## Abstract

The wide range of uses of computational fluid dynamics (CFD) for aircraft design is discussed along with its role in dealing with the environmental impact of flight. Enabling technologies, such as grid generation and turbulence models, are also considered along with flow/turbulence control. The large eddy simulation, Reynolds-averaged Navier–Stokes and hybrid turbulence modelling approaches are contrasted. The CFD prediction of numerous jet configurations occurring in aerospace are discussed along with aeroelasticity for aeroengine and external aerodynamics, design optimization, unsteady flow modelling and aeroengine internal and external flows. It is concluded that there is a lack of detailed measurements (for both canonical and complex geometry flows) to provide validation and even, in some cases, basic understanding of flow physics. Not surprisingly, turbulence modelling is still the weak link along with, as ever, a pressing need for improved (in terms of robustness, speed and accuracy) solver technology, grid generation and geometry handling. Hence, CFD, as a truly predictive and creative design tool, seems a long way off. Meanwhile, extreme practitioner expertise is still required and the triad of computation, measurement and analytic solution must be judiciously used.

## 1. Introduction

Nowadays, the uses of computational fluid dynamics (CFD) in aerospace engineering are vast, extending beyond traditional design conditions (Spalart & Bogue 2003) to numerous peripheral components and aerospace aspects. These include cabin ventilation and noise (also encompassing outflow valves and their acoustic influence), avionics/electronics, combustion and fire management. Also, there are environmental issues such as wake vortices, during and prior to take-off the resilience of craft/engines to airport environment (Strelets 2001) and engine ground vortices (Yadlin & Shmilovich 2006). The latter self-generated vortices can cause catastrophic engine damage (this is mainly owing to large debris ingestion). Owing to space constraints, it is not possible to cover all of these aspects here. Furthermore, the current issue is restricted to fixed wing aircrafts and excludes rotorcraft or hybrids (Spalart *et al*. 2003).

The environmental impact of aviation is currently very much to the fore and the reduction of noise and carbon dioxide emissions is currently a key European and US aerospace priority. To reign in the latter, the European Parliament is seeking to introduce extra charges (via a quota system similar to the one that industry is subjected to) starting from 2011 based on carbon dioxide emission levels. For engines, the noise sources can be broken down into turbomachinery noise (relating to rotating and stationary blades in close proximity for fans, turbines and compressors), core noise (due to the combustion process) and jet noise. For airframe noise, sources are high-lift devices such as slats and flaps and also the landing gear. Discussion of computational aeroacoustics modelling of the latter can be found in Hedges *et al*. (2002) and Souliez *et al*. (2002). However, this current issue focuses on jet noise.

A massive proportion of an aircraft's cost is in the avionics/electronics. With fly-by-wire, unmanned vehicles, automatic landing and the large amounts of electronics monitoring contained inside modern gas turbine aeroengines the application of CFD to electronics/avionics is an area of emerging importance. The environment is generally hostile. However, CFD application expertise in electronics/avionics (Tucker 1997) seems to lag that in other aerospace areas and so this is not addressed here. However, it is sufficient to say that many electronic/avionic system flows involve non-aerodynamic geometries and consequently exhibit massive separation and hence serious turbulence modelling challenges (Tucker & Liu 2005). This is also likely to be true of cabin ventilation flows.

This theme issue has papers in the following areas: turbulence (Gatski *et al*. 2007); flow/turbulence control (Carpenter *et al*. 2007); propulsive jet dynamics and noise (Birch *et al*.); aeroengine external air systems (Dawes 2007); aeroengine internal air systems (Chew & Hills 2007); aeroelasticity for aeroengines and external aerodynamics (Bartels & Sayma 2007); design optimization (Keane & Scanlan 2007); and unsteady flow modelling (Hassan *et al*. 2007).

