Case Studies for Conceptional Design of Supersonic Transport Aircraft.pdf

1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/367693760 Case Studies for Conceptual Design of Supersonic Transport Aircraft Technical Report · February 2023 CITATIONS 0 READS 3 1 author: Some of the authors of this publication are also working on these related projects: Mesh Generation View project Independent CFD Reasercher View project Ideen Sadrehaghighi CFD Open Series 80 PUBLICATIONS 105 CITATIONS SEE PROFILE All content following this page was uploaded by Ideen Sadrehaghighi on 01 February 2023. The user has requested enhancement of the downloaded file.

2. CFD Open Series/Patch 2.55 Edited and Adapted by: Ideen Sadrehaghighi A N N A P O L I S , M D High Speed Civil Transport Concept

3. 2 Contents List of Figures: .....................................................................................................................................................................2 1 Case Studies for Conceptual High Speed Transport Aircraft....................................... 5 1.1 Case Study 1 - Generic High Speed Civil Transport (HSCT) Configuration....................................5 1.2 Case Study 2 - Concept Study for a Mach 6 Transport Aircraft...........................................................6 1.2.1 Introduction.................................................................................................................................................6 1.2.2 Airplane Shape Definition by Multidisciplinary Multiple-Point Design Optimization...................................................................................................................................................................8 1.2.3 Propulsion Integration by Multidisciplinary Design Optimization....................................14 1.2.4 Structure Model & Internal Layout..................................................................................................16 1.2.5 Sonic Boom Assessment & Mitigation............................................................................................18 1.2.6 Design Verification.................................................................................................................................22 1.2.7 Conclusions ...............................................................................................................................................23 1.2.8 References..................................................................................................................................................24 1.3 Case Study 3 - Aerodynamic Analysis of a Supersonic Transport Aircraft at Low and High Speed Flow Conditions.......................................................................................................................................25 1.3.1 Abstract.......................................................................................................................................................25 1.3.2 Introduction..............................................................................................................................................25 1.3.3 Aircraft Static Stability..........................................................................................................................27 1.3.4 Aerodynamic Analysis ..........................................................................................................................29 1.3.4.1 Aircraft Configuration...............................................................................................................29 1.3.4.2 Flight Envelope............................................................................................................................32 1.3.4.3 CFD Test Matrix...........................................................................................................................33 1.3.4.4 Grid Generation...........................................................................................................................33 1.3.4.5 CFD Modeling and Numerical Discretization..................................................................35 1.3.4.5.1 The FLUENT Solver..............................................................................................................35 1.3.4.5.2 The SU2 Solver.......................................................................................................................35 1.3.4.5.3 Remarks on JST Scheme ....................................................................................................36 1.3.4.5.4 Effect of Dissipation Operator.........................................................................................37 1.3.5 Computation of the Aircraft Aerodynamic Coefficients and Aerodynamic Center......37 1.3.6 Aerodynamic Results.............................................................................................................................38 1.3.6.1 Force and Moment Coefficients Versus Attitude...........................................................39 1.3.6.2 Force and Moment Coefficients Versus Mach.................................................................41 1.3.7 Conclusions ...............................................................................................................................................46 1.3.8 Appendix A ................................................................................................................................................47 1.3.9 References..................................................................................................................................................47 List of Tables: Table 1.3.1 CFD Test Matrix..........................................................................................................................................32 Table 1.3.2 Position of the aerodynamic center: comparison between ANSYS-FLUENT and SU2..45 Table 1.3.3 CFD results in terms of aerodynamic force and moment coefficients. Ansys-Fluent code. .......................................................................................................................................................................................................47 Table 1.3.4 CFD results in terms of aerodynamic force and moment coefficients. SU2 code. Clean configuration...........................................................................................................................................................................48 List of Figures: Figure 1.1.1 CFD Grid Boundaries Result for Euler Analysis of HSCT Wing-Body in.............................. 5

4. 3 Figure 1.2.1 Aerodynamic performances of the ATLLAS Mach 6 reference design configuration, ATLLAS M6 RD (blued dots), compared with published data for different airplanes with similar mission objectives................................................................................................................................................................... 9 Figure 1.2.2 Airframe-MDO works flow (DLR-AS)..............................................................................................10 Figure 1.2.3 CFD computation of the resulting flow field of the ATLLAS M6 RD during cruise (DLR- AS). Top: full ............................................................................................................................................................................10 Figure 1.2.4 Turbo-Ram-Jet Performances Data. (DLR-SART).......................................................................11 Figure 1.2.5 Scheme of force-balance used for trim estimations (DLR-AS)..............................................11 Figure 1.2.6 Modular Grid Generation arrange strategy showing the different modules (DLR-AS)12 Figure 1.2.7 Impact of the horizontal tail deflection on center of pressure location for different Mach numbers.....................................................................................................................................................................................12 Figure 1.2.8 MDO results for a 1-point, cruise, optimization (DLR-AS)......................................................13 Figure 1.2.9 MDO on-going results for a 3-point (acceleration, beginning- and end of cruise) optimization. Top: configuration changes after arbitrary number of MDO loops. Bottom: MDO- convergence (DLR-AS) ........................................................................................................................................................14 Figure 1.2.10 MDO process for the propulsion integration (ONERA).........................................................15 Figure 1.2.11 MDO parameterization for the propulsion integration (ONERA).....................................15 Figure 1.2.12 Preliminary bending analysis of the aircraft’ structure (FOI)............................................17 Figure 1.2.13 Mass model left and variation of the centre of gravity location as a function of fuel charging (FOI & DLR-AS)....................................................................................................................................................17 Figure 1.2.14 A Multi-lobe Tank extension module is successfully used for fast design of the internal volume (DLR-SART).............................................................................................................................................................18 Figure 1.2.15 CFD near field pressure footprint extraction from a DLR CFD solution (ONERA).....18 Figure 1.2.16 Example of delta pressure carpet prediction (UPMC)...........................................................20 Figure 1.2.17 Near pressure field modifications by spikes, aero-jet-spikes and energy deposition. Left from top to bottom: energy deposition case B; energy deposition case B’, aero-jet-spike, 2nd generation spike. Right top: pressure signature. Right bottom: aerodynamic performances (DLR-AS) .......................................................................................................................................................................................................21 Figure 1.2.18 Computed surface pressure distribution for the HYCAT configuration. Left: leeward side. Right: windward side (ESA-ESTEC) ....................................................................................................................22 Figure 1.2.19 Computed pitching moment coefficient vs. AoA for the HYCAT configuration (ESA- ESTEC)........................................................................................................................................................................................23 Figure 1.3.1 The aircraft configuration with dimensions.................................................................................28 Figure 1.3.2 Design parameters of the aircraft configuration ........................................................................30 Figure 1.3.3 The Concorde flight envelope in the altitude-airspeed plane with iso-Mach lines [26,29] .......................................................................................................................................................................................................31 Figure 1.3.4 Subsonic computational domain with mesh on the aircraft wall and symmetry plane .......................................................................................................................................................................................................33 Figure 1.3.5 Typical boundary layer prismatic cells with mesh on the aircraft wall and symmetry plane............................................................................................................................................................................................34 Figure 1.3.6 Supersonic computational domain with mesh on the aircraft wall and symmetry plane .......................................................................................................................................................................................................34 Figure 1.3.7 Body (XB, YB, ZB) and Wind (XW, YW, ZW) Reference Frames with Aerodynamic Force and Moment Coefficients.............................................................................................................................................................38 Figure 1.3.8 Aircraft root chord dimension and wing leading edge position with respect to the nose .......................................................................................................................................................................................................39 Figure 1.3.9 Pitching moment coefficient versus a and for different positions of the pole reduction point along with the wing Root Chord (RC) for M¥ = 2.0 and ReLref = 1.01 x108.........................................39

