onto meshing based on these principles. Mesh adaptation based on error estimation and Chimera techniques are also considered as a way forward for improved mesh and solution quality. Over a wide range of the flight envelope, i. It can be predicted pretty well using the Navier Stokes equations [ 9 ] as basic physical model.

However, physically relevant scales of the flow range from the order of kilometres downstream wake effects down to the order of microns near wall turbulence or even less. For a computational mesh resolving these scales would mean a mesh size of 10 9 points, which results in a nonlinear system of 10 10 equations.

This is also true for the semi-deterministic computations such as LES Large Eddy Simulation which on top need quite a big number of time steps to converge to sufficiently accurate statistics of turbulence. Therefore the smaller scale physical effects need to be modelled, e. The Navier-Stokes equations comprise of 5 differential or integral equations, arising from the conservation laws of mass, momentum and energy.

The open element in these equations is the so-called Reynolds stress tensor, which in 3 dimensions needs to correlate 9 entities - the Reynolds stresses - to the flow variables. By assuming an isotropic behaviour of the fluid medium we end up with 6 quantities for which we seek additional equations. There are however no conservation relations known for a direct closure of the resulting system. Therefore these quantities are modelled using specific assumptions on the flow. The development and calibration of such models depend on the flow phenomena that appear in the aircraft flight envelope.

## Numerical and Physical Aspects of Aerodynamic Flows IV | SpringerLink

Figure 5 provides an overview of the flow conditions and effects that specifically appear at the borders of the envelope. Massively separated flows at high-lift low speed conditions, low local Mach number flows low compressibility flow weekly coupled with the mean flow , strong nonlinearity at buffet boundary and shock boundary layer interaction and finally unsteady effects in separated flows are all situations where numerical simulation suffers low accuracy and very high cost and time.

Flight envelope challenges on CFD. While CFD is widely developed for the cruise design regime it still faces essential challenges towards the borders of the flight envelope. The effects of pressure, surface curvature and surface quality, viscosity and even temperature on local flow behaviour have to be taken into account.

Increasing demands on accuracy have necessitated a move from 2-equation models to more sophisticated Reynolds-Stress models RSM. The objective is to correctly predict with high accuracy all local flow phenomena for a wide range of flow parameters, mainly Mach, flow incidence and Reynolds numbers. For the sake of consistency and generality in prediction it is highly important to avoid any hard switch between turbulence models, depending on the flow conditions.

The RSM model class seems to provide the best results for the whole flow regime. With these considerations at hand, the flow stability is looked at as a separate phenomenon. So-called transition models have been developed to predict the location of transition from laminar to turbulent flow. These models more or less deal with the analysis of amplification factors of relevant modes natural to the flow. Once these factors have reached a certain threshold this is marked as transition location and the turbulence model can be activated.

A remaining difficulty is to predict the onset of flow separation. This physical effect is not fully understood up to now, however, designers need this information for reasons of safety, comfort, and handling qualities of the aircraft. Unfortunately the onset of separation is very sensitive to local properties of the surface roughness, curvature, kinks, etc.

For the correct prediction of separated flow the turbulence model plays a major role and currently best practices on how to predict separation onset using such models is the preferred approach. Even more important to aircraft design is the appearance of massive flow separation. As long as a flow separation is confined to a small area of the wing or tails only, it might be controllable and the pilot can counteract.

## An industrial view on numerical simulation for aircraft aerodynamic design

However, when separation starts to cover large areas this normally drives the aircraft into a complete lift loss and thus a catastrophic situation. Thus massive separation prediction is directly coupled to the prediction of maximum lift properties of the aircraft, which is a limiting factor in take-off and landing performance. This prediction depends on the ability of the turbulence model to detect the local separation and to describe the extension of the separation up to the massive breakdown of the flow.

Figure 6 provides a typical picture of such extension of separated flow areas on an aircraft model in the wind tunnel.

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For this high lift configuration at low Mach number, the local extension grows with increasing angle of attack. Typical successive growth of separation region on aircraft. Starting at the trailing edge of the wing separation increases with increasing angle of attack.

Specifically the inboard region is prone to develop larger areas that finally extend to major parts of the wing surface. CFD simulation in practical industrial application is mainly confined to maximum 2nd order approximations on computational meshes that are specifically dense in those areas of the flow field where some specific features need to be resolved.

However, as we are not sure on the appearance of such phenomena conservative approach is employed with a high number of mesh points.

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But it is clear that this recipe does not solve the problem. Future solutions will hopefully provide means to automatically adapt the mesh and even the discretization accuracy to the local error information. Through the formulation of a so-called adjoint problem it is possible to compute gradient information by which the sensitivity of a quantity like lift, drag or moment against movement or placing of mesh points can be determined [ 10 — 13 ]. Much progress has been achieved using modern iterative solution techniques.

Effective preconditioning schemes are available in context with implicit and multi-grid iterative algorithms for the nonlinear equation system. Numerical dissipation is also more and more under control, thus minimising the artificial or numerical effects in the CFD flow solutions.

A next step will deal with mixed meshes, i.

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The essential element of this so-called HyperFlex approach [ 14 ] is to preserve the typical structured discretization accuracy in most of the flow field while allowing for the flexibility provided by unstructured meshes. This will free the need of an overall structured multi-block mesh for which there is no chance of full automation.