## 2. Turbulence

Obviously, at the high Reynolds numbers experienced with most aerospace flows, turbulence modelling is a key issue and so the review of Gatski *et al*. (2007) is dedicated to this important area. The modelling of complex time-varying turbulent structures that involve a large range of temporal and spatial scales (the smallest of which is the *Kolmogorov* microscale) has always been the weak link in the numerical prediction of fluid flows. This is perhaps not surprising since (although the Navier–Stokes do provide a complete description of turbulence) as Richard Feynman said ‘Turbulence is the last great unsolved problem in classical physics’.

The move to explore off-design conditions such as aircraft at take-off and landing, where there are flaps at high angles of deflection and hence massively separated flows, has recently drawn greater attention to turbulence models and their inadequacies (Spalart & Bogue 2003; Tucker 2006). The large-scale, geometry-dependent eddies arising from massively separated flows ideally need special eddy-resolving turbulence modelling treatments. However, to resolve scales *approaching* the Kolmogorov inertial sub-range requires especially fine numerical grids and ideally higher-order schemes applicable to unstructured meshes. Eddy-resolving strategies that reduce grid demands (through incorporating a degree of modelling) such as large eddy simulation (LES) and detached eddy simulation (DES; Spalart 1999) are mostly discussed in the article by Secundov *et al*. (2007). With LES, the larger eddies are resolved and the smaller ones modelled. DES is similar but full Reynolds-averaged Navier–Stokes (RANS) modelling is used near walls, i.e. it is a hybrid LES–RANS method. Eddy-resolving methods are potentially important for the exploration of approaches to the reduction of turbulence-generated noise where the delicate control of turbulence interactions is necessary as well as the accurate prediction of turbulence information. However, the key questions are as follows: when will computer power be sufficient for their practical design use and meanwhile what is their value? Secundov *et al*. (2007) grapple with this question.

The review of Gatski *et al*. (2007) gives the state-of-the-art and RANS development priorities along with much background information on RANS modelling. This turbulence modelling approach is still a mainstay of aerospace design and will, according to estimates, be so for many years to come. Indeed, it seems important to note that the design of an aircraft requires many thousands of simulations and so in many aerospace companies solution of even the RANS equations is relatively rare with Euler or even full potential flow solutions (Samant *et al*. 1987) being made. Even the latter at design conditions can predict incremental drag for geometry changes with acceptable accuracy (Tinoco 2001). However, it should be stressed that incremental changes are considerably easier to quantify than actual drag values. However, knowledge of the latter is vital if the designed aeroplane is to meet its design specifications and not end up languishing in a desert scrap heap, hence RANS will soon dominate simpler design methods. The averaging processes, necessary to give tractable solutions, in both RANS and LES are compared by Gatski *et al*. (2007); the discussion includes the use of temporal averaging in LES (standard LES uses averaging in space). Such information is important for eventually conceptualizing sound hybrid LES–RANS methods. Currently, these are showing promising results (albeit at considerable computational expense) for flows where RANS models fail. However, the interfacing of time- and space-averaged equations, although easy, is theoretical questionable. Hence, the detailed discussion is not just helpful in setting out the foundations for RANS models. Gatski identifies the following current challenges: transition modelling, relaminarization, separation and flow control. It perhaps seems doubtful with the complex physics involved in these processes that RANS modelling will ever be adequate. As noted by Spalart & Bogue (2003), unsteady RANS (as with virtually all other applications) is unlikely to be of use for flow control. The fascinating issue of multiple solutions arising as a result of the chosen RANS model is also briefly addressed by Gatski *et al*. (2007). Further discussion on such issues can be found in Rumsey (2006) and Rumsey *et al*. (2006).