5. 4 Figure 1.3.10 Figure 10. Lift and drag coefficients versus a. Comparison between ANSYS-FLUENT and SU2 for M∞ = 0.5, 0.8, 1.5, and 2.0..........................................................................................................................40 Figure 1.3.11 Pitching Moment Coefficients versus a. Comparison between ANSYS-FLUENT and SU2 for M∞ = 0.5, 0.8, 1.5, and 2.0...................................................................................................................................41 Figure 1.3.12 Mach contours at M∞ = 0.5, 0.8, 1.5, and 2.0 and for α= 0∘..................................................41 Figure 1.3.13 Pressure contours and surface streamlines at M∞ = 0.5 and α = 10∘..............................42 Figure 1.3.14 Pressure contours at M∞ = 0.8 and α = 5∘ ...................................................................................42 Figure 1.3.15 Pressure contours at M∞= 1.5 and α = 5∘....................................................................................43 Figure 1.3.16 Pressure contours at M∞ = 2.0 and α = 3∘...................................................................................43 Figure 1.3.17 Force and moment coefficients versus M∞. Comparison between Ansys-Fluent and SU2...............................................................................................................................................................................................44 Figure 1.3.18 Figure 18. Shift of aerodynamic center with Mach number: Concorde literature data (solid line), CFD results (dotted data) [26].................................................................................................................44 Figure 1.3.19 Axial and normal force coefficients versus M∞ in supersonic flow conditions. ..........45

6. 5 1 Case Studies for Conceptual High Speed Transport Aircraft 1.1 Case Study 1 - Generic High Speed Civil Transport (HSCT) Configuration Figure 1.1.1 illustrate data visualization of a generated configuration derived from a Boeing HSCT design case for Mach 2.41. The configuration consists of 10 components, engine pylons are not yet included. Wing and horizontal and vertical tail components are spanwise defined, fuselage and engines are axially defined components. The wing has a subsonic leading edge in the inner portion and a supersonic leading edge on the outer portion. For this study a minimum of support, airfoils is used to get a reasonable pressure distribution a rounded leading edge section in most of the inner wing and a wedge-sharp section in the outer wing portion define the basic shape of the wing. Wing root fillet blending, the smooth transition between rounded and sharp leading edge and the tip geometry are effectively shaped by the previously illustrated wing keys, the fuselage here is a simple slender body requiring just the baseline body tool with elliptical cross sections. Preprocessing input data for CFD requires providing a grid surrounding the configuration. For application of either structured or unstructured grids additional geometric shapes need to be provided. In the case of the generic HSCT with given supersonic flight Mach number the far-field boundary is chosen to engulf the expected bow shock wave (Figure 1.1.1-a) and a cross sectional grid for both wing and body is generated, either as simple algebraic trajectories or using elliptic equations. Short runs using an the inviscid flow Euler option of a flow solver2 were carried out on a coarse (33 x 81 x 330) grid, here only to get an idea about the needed wing section and twist modifications for acceptable pressure distributions. Visualization of the results in various grid surfaces is needed, like pressure distributions in cross section planes as shown in Figure 1.1.1-b. 1 Kulfan, R. High Speed Civil Transport Opportunities, Challenges and Technology Needs. Lecture at Taiwan IAA 34th National Conference, 1992. 2 Kroll, N., Radespiel, R. An Improved Flux Vector Split Discretization Scheme for Viscous Flows. DLR-FB 93-53, 1993. Figure 1.1.1 CFD Grid Boundaries Result for Euler Analysis of HSCT Wing-Body in Supersonic flow M∞ = 2.4 - Courtesy of Sobieczky (a) farfield boundary is chosen to engulf the expected bow shock wave (b) Pressure distributions in cross section planes