However, a robust industrialized production code for complex applications based on these new methods is not foreseen before Many of the above mentioned topics are still open for further development. The success of aircraft is based on the fact that air flow behaves in a rather controllable manner throughout a wide range of flight conditions. However, towards the border of the envelope some major changes happen, which need careful consideration.

Two main aspects can be observed: shocks appear if Mach number increases beyond a certain geometry-dependent threshold, which makes the flow behaviour non-linear. Heavy loading of the aircraft, i. While the transonic non-linearities e. Finally, aircraft design and data work requires a large amount of flow simulation data. However, this does not just mean a repetition by simulation of what has been done with the wind tunnel in the past.

On the contrary, it is expected that new ways of sorting and organizing simulation processes will save quite a number of those computations. Sophisticated technologies like Design of Experiments, Variable Fidelity Methods, Reduced Order Methods and other techniques will be used to provide a full map of data at a minimum number of high fidelity simulations. For these techniques, error estimators and error propagation control will enable provision of results at guaranteed accuracy.

Looking into nature of flow there is nothing steady. It is only the small scales or high frequencies that are not really recognized by an aircraft and its passengers. This is a lucky point for aircraft flight overall, however, the more we go into detail with our analysis the more we detect that the non-deterministic unsteadiness of flow plays an essential role Figure 7.

Small scales are becoming more and more relevant, specifically in context of simulation of turbulence. But also larger scale unsteadiness poses a problem on numerical simulation. The numerical effort to solve the unsteady flow equations with certain accuracy in space and time is at least one order of magnitude higher than for the steady case.

Slat cove and upper wing surface turbulent flow. Unsteady flow is present in many areas of the flow field. For aircraft development it is essential to know the scales of unsteady effects. Seeking for higher accuracy of a flow solution via subsequent mesh refinement may lead us into the middle of the problem: Resolution of the flow down to very small scales in boundary layers with a steady flow solver probably provokes a non-converging iterative process, because the flow is inherently unsteady.

Therefore new approaches have to be taken to allow automatic switching to an unsteady simulation if the steady solution does not converge. This is a topic for further investigation. Efficiency, reliability etc. Multiple interactions determine what the customer finally sees as the product performance. With increasing mono-disciplinary simulation accuracy it has become necessary now to also model and simulate all relevant interactions.

A major link exists, for example, between the aircraft structure and aerodynamics. Structural deformation due to aerodynamic loads influences the aerodynamic efficiency. This circuit has to be converged until an equilibrium state is achieved. Numerically speaking we have to couple aerodynamic and structural simulation via a local feedback transmission scheme. This type of integrated process is more and more entering the routine simulation for static deformation.

An example of static deformation on a complex configuration is depicted in Figure 8. Static deformation on complex aircraft configuration. Demonstration of coupled aero-structures simulation capability on an A aircraft in high lift configuration. The picture shows the geometrical deformation.

More specific is the simulation of aero-elastic effects, like limit cycle oscillations, buffeting or flutter. Here people are interested in the time accurate behaviour of the interacting mechanism which finally may lead to exceed the structural load limits of the aircraft which could be potentially catastrophic.

This technology is still under development. Even if we were able to do an absolutely exact numerical simulation of aircraft flight we will have to deal with problems: Weather conditions, air turbulence, payload distribution, fuel distribution, engine performance and other parameters may vary. In order to manage these type of uncertainties we need to know about the sensitivity of all of the aircraft coefficients to changing input parameters.

This is quite a new mathematical challenge. Statistical and heuristic methods are being applied; however, the numerical effort can hardly be acceptable. Therefore more efficient approaches have to be developed that would allow a judgement on potential risks. Flow simulation plays a major role in aerodynamic design and its predictive quality is crucially dependent upon both discretization techniques and the capabilities of turbulence modelling over a broad range of configurations and flow situations up to the borders of the flight envelope.

This will directly impact the quality of aircraft design and as a consequence in drag and weight reduction, which in turn lead to reduced fuel consumption and CO 2 emission. These are major objectives of the Green Aircraft Area. With the clear tendency of the airframe industry to base their design cycles much more upon numerical simulation and to perform experiments with a significantly reduced frequency at a later point in the development cycle, it is of utmost importance to increase the reliability and the trust in numerical predictions.

It obvious that improved simulation capabilities will have a rather large impact on improving cost efficiency both with respect to aircraft development cost and aircraft operational cost. With advanced numerical simulation tools becoming less error-prone, this will not only improve the flow simulation alone, but also influence coupled computations, like design optimization, simulations of fluid-structure interaction or multi-disciplinary optimization. The quality of flow simulation has an even stronger impact in these fields where quantitative errors easily multiply. Thus the whole design chain will become not only more competitive, but also more productive, contributing to the reduction of the time-to-market of the products and to the reduction of aircraft development costs, leading in turn to stable or even reduced travel charges.

Airbus - together with major research partners and companies in the field - is working on the FuSim [ 15 ] initiative to develop Aerodynamics and Flight Physics towards a new paradigm of simulation. This treats all aspects of simulation physics, turbulence modelling, mathematics, algorithms, hardware, software, computer science, information technology, man-machine interface, overall system, data handling, applications, etc.

Enormous effort is needed to develop the simulation capabilities to the level required to be fully deployed for aircraft design.

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Major centres of expertise in numerical simulation in several countries are working together on this initiative with emphasis on specific aspects of simulation technology and application. In this paper we have not tackled the extension to numerical optimization. This is another field of mathematical activities where we are looking for fast and comprehensive search algorithms for local and global optima of a variety of cost functions.