## 3. Flow/turbulence control

Turbulence governs airframe drag and so to reduce environmental emissions (from excessive fuel burn) clearly, it is important to control it. Carpenter *et al*. (2007) outline the various drag sources and their relative importance. Aerodynamics design has improved so much that now over 50% of aircraft drag is due to skin friction, hence there is a pressing need to reduce it. Intricate, elongated near-wall structures (sublayer streaks) play a key role in the generation of skin friction. Hence, a novel numerical model for sublayer streak prediction is presented by Carpenter *et al*. (2007). Also, practical aspects relating to the control of near-wall structures are discussed along with elements of flow control in general. The use of microelectromechanical systems (MEMS) and other active control devices in aerodynamic flow control (for both the propulsion units—especially with respect to jet noise—and airframes) is finding increasing interest. Hence, the assessment of the future potential of such technologies through numerical modelling is important. A deeper understanding of near-wall behaviour and streak generation is also likely to be of importance in improving the theoretical foundations of RANS, hybrid LES–RANS and pure LES methods, thus adding to the importance of the work of Carpenter *et al*. (2007). As noted by Pope (2004), at cruise, a Boeing 777 wing has approximately 10^{8} streaks (these estimates probably do not include the effects of pressure gradient and sweep) presenting a key LES resolution issue. Similar stark statistics relating to spatial and temporal scales, but this time for the fuselage of an Airbus A340-300, are brought out by Carpenter *et al*. (2007). According to their estimates for the Airbus 340-300, there are 2000 streaks m^{−1} and approximately 20×10^{8} for the whole fuselage. Indeed, it is primarily owing to these structures that Spalart & Bogue (2003) estimate it will not be possible until 2050 to carry out a LES of a full airframe and direct solution of the Navier–Stokes equations without recourse to turbulence modelling will have to wait until 2080. It is these daunting statistics that the hybrid LES–RANS methods are intended to overcome. This being achieved by covering the streaks with a RANS model.

The projected demand for air transport suggests a doubling of the world aircraft fleet by 2020. Hence, it is becoming urgent to take steps to reduce the environmental impact of take-off noise. In the worst case, this can be more than just annoying. It is potentially a contributory factor towards illnesses such as hypertension (Rosenlund *et al*. 2001). Also, continual reductions in permitted take-off noise levels are placing the commercial viability of more established aircraft designs in jeopardy. At take-off, a major noise source is the propulsive jet. The article by Secundov *et al*. (2007) largely focuses on the RANS modelling of various jets and the prediction of far-field noise along with the escape trajectories of acoustic rays from within jets.

## 4. Propulsive jet dynamics and noise

Secundov *et al*. (2007) outline the daunting task of using RANS to model the substantially different flow physics for isothermal, non-isothermal, sub- and supersonic jets for the range of complex nozzle geometries found in different aerospace contexts. Modelling challenges identified are twin nozzle rocket plumes, jets with co-flow and wall jets. Study of the last relates to jet blast, i.e. the damage to cargo, small craft and buildings from propulsive jets. Co-flowing jets occur in commercial aircraft engines. The surprising lack of understanding of the flow physics of even basic jets is outlined.

Most importantly, Secundov and colleagues show that for jets with co-flow, the flow structure is very sensitive (with respect to concentricity) to inflow conditions potentially rendering much of the past data for this configuration invalid. It is well known that jets are highly sensitive to external environmental conditions but the concentricity aspect is new. The addition of a pylon, which is representative of the real engine operating geometry, improves the situation. Hence, this aligns with the work of Dawes (2007) in this issue, which strongly advocates the need to model real geometry influences. Spalart & Bogue (2003) also raise this matter.

Secundov and colleagues highlight RANS models, which can be of value; for example, in scenarios where the global flow structure complexity is pressure and not turbulence stress driven. Also, the importance of appropriately modelling inflow conditions is noted and the general incomplete information on this with regard to measurements is highlighted. Hence, it appears that more work on creating adequate validation data is required, with perhaps both experimentalists and CFD practitioners being brought together at the outset of new experimental programs. In this way, it could be ensured that the measured data have adequately defined boundary conditions for the meaningful validation and refinement of numerical models. Indeed, preliminary CFD simulations could obviously contribute to the design of the experiments.

Secundov and colleagues also discuss the use of LES in a jet noise context. LES results incorporate a new use of the modified Eikonal equation to explore how instantaneous velocity (which vary dramatically from the mean) and temperature gradients deflect acoustic rays. The Eikonal equation is an approximation to the wave equation for short waves. Acoustic waves are shown to be dramatically deflected (in relation to mean velocity and density gradients) by turbulence. The turbulence is shown to make the jet opaque to short waves. Hence, acoustic sources in one quadrant do not produce acoustic rays in others.