7. 6 1.2 Case Study 2 - Concept Study for a Mach 6 Transport Aircraft Authors : J.M.A. Longo*, R. Dittrich1, D. Banuti1, M. Sippel1,2, J. Klevanski1,2, U. Atanassov1,2, G. Carrier3, Ph. Duveau3, I. Salah El Din3, R. Thepot3, A. Loubeau4, F. Coulouvrat4, R. Jarlas5, H. Rabia5, D. Perigo6, J. Steelant6 Affiliations : *Head Spacecraft Branch, Lilienthalplatz 7, 38108 Braunschweig 1German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Braunschweig, Germany 1,2 German Aerospace Center (DLR), Institute of Space Systems, Bremen, Germany 3Office National d’Etudes et de Recherches Aérospatiales (ONERA), FR-92190 Meudon, France 4Université Pierre et Marie Curie (UPMC), place Jussieu 75252 Paris cedex 05, France 5 Swedis Defence Research Agency, (FOI), 164 90 Stockholm, Swedish 6 European Space Agency Technical Center, (ESA-ESTEC), 2200 AG Noordwijk ZH, the Netherland Citation : Longo, J.M., Dittrich, R., Banuti, D.T., Sippel, M., Klevanski, J., Atanassov, U., Carrier, G., Duveau, P., Din, I.S., Thépot, R., Loubeau, A., Coulouvrat, F., Jarlås, R., Rabia, H., Perigo, D., & Steelant, J. (2009). Concept Study for a Mach 6 Transport Aircraft. Source : American Institute of Aeronautics and Astronautics, AIAA 2009-435 A conceptual study is here presented and discussed on the possibility to transport 200 passengers over a distance of about 7000km in a nominal point-to-point mission through the Atlantic (either London-New York or London-Rio) at a cruise Mach number of 6 and an altitude about 30km. The aim of the study is not to design a specific airplane but to explore today’s state of the art technology limits to realize such kind of concept, i.e. to identify if such a mission could succeed today. Because of the challenge the mission poses, it is being optimized with the major disciplines involved by means of Multi-Disciplinary Optimization (MDO) tools as a way to realize an optimum integrated airframe/propulsion aircraft. The environmental impact is being analyzed in terms of the resulting sonic boom. No experimental data but CFD results by means of independent assessments has been generated. The study indicates that today the available technology provides with sufficient maturity to accomplish with the mission in areas like aerodynamic and thermal resistance materials but in others like sonic boom mitigation it is required a deeper insight in the physics. Finally while the present investigation clear identify that complex designs involving large amount of variables from different disciplines could be only possible via MDO/MDA strategies, today such processes still suffer on lack of robustness of the involved tools. 1.2.1 Introduction Already more than sixty years ago, in March 1947, for the first time an airplane was able to flight beyond the sonic barrier. Yet, despite the early promise of supersonic developments and the routine Mach 1-plus capabilities of today frontline combat aircrafts, it could be argued the wider potential benefits of faster-than-sound travel have failed to materialize. Indeed, the touchdown of the last Concorde, in November 2003, effectively represents the first time in human history that progress in travel time has gone into reverse. However, current thinking to develop a high-speed transport aircraft by very high ecologic and economic requirements is based on continued air travel growth since part of this growth also asks for reduced travel times. The potential to reduce overall travel times by reducing the ground service period is limited. Therefore, this demand requests for high- speed air transport. Major impediments to high-speed transport development are environmental impact (take-off/landing noise, sonic boom and ozone depletion), light-weight high-temperature materials, aerodynamic and propulsion efficiency.

8. 7 These points are all critically dependent on the vehicle configuration. Indeed, propulsion and aerodynamic design must be efficiently integrated combined with lightweight high temperature resistant materials necessary in order to realize a globally performant vehicle. Designs with high aerodynamic efficiency tend to demand higher performance materials for example by involving thin flat shapes that are inherently inefficient structures resulting in high material stresses and so on. Further, at these high speeds, classical turbo-jet engines need to be replaced by advanced airbreathing engines. Therefore, there is a strong need to identify critical technologies for both the external airframe and the propulsion units such as lightweight airframe components, lightweight engine components, novel cooling techniques for airframe and engine, modelling and validation of numerical simulation tools for combustion physics, dedicated combustion and aerodynamic experiments, aerodynamic and material interaction modelling and verification; computational fluid dynamic tools for advanced turbulence & transition models among others. To overcome that situation the European Union decided to support two proposals presented in 2005 and 2006, by large consortiums of major European institutions on high speed flow, under the coordination of the European Space Agency, ESA, through its European Technology Centre, ESTEC. The proposed research programs are the Long term Advanced Propulsion Concepts And Technologies (LAPCAT) and the Aerodynamic and Thermal Load interactions with Lightweight Advanced materials for high Speed flight (ATLLAS). These two programs target on sustained hypersonic flight where the former focuses on propulsion concepts and the latter on high temperature resistant materials which can withstand ultra-high temperatures and heat fluxes enabling high-speed flight above Mach 3. Both programs benefit from the participation of 7 European countries and 19 institutions with a broad know-how in these fields. Further, the system requirements necessary to define realistically the research constraints and directions as well as to assess the results are derived from six specific vehicle concepts, which are also integral part of the studies, i.e. (1) a 300-seat SST concept designed to meet an operational requirement of Mach 3 flight over a 7000 km range; (2) a Mach 4.5 design based around a variable cycle including turbofan technology; (3) a Mach 5 pre-cooled, 400Tn-300 passenger vehicle; (4) a turbo-ram-jet Mach 6 aircraft; (5) a cruise flight Mach number 8.0 vehicle using a hydrogen-fueled dual-mode scramjet and finally (6) a rocket propelled 50 seats space liner. Here a conceptual study is presented exploring the possibility to transport 200 passengers over a distance of about 7000km in a nominal point-to-point mission through the Atlantic (either London- New York or London-Rio) at a cruise Mach number of 6 and an altitude of about 30km. The dramatic fall in lift to drag ratio at supersonic/hypersonic speeds and the poor propulsion efficiency during acceleration, not compensated by the better propulsion efficiency during cruise, requires a design with highly efficient propulsion-airframe integration to avoid high fuel consumption. Previous supersonic research in Europe was mainly focused on cruise Mach numbers similar to Concorde, around Ma=2. The challenges in designing a transport aircraft for a cruise Mach number of 6 largely exceed those recognized to achieve flight in the conventional supersonic regime. Between the seventies and the nineties, the SR-71, a military high altitude reconnaissance aircraft (i.e. a high altitude high cruise Mach number) was operating at Mach 3. On the other side, no operational Mach 6 aircraft has existed at all at any time. The only experimental Mach 6 vehicle to have flown is the X- 15 but it was conceived to perform an acceleration climb by a non-airbreathing engine followed by an almost parabolic non-powered descent flight for a total duration of about 1 minute, i.e. a mission far away from a high altitude high cruise Mach number. Indeed, still today there is no clear evidence if one can realize a high altitude Mach 6 aircraft.