With regard to industrial use of LES, it is concluded that issues of problem definition (especially with respect to inflow boundary conditions), solution uniqueness, near-wall modelling, transition issues and grid structure along with its implications on filtering (to achieve spatial averaging) are of potentially greater importance for practical jet flows than the LES model itself. The latter being theoretically questionable. This conclusion implies that much time is spent on the implicit LES (where the numerical discretization partly acts as an LES model; see Boris *et al*. 1992) versus LES debate. It seems focused that LES simulations should provide flow physics insights and help with RANS model development. The value of LES at impacting on the design context more directly as yet remains unclear.

The full coupling of the structural dynamics, pilot input/response (Spalart & Bogue 2003) and also manufacturing constraints with aerodynamic design is an ultimate future goal. This coupling allows quicker, safer and more innovative aerospace designs.

## 5. Aeroelasticity for aeroengines and external aerodynamics

Bartels & Sayma (2007) present an extensive review on the state-of-the-art for both aeroelasticity in airframe and turbomachinery design. NASA's recent mandate to deliver payloads to Mars and ultimately return samples to Earth has brought about the need to model highly flexible, inflatable thin membrane decelerators, reminiscent of parachutes. This has motivated the need for aeroelasticity studies that can model highly nonlinear structures with nonlinear material properties. The high temperature of re-entry needs coupling of the thermal fields in the fluid flow and structure. Full validation of such simulations presents a significant challenge. However, Bartels & Sayma (2007) report encouraging agreement for the measured maximum deflection at a high Mach number. This work perhaps represents the state-of-the-art in nonlinear aeroelasticity modelling. Most aeroelasticity validations involve lower-order quantities.

A fuller comparison of model performance assessment with actual flow field (mean velocities and turbulence statistics) and surface heat transfer data would help to better diagnose model deficiencies.

Presumably, inflatable decelerators exhibit massively separated flow. Hence, ideally these aeroelasticity studies should make use of hybrid LES–RANS techniques. However, due to computational expense, aeroelasticity work using this turbulence modelling approach seems to be rare. Bartels & Sayma (2007) discuss the use of reduced order models as well as the extreme of full nonlinear aeroelasticity models. These will form an essential ingredient in more routine design studies, computer-driven design optimization procedures and perhaps models of the way pilots interact with aircraft. With design optimization, for given targets and constraints (including, for example, those arising from the manufacturing process and also component weights), mathematical models coupled with CFD are used to seek optimal solutions. These are now an important part of aerospace engineering.

## 6. Design optimization

The aerospace design-led optimization paper by Keane & Scanlan (2007) gives some idea of the daunting task the aerospace design engineer faces. Many challenges arise from the numerous conflicting design requirements. Keane & Scanlan (2007) review design search and optimization approaches. A multi-objective, multidisciplinary example for a transonic civil aircraft design is given. The analysis encompasses structural integrity, weight, manufacturing cost and aerodynamic performance. Strength and weight are modelled using semi-empirical schemes based on aerospace company practice. Costing is component based and considers elements such as spars, ribs and skins. The analysis requires the automated linking of numerous different codes. Hence, presumably good scripting skills are needed. Despite the numerous elements (CAD engine, mesh generator, analysis codes, post-processing and optimization tools) and the CFD solution being Euler based, it still proved to be the most expensive element needing about half the total solution time. Perhaps not unexpectedly, around 50% of CFD solutions in the design optimization cycle failed. This shows the need for improved automatic mesh generation and CFD solver technology. Clearly, the use of advanced turbulence modelling strategies (except for more basic design optimizations) is some way off—the designer, needing to balance so many things, is always forced to use methods that are less expensive, and thus less accurate, than the pure analyst. It seems probable that computational-based optimization tools, in an environment with many diverse requirements that must be held in tension, offer a rational basis for design decision making, which must make a very positive impact on the design process.