9. 8 The target of the study is not to maximize the efficiency of the mission but to identify if such a mission could be successful today. Further, to minimize cost and time, the study departs from the most “close to the target” configuration selected by the working team from a group of configurations identified in available literature. A multiple-point MDO process relying on high fidelity tools for flight phase models involving the disciplines of aerodynamics, structures and flight mechanics, is being developed during the study, to design a high-speed transport aircraft for a cruise Mach number of Ma=6, with sufficient capacity for transonic acceleration and landing. This MDO takes into account a specific propulsion system by using integral performance data and also takes into account a structural model. Further, trajectory assessment, internal layout and mass estimation are provided in the study. A second MDO process is being developed and applied for the design of the air-intake, to satisfy the demands of the propulsion system. The pre-optimized forebody will be integrated in a final multiple- point airframe MDO loop, allowing a reduction in the overall computational effort. Since no experimental data are planned for the present study, two evaluations of the configuration are scheduled at the early stage and at the end of the study by means of independent CFD results. This process uses a Navier-Stokes code previously validated with experimental data available for the base line configuration. Finally, the environmental impact of such a vehicle is focused onto specific analyses of the resulting sonic boom, accounting for atmospheric dispersion at high altitudes. From the aerodynamic point of view it is clear that in order to realize cruise at hypersonic speed, high lift over drag ratios must be achieved, but that is in opposition to sonic-boom mitigation guide- lines requirements. The concept of boom minimization is based on suppressing the coalescence of multiple secondary shock waves caused by the airplane in supersonic/hypersonic flight, so that the overpressure at ground level is reduced. This can be achieved through the manipulation of aircraft’s design characteristics, resulting in an optimized wave pressure signature with significant sonic boom loudness attenuation. Advanced low-boom configurations may be achieved by a more uniform lift distribution stretched over a longer length, so that the sonic boom maintains its weaker mid-field features with a lower bow shock. In order to obtain adequate boom loudness suppression, the area distribution of an aircraft must be carefully determined aerodynamically but, such advanced low- boom designs induce drag penalties. An integration of low-boom design parameters within the MDO process is not foreseen in the frame of the present investigation but could be a rational next step for a future study. The following chapters present an overview of the working-team individual contributions to the study, while the present results for the MDO process can be still considered as preliminary since the project continues running. 1.2.2 Airplane Shape Definition by Multidisciplinary Multiple-Point Design Optimization In the past different approaches were used to realize high lift over drag configurations resulting in different designs like ‘wave rider’ concepts or long slender fuselage designs with highly swept wing leading edges. Unfortunately most of them stayed in theoretical status due to the huge amount of physical and technical problems for high aerodynamic performance, feasible airframe structure design, efficient propulsion integration or light, robust material applications. Therefore the design should be approached by means of a multidisciplinary optimization. However and in order to save some time, the study is initiated reviewing the literature of past projects to find out an initial configuration as close as possible to the ATLLAS Mach 6 targets. In the eighties the HYCAT-1A airplane was designed for a 7000km flight range taking 200 passengers on board, i.e. similar mission objectives than the ATLLAS one, and a huge amount of technical data like structural masses and wind tunnel tests are today available in open literature [1-2]. With a fuselage of 105 meter long and a span wise of 28 meters it presents a promising compromise between hypersonic and subsonic performance as well as good trim capabilities, both major requirements for future hypersonic aircrafts. Also favor the HYCAT-1A selection the fact it has classical horizontal tail, characteristic sharp forebody leading edges and as like is thought for the ATLLAS Mach 6, it was designed to be propelled by a combined turbojet-ramjet engine based on hydrogen fuel. However, being strictly here

10. 9 is not used the HYCAT-1A vehicle but based on published drawing of such airplane, a vehicle configuration is here build up resembling to some extend such geometry. The ATLLAS Mach 6 reference design configuration, ATLLAS M6 RD, has a fuselage characterized by elliptic shaped cross sections added by a sharp leading edge for the outer forebody which merges to the wing leading edge. This forebody shape is derived from the wave rider principles offering high lift to drag ratios. Initially wing and elevator have double trapezium profiles. Figure 1.2.1 presents computed CFD aerodynamic performances of this configuration as a function of the Mach numbers range compared with published data of other projects with similar mission objectives. It turns out, the ATLLAS M6 RD not only resembles geometrically the HYCAT-1A but also its aerodynamic performances are similar. Further, completes the data base of the ATLLAS M6 RD a mass budget estimation, turbojet-ramjet engine performance, mission profile arrangement, aerodynamic CFD calculations in subsonic, transonic and hypersonic, dynamic FEM analyses and trim capability calculations . The principle work flow for the MDO tool developed by DLR-AS is shown in Figure 1.2.2 and consists of several modules for different subtasks which are added to a functional chain where at the end a defined objective function is updated [3]. There are modules for parameterized geometry generation, mass modelling for component masses and center of gravity computation, CFD grid generation, numerical aerodynamic flow solving, thrust and trim capability determination, FEM grid generation and dynamic structure analysis, constraints check and objective function update. Most of the modules are mission-flight depending e.g. transonic or cruise condition. Further, the propulsion system is integrated in the MDO in a form that intake and nozzle-flow are computed by means of CFD as shown Figure 1.2.3 but the combustion chamber is covered as a black box with given properties so the gross thrust is determined. Figure 1.2.1 Aerodynamic performances of the ATLLAS Mach 6 reference design configuration, ATLLAS M6 RD (blued dots), compared with published data for different airplanes with similar mission objectives

11. 10 Indeed, to perform the computations, engine parameters obtained by DLR-SART are used to provide the flow solver with the flow properties required at the entrance and exit of both turbo and ram-jet engine types (Figure 1.2.4). Also, the specific fuel consumption is calculated from the net thrust given by intake, combustion chamber and nozzle force and fuel mass flow for the current engine mode. This is needed for later range estimation. Finally, along the flight envelope the MDO has to take into account not only the differences on engine-performances but also intake and nozzle engine- geometrical changes due to changes in flow regime. The numerical flow solver code TAU [4] of DLR is one of the main items of the multidisciplinary analysis tool. It is a three-dimensional Reynolds- averaged Navier-Stokes solver based on a finite volume method delivering flow properties in a wide range of Mach numbers from low subsonic up to super-orbital re-entry velocities. Both structured and unstructured grids are supported. To reduce computational effort for the flow solver, the Euler equations combined with a turbulent flat plate model for skin friction estimation is preferred instead of Navier-Stokes solutions. With this method three main parameters of the system are defined: first, the resulting force coefficient in flight direction; second, the aerodynamic lift to drag Figure 1.2.2 Airframe-MDO works flow (DLR-AS) Figure 1.2.3 CFD computation of the resulting flow field of the ATLLAS M6 RD during cruise (DLR-AS). Top: full view. Bottom: detail view of the flow around the engine

12. 11 ratio and third, the geometric point where all pitch moments are equal to zero. Indeed, the force balance is calculated from the CFD results plus a force model for the combustion chamber including the gross thrust and small intake corrections as presented in Figure 1.2.5. Since forces for intake and nozzle are already included in the CFD calculation, the main force coefficients for lift, drag, thrust and pitch moment are determined. Hence, the determination of the pressure point is possible and comparing the location of this point with respect to the center of gravity gives trim capability of the configuration. Here the aerodynamic efficiency of a deflected horizontal stabilizer plays an important role. As Figure 1.2.7 shows, the horizontal tail decreases its trim capability at high Mach numbers. Also, to speed up the MDO process special methods are developed like a modular mesh generation procedure which strongly reduces meshing time. Indeed, the geometry generation is one of the major modules of the MDO tool due Figure 1.2.4 Turbo-Ram-Jet Performances Data. (DLR-SART) Figure 1.2.5 Scheme of force-balance used for trim estimations (DLR-AS)

13. 12 to most of the engaged modules are depending on the geometry. For the geometry generation an own tool is developed based on NURBS (Non Uniform Rational B-Splines) curves described by a set of control points [5]. A certain number of NURBS curves are arranged in 3D-space resulting in a surface. The geometry is divided in several surfaces and changing NURBS attributes offers different kinds of surface interfaces from complete smooth to kink. The geometry description is completely parameterized hence the airframe is controlled by about 100 parameters and the engine by 40 parameters. The tool allows global and local geometry changes modifying NURBS control points and guaranties water closed geometry. Additionally inner surfaces for front and rear inner tanks and passenger cabin needed for mass estimation are created. Furthermore the geometry tool can be used directly for structure model node creation. Finally, the geometry changes resulting during the MDO process requires a re-meshing for the CFD computation within every optimization loop. Therefore the commercial unstructured grid generator CENTAUR [6] is used. For higher accuracy grids with about 1.8 million nodes are used whereas almost half of the nodes are located in the engine zone. Suitable source placement guaranties fix mesh refinement for certain local geometry parts like wing leading edges. It has to be noted that for a multi-point MDO process also multiple meshes are needed due to different far field requirements, engine operating modes and horizontal stabilizer deflections. It turns out CFD grid generation is one of the main driver for the overall loop time. To strongly reduce the meshing time, a special modular grid generation procedure is developed by splitting the 3D-field around the configuration into several zones which can be re-meshed independently as is shown in Figure 1.2.6. Indeed, in the MDO tool commercial software as well as own developed source codes are used. All modules are embedded in a new and fully automated PYHTON environment Figure 1.2.7 Impact of the horizontal tail deflection on center of pressure location for different Mach numbers Figure 1.2.6 Modular Grid Generation arrange strategy showing the different modules (DLR-AS)