## 7. Unsteady flow modelling

Hassan *et al*. (2007) discuss techniques for solving unsteady flow equations with moving unstructured meshes used to resolve either flow features or boundary movement. As might be expected, such problems present the major challenge of maintaining a valid mesh. Approaches suitable for problems with extreme boundary movement are discussed. To remove the serial bottlenecks discussed by Dawes (2007) (see §8), these involve parallel local remeshing. Such approaches are important for store release, formation flying (Aftosmis *et al*. 1997), air refuelling, extreme control surface movement, aeroelasticity for highly flexible structures (as discussed by Bartels & Sayma (2007)) and design optimization—when the development of radically different design solutions is sought. Flow-based adaptation potentially lends itself to LES and hence appears to be an important emerging area. Explicit and implicit temporal integration schemes are contrasted. New approaches for alleviating the severe Courant–Friedrichs–Lewy condition constraint for explicit schemes are discussed. Again, the question of whether the potentially more efficient, for certain classes of problems, explicit schemes can be implemented is strongly linked to adequate mesh control. However, clearly an implicit solver is most desirable. Also, spatial truncation errors will interact with those from the temporal schemes. Hence, these two elements should be carefully selected to ensure that they work in harmony and are compatible with the class of problem being considered.

## 8. Aeroengine external air systems

Dawes (2007) charts the historical evolution of CFD analysis for external systems related to aeroengine flows (i.e. blade-related flows). This spans simple idealized geometries to the current status where, to affect engine performance, real geometry (elements of geometry that have largely been ignored in the past) influences must be taken into account. According to Spalart & Bogue (2003), real geometry modelling is also essential for airframe aerodynamics. Dawes (2007) presents a grand vision utilizing technology from the computer games industry. The work gets to grips with the key issues involved in taking CFD from being an analysis tool to a true aerodynamics design tool that does not stifle creative activity. The use of CFD in the games/graphics industries is more advanced than one might expect and the industry now provides much advanced computational modelling technology. With the initial use of body-fitted grids in turbomachinery engineering, boundary representation geometry models were perfectly adequate. However, with the drive towards modelling the full geometry, such approaches make geometry modification slow with CAD geometry clean-up (to get watertight geometry) taking a substantial time. Hence, the case for moving from explicit to implicit geometry is made, the use of signed distance fields for the latter being advocated. Indeed, this distance field is also necessary in many robust turbulence models and can, as noted by Dawes (2007), be used as a basis for generating high-quality surface meshes. As noted by Spalart & Bogue (2003), with a mind on turbulence modelling, the capability to model real geometry will enable a clearer picture of the capabilities of turbulence models for certain complex geometry applications. Parallel processing (and partly memory-based) bottlenecks, arising from inherently serial elements such as geometry modelling, mesh generation and partitioning, post-processing and data exchange between different packages, are discussed by Dawes (2007). With reasonably effective use now being made of parallel processing for solution of the flow equations, the need to remove these bottlenecks is becoming more apparent. This point, along with the need to model real geometry and hence use unstructured solvers, is echoed by Chew & Hills (2007).

## 9. Aeroengine internal air systems

Chew & Hills (2007) focus on aeroengine internal air systems. Since up to 5% of the engine's power can go into supporting these systems, through, for example, supplying blade cooling, they are of significant importance. These enclosed rotating system flows exhibit complex physics with many aspects being reminiscent of geophysical flows. LES has its origins in such flows. It is clear from this paper that, for internal air systems, LES holds promise. Generally, due to the complex flow physics, RANS models perform poorly for these flows. The need for robust meshing (and automatic adaptation) especially in a design optimization context is again identified. The internal air systems can have significant geometrical complexity. It is clear that design optimization is beginning to play a role in internal air systems and helping with the practical uptake of design improvements. The need for greater automation of the CFD process to reduce user dependence on results is identified. In the multiphysics, internal air systems environment, where the thermal coupling of the solid and fluid zones is important, robust automation becomes even more important. The internal air systems discussed by Chew & Hills (2007) feed passages inside turbine blades that provide blade cooling. The computation of these flows, which again present severe turbulence and geometry modelling challenges, is discussed by Iacovides & Raise (1999).

## 10. CFD and measurements

For much of the work discussed above, it appears that there is a lack of detailed measurements to provide validation and even a basic understanding of the flow physics. This makes serious assessment of turbulence models and, in some cases, development impossible. Frequently, for aerodynamics configurations, wind-tunnel data just consist of global data on lift and drag coefficients with perhaps surface pressure measurements. Also, wind-tunnel influences can be excessive. This is especially a problem when studying high-lift configurations where severe flap deflections can generate large vortices adjacent to the wind-tunnel wall. However, for serious assessment and refinement of turbulence model performance, turbulence statistics data, free from wind-tunnel wall interference, are necessary. For jets, inflow conditions are generally inadequately defined, the measurements being focused on the actual jet flow away from the outlet. Again, this makes serious assessment of numerical modelling extremely difficult. Also, for jets with co-flow, it seems to have taken a surprisingly long time for the sensitivity of the flow-to-inflow concentricity to come to light. This must be due to experimentalists restricting measurements to just one plane and erroneously taking axisymmetric flow for granted. This is also, in a sense, reminiscent of internal air systems in gas turbine aeroengines. For many years, axisymmetric flow was assumed and complex flow instability mechanisms ignored. Importantly, when wind-tunnel tests are repeated, shock locations can vary by 20% of the wing chord. However, repeat measurements are seldom made. Hence, these ‘uncertainty data’ cannot be supplied to the CFD practitioners. In the light of this, it seems surprising, considering the potential data scatter, that most CFD simulations seem to capture shock location very well. The surprising level of agreement perhaps reflects the fact that CFD is still a heavily postdictive process. With many applications, the CFD practitioner has to make a wide range of modelling assumptions. Through these, solution control can be exerted. This appears especially true for the prediction of jet noise.

At perhaps a more fundamental level, it has been fairly widely assumed that the Kármán constant (*κ*), used in Prandtl's mixing-length expression, is universal, having an established value of approximately 0.41. However, recent evidence suggests that the ‘constant’ is more dependent on the nature of the boundary layer with values in the range 0.38<*κ*<0.45 (George 2006). Spalart (2006) notes that for modern passenger aircraft, a 2% *κ* decrease will cause a 1% decrease in predicted drag. This difference is of extreme importance. If the aircraft, which is initially sold and manufactured based on CFD, does not achieve the expected range, then the consequences for the manufacturer could be disastrous. Hence, even basic boundary layer measurements to establish key CFD code constants are of high importance. As noted by George (2006), improved wind-tunnel facilities are necessary. Then boundary layer measurements for flows that have sufficiently high Reynolds numbers to be considered truly turbulent can be made. The same is true for jets for which, when heated, the Reynolds number can drop fast. Much of the available jet flow and noise data, particularly at lower Mach numbers, has been taken at relatively low Reynolds numbers, and so this data seems suspect. This is important—the effective Mach number (based on the velocity difference between the primary and fan streams) of hot jets encountered in real airplane applications can be low. Hence, it seems important to create high-quality datasets, both for canonical flows and complex geometries. Currently, the trend unfortunately seems to be for the data quality to decrease with increasing realism in geometrical complexity and testing.

I had encouraged authors to be prophetic in this theme issue but sadly they (perhaps wisely) refrained. Chapman *et al*. (1975) predicted the demise of the wind tunnel in around 1985. However, turbulence is still the weak link. Both understanding and directly predicting turbulence needs powerful computers and the ability to visually interpret the data produced. Processor power increases are being strongly driven by the children's computer games industries and even computer graphics (technology in this area being driven by blockbuster movies such as Jurassic Park). Perhaps the next generation will have access to truly predictive CFD technology. Meanwhile, extreme practitioner expertise is still required and the triad of computation, measurement and analytic solution must be judiciously used.

## Footnotes

One contribution of 9 to a Theme Issue ‘Computational fluid dynamics in aerospace engineering’.

- © 2007 The Royal Society