14. 13 taking over running and monitoring of modules, data exchange and conversion, machine communication and database update. The modular concept of the MDO process allows simple removing, adding and modifying of several modules. The MDO tool is linked to the commercial software SYNAPS POINTER PRO [7] which offers several types of optimizers, like scanner, gradient based or genetic methods. In the presented MDO the Sub plex optimizer, a function ranking method, is favored. The sub plex optimizer is based on the Nelder-Mead simplex (NMS) method which is often recommended as best optimizer for noisy function due to a function value ranking system which is not depending on absolute objective function values. Furthermore no parameter sensitivity study is necessary, but NMS is limited to low dimensional problems (n < 6). The Subplex optimizer now makes the NMS feasible for high dimensional problems by determining subspaces of the parameter space where the NMS can be applied: a so called sub plex cycle is evaluated. Convergence can be observed after 3 to 5 sub plex cycles [8]. As objective function for the MDO process it is chosen the range, due to linkage of aerodynamic and engine performance as well as fuel and operating empty mass. For a 1-point MDO the Breguet range is used but also new range estimations for multiple cruise points are evaluated by integration of the basic range equation for nonaccelerated horizontal flight. Indeed, except from take-off and landing, two flight points of mission profile are identified as critical and hence suitable for the optimization: start of cruise at Mach 6 and transonic ascent at Mach 1.3. Both points are very important for the overall design and have different requirements. The cruise mode has to be characterized by a high lift to drag ratio, low fuel consumption and fulfilling the trim conditions. Due to the peak of wave drag at transonic Mach numbers the priority is set in the availability of sufficient thrust. Minimizing thrust in transonic flight means more fuel available for cruise. It has to be remarked that hypersonic vehicles can consume 40-50% of overall fuel mass during ascent up to cruise altitude. Both points have big impact on the maximum cruise distance which is defined here as goal function for the MDO. Further, the configuration constraints which cannot be found in the range equation are added to the objective function in form of a penalty function which gives the final objective function. Hence the constrained optimization problem is changed to an unconstrained optimization problem and further constraints can simply add to the MDO process in future. So far main constraints are the intake air mass flow for begin of cruise, the distance between center of gravity and pressure point for all calculated mission points, gross lift off weight and the resulting force in flight direction for all cruise points. As a disadvantage of this method a noisy objective function characteristic is expected. Since the development of the structural module is being carried out in parallel to the first MDO applications it is not included in the MDO results here discussed. A first 1-point MDO for begin of cruise is performed to validate the functionality of the tool. In every loop the mass estimation at the beginning of cruise gives the targeted lift for CFD calculations. Overall 13 geometrical design parameters, 4 for wing, 4 for horizontal stabilizer and 5 for fuselage are chosen. The result of the 1-point MDO by comparing initial and final design is shown in Figure 1.2.8. The cruise range is increased by 10 percent due to increase of L/D and tank volume. The 1-point MDO then is extended to 3-point Figure 1.2.8 MDO results for a 1-point, cruise, optimization (DLR-AS)

15. 14 MDO by adding a transonic acceleration point at Mach 1.3 and the end of cruise point due to the critical trim condition mentioned above. Hence configuration mass at begin of cruise is now depending on transonic performance which determines fuel consumption during acceleration and climb. The number of design parameters is increased up to 22. Assuming the lift proportional to weight, constant cruise velocity and flight height, the basic range equation is integrated in a form that the aerodynamic performance at the end of cruise is included in the cruise range calculation. Figure 1.2.9 demonstrates the current characteristics of the 3-point MDO. The functionality of various configurations is shown as well as the optimizer capability leading out of a penalized system and increase objective function by 9 percent. At the moment the major issues that have to be considered during the MDO are the mandatory integration of the engine due to the lift increase, the identification of the end of cruise point with worst trim conditions and the low frequency lateral and vertical bending of the configuration due to the large dimensions. 1.2.3 Propulsion Integration by Multidisciplinary Design Optimization ONERA, as a contributor to the MDO, focuses on the forebody and inlet design as they are closely integrated. The first stage consisted in designing a relevant inlet baseline. A detailed aero-propulsive performance of the configuration equipped with the inlets is assessed in order to set the reference for the MDO process. The baseline air-intake is designed using 2D-RANS calculations (Spalart- Allmaras turbulence model) on a structured mesh. A mixed compression intake is selected since it allows a good trade-off between kinetic energy efficiency at high Mach number and reduced cowl drag. In the selected baseline configuration, the flow is supersonically compressed by three external ramps extending between 45m and 55m downstream from the fuselage nose and the internal cowl profile. The flow compression is then achieved by a terminal normal shock and a subsonic diffuser (end of the diffuser at X = 65m). The upper wall internal profile is designed so as to cancel as much as possible the reflected shocks. Only a virtual terminal shock (VTS) is considered at this stage instead of considering complete more realistic throttling device which would require time consuming NS calculations. To take this VTS into account in the efficiency assessment an average one- Figure 1.2.9 MDO on-going results for a 3-point (acceleration, beginning- and end of cruise) optimization. Top: configuration changes after arbitrary number of MDO loops. Bottom: MDO-convergence (DLR-AS)

16. 15 dimensional flow field conserving the mass flow, momentum and total enthalpy fluxes of the two- Figure 1.2.10 MDO process for the propulsion integration (ONERA) Figure 1.2.11 MDO parameterization for the propulsion integration (ONERA)

17. 16 dimensional flow has first to be calculated slightly downstream from the intake throat. With the proposed design, considering 4 rectangular intakes of 2m width each, the engine demand is matched (425 kg/s per intake). The average VTS Mach number is around 1.5. Neglecting the diffuser losses but taking into account the VTS, kinetic energy efficiency amounts to slightly above 0.96. Four modules of this baseline intake configuration are integrated into the ATLLAS M6 RD. The 2D pressure distributions along the external and internal walls are also used as an input for the structural model improvement. The MDO for the propulsion unit consists in finding an enhanced inlet geometry satisfying the following problem: total drag as objective function with minimum lift and inlet mass flow requirement as constrains. The overview of the corresponding process is illustrated in Figure 1.2.10. It can be decomposed into two main parts which are the analysis module and the optimizer. The latter is based on a suitable algorithm, according to the optimization problem to solve. On the other hand, the analysis module provides the performance in terms of objective function and constraints values. A 16 variables parameterization is chosen in order to define the most appropriate design space of research of the optimum for the given optimization problem, see Figure 1.2.11. The new mesh corresponding to a set of design variables is generated using a combination of volume mesh deformation techniques such as free form [9] or similar analytical linear deformations. Furthermore, an optimization algorithm based on a global (genetic algorithm) approach is chosen to search the optimum in the design space, which is typical for an optimization problem with a significant number of design variables. The optimization is performed using an automated PYTHON based program to ensure synchronized communication between the optimizer and the analyzer, while the CFD-RANS calculations are performed with the ONERA elsA solver [10] using a structured mesh. 1.2.4 Structure Model & Internal Layout One of the activities for the MDO processes described in the above chapters is the structural design. FOI is responsible for the structural model and analysis of the airframe and the intake. The structural design requirements are short load-paths and sufficient interior space so that structural members such as beams and frames can meet stiffness and strength-requirements without jeopardizing the weight budget. Stiffness requirements originate either from aircraft handling and aeroelastic considerations, including, for instance, flutter and control-surface authority, or from buckling constraints. Strength (stress) requirements depend on material selection, operating temperature and detail design. In the early design-phases it is important to find out what is driving the structural weight, for instance the slenderness of the fuselage or wing or the layout for principal load-paths. Further, an efficient interface to the aerodynamic surface-description has been created for the MDO- processes, taking into account flexibility with respect to design changes. This computational tool automatically creates a complete model for a structural finite element analysis suitable for the preliminary design. The input file is created by executing in a sequence nine programs: fuselage, wings, fuel-tanks, mass-distribution etc. The model consists of 4-node shell elements for cover plates while bar elements are simulating frame stations. Spars and stringers and rigid body elements are used for component connections while the fuselage tanks contribute to the bending-stiffness of the airplane. For FEM computations the numerical structure solver NASTRAN is used. As a forerunner to the MDO-process a sequence of FEM runs are performed, where the structural design is modified for each calculation in order to increase the lowest vibration natural frequency of the airframe, without increase of the total weight of the structure.

18. 17 Figure 1.2.12 shows the results of this preliminary structural analysis. It turns out the frequency for vertical fuselage- bending is very low which could cause flight-mechanics/control problems. On the other hand, the present structural design has sufficient flutter margin and no problem with aeroelastic divergence. Also non-structural masses are distributed over the whole structure. The mass estimation is performed by determining the surface areas and the geometrical center of gravity of these surfaces resulting from the geometry module. Every surface is loaded with a mass distribution and an additional fix mass which is not changed during the MDO. The initial mass budget of the ATLLAS M6 RD configuration provides the input while the updates are obtained from the changes on configuration geometry, as presented in Figure 1.2.13- left, and from the changes on fuel charging, as is shown in Figure 1.2.13-right. The location of the center of gravity is updated as result of these changes. The internal layout of the vehicle is responsibility of DLR-SART. The design of non-integral tanks has been done using a new Multi-lobe Tank Extension Module. This extension accounts for load factors, heat fluxes and fuel mass. The Program Tasks are (i) tank pre-designing (dimension mass); (ii) propellant feed-line design (dimension, mass, pressure Losses); (iii) tank filling (dimension, mass); (iv) tank-pressurization (integration of ODE for determination of the thermodynamic environment, pressurization gas mass, pressurization system mass). Further, special features for hypersonic aircrafts are included like (i) complex body/fuselage geometry as a result of the aerodynamic demands; (ii) need for storage of very large amount of low Figure 1.2.12 Preliminary bending analysis of the aircraft’ structure (FOI) Figure 1.2.13 Mass model left and variation of the centre of gravity location as a function of fuel charging (FOI & DLR-AS)

19. 18 density propellant; (iii) need for highly efficient use of the internal volumes. The major design objectives are minimal number of input parameters but maximal flexibility and very fast generation of regular mesh under the assumptions that separating walls should be flat (due to stress consideration), intermediate parts of Multi-lobe tanks should be cylinders or cones and finally dome parts (incl. separating walls) should be independent from tank length. Typical examples of the geometry automatically generated by the new module for a symmetrical five-lobe large cryogenic tank are here demonstrated. The software is successfully used for a fast design of tanks containing 99050 kg of LH2 (assuming the fuel is stored under sub-cooled conditions of 15.25 K) that fit quite well inside the airframe geometry ( Figure 1.2.14). Figure 1.2.14 A Multi-lobe Tank extension module is successfully used for fast design of the internal volume (DLR-SART).

20. 19 1.2.5 Sonic Boom Assessment & Mitigation The major technologically challenging problem in the design of environmentally compatible high-speed cruise vehicles is the management of the sonic boom and the resulting reflection of the shock system on the ground. The sonic boom is a footprint of the aircraft wake in the far field. With the aircraft at high altitude the footprint is spread over a large area and energy considerations alone indicate that it should be a weak disturbance. However the human ear is very sensitive and pressure waves produced by supersonic aircraft like Concorde are too strong to allow supersonic overland flight. Here UPMC investigates the sonic boom ground impact for the ATLLAS M6 RD flying at Mach 6 cruise at a 28km altitude. Different options in the UPCM code are utilized to calculate ground track waveforms, sonic boom carpet, and limiting rays. All calculations are done for a rigid ground and account for pressure doubling due to the ground reflection. This assumption leads to an overestimation of sonic boom levels relative to a finite-impedance ground such as grass [11]. In addition to meteorological data, the other input to the sonic boom propagation code is the aircraft wave-form. The ATLLAS M6 RD near-field signature at a 28km altitude is extracted from the DLR-CFD results by ONERA applying a multi-layer sonic-boom evaluation approach to calculate the ground pressure resulting from the supersonic flight. The method uses as input the CFD near-field pressure information, taken on cylinders parallel to the freestream location and passing through the vehicle forebody, at a distance of 0.15m (Figure 1.2.15). This short distance gives a distance-to-aircraft- length parameter of R/L = 0.15. This wave-form may not be ideal for the acoustic code because it is extracted very close to the aircraft, whereas an R/L = 1 is usually recommended. An ONERA in-house developed multipoles matching method [12] based on an azimuthal Fourier transform of the near- field pressures is employed to generate a locally asymmetrical pressure signal that is then propagated to the ground through a standard atmosphere with the non-linear acoustic propagation code from UPCM. Aircraft signatures are provided for azimuth angles of emission between 0± and 180± in steps of 5±. Sonic boom impact is estimated in terms of peak overpressure at the vertical of the flight track, front shock rise time, and lateral extent of the geometrical carpet. The first two parameters provide an estimation of the loudest boom likely to induce maximum annoyance, while the third parameter estimates the lateral impact of the boom during the cruise phase. The shock overpressure Δp is the maximum pressure at the shock, and the rise time t is defined as the time it takes for the amplitude to increase from 10% to 90% of the maximum. The rise time is a key parameter in sonic boom analysis because it is linked to human annoyance. The sharper the shock, the shorter the rise time, which leads to human perception of a louder, more annoying sound [12-13]. The first computations are ground track sonic booms, which result from the acoustic ray emitted at 0±, directly below the right path. As a sonic boom propagates over long distances, it is strongly affected by the atmosphere and thus is dependent on meteorology and geographical location. The impact is quantified statistically, based on numerical simulations using an extensive meteorological database. To perform the statistical analysis of the variability of sonic booms for the configuration, UPMC has extracted meteorological Figure 1.2.15 CFD near field pressure footprint extraction from a DLR CFD solution (ONERA)

21. 20 data from the ERA40 database of the European Centre for Medium-Range Weather Forecasts (ECMWF) for the year 1993, at two geographical points near Le Havre (France), which was the beginning of the Concorde's supersonic flight between Paris and New York, and near Edwards AFB (California, USA), where most of the recent sonic boom flight tests have been performed. The two points also are characterized by a very different humidity and temperature (and hence absorption) near the ground level, due to Le Havre being on the seashore while Edwards is in the Mojave Desert. The sonic boom propagation predictions include ray tracing in a stratified atmosphere with horizontal winds, nonlinear distortion, atmospheric absorption due to classical thermo-viscous effects and rotational relaxation, and atmospheric absorption due to molecular vibrational relaxation of nitrogen, oxygen, and carbon dioxide. The sonic boom emitted in the vertical plane at a 0° azimuth angle was computed every day and for two different flight directions, which demonstrate the effect of winds on propagation. The direction West is referred to as 0±, and East is referred to as 180±. Sonic boom carpets are also simulated systematically along with lateral distributions calculated once per month, using the full complement of azimuthal aircraft signatures to predict the area of ensonification at the ground. An example of such carpet computation is shown in Figure 1.2.16. The carpet for Edwards at 0± shows a mean carpet width of 148.4 km, with a standard deviation of 11.5 km. In contrast, the mean carpet width for Edwards at 180± is 157:3 km larger. The standard deviation is also larger, 15.7 km, indicating a greater variability. In a few cases, there are carpet widths which reach almost 250 km. For Le Havre, the mean carpet width of 160.1km at 180± is larger than the 153.6 km at 0±. In addition, the standard deviation is larger at 180±. In comparison to Edwards, the Le Havre carpet widths are larger, most likely due to the stronger W-E winds above 20km at Le Havre. While varying in direction throughout the year, the S-N winds at Le Havre are also stronger than those at Edwards. With standard deviations of 19.2 and 21.1 km, there is also more variability in the carpet widths at Le Havre, which can be linked to the greater variability in wind direction below 20 km. Key sonic boom parameters are compared to predictions for other aircraft configurations at Mach 1.6 and to a previous study for a Mach 2 aircraft [14]. The ground track sonic boom of the ATLLAS M6 RD reaches amplitude of approximately 65 Pa, comparable to that of existing aircraft, most of which are comprised between 50 and 100 Pa (this last value being typical for the Concorde). As expected, the rise time is somewhat larger at Edwards (mean value 1.7 ms) than at Le Havre (mean value 1.0 ms) and in both cases shows a strong variability, the minimum and maximum values being separated by almost one decade. The ICAO standard atmosphere tends to slightly overestimate the sonic boom at the ground level. The carpet width also shows a significant variability, with larger values and more scattering at Le Havre due to stronger winds. Note that atmospheric turbulence is not included in the prediction model, and turbulence would increase the variability even further. Random fluctuations in temperature and wind velocity cause turbulent eddies which scatter sound energy from a wave propagating in the atmosphere, causing fluctuations in amplitude and phase of the sound wave. Figure 1.2.16 Example of delta pressure carpet prediction (UPMC)

22. 21 Experimental studies of spark-generated N waves to model sonic boom propagation through turbulence show that turbulence almost always decreases shock overpressures and increases rise times [15-17]. Thus it is believed that turbulence would generally decrease the sonic boom impact predicted here. As a conclusion, the ATLLAS M6 RD configuration would induce at the ground a sonic boom level comparable to existing supersonic aircraft but covering a larger geographical area, due to a higher Mach and a higher altitude. As a consequence, overland supersonic flight by such a hypersonic vehicle is likely to be considered unacceptable by a significant proportion of the population, and hence justifies the necessity of other studies towards boom shaping and minimization with new aircraft designs. Here the study follows Seebass and George [18] who state that the sonic boom of an aircraft can be controlled by carefully designing its lift and cross-sectional area distribution. Seabass and George suggest creating a strong bow shock by blunting the body, which is expected to cause a penalty in aircraft drag. As the general design of the ATLLAS M6 RD is fixed, altering the overall lift distribution is not an option. Instead, the effect of aero-spikes is regarded. The characteristic of the N wave can potentially be modified employing a spike system on high speed vehicles which could significantly weaken and disperse the strong shock system. Generally, three types of spikes can be distinguished: (i) Physical spike; (ii) Mass deposition; (iii) Energy deposition. Physical spikes mean an actual attachment to the forebody of the aircraft. Mass deposition means ejection of matter to cause an effect in the incoming flow, also called aero-jet-spike or counter-flow jet. The third method encompasses flow manipulation by transferring energy to some point upstream of the aircraft, e.g. by means of laser, microwaves, electrical discharge, or external combustion, in order to heat or even ionize the flow.

23. 22 Calculations are carried out using DLR flow solver TAU. An inviscid equilibrium model is used. Since this study is concerned with forebody modifications, the computational domain spans the first 50m of the configuration, i.e. before the wing root, taking advantage of the symmetry of the aircraft. The computations show that the near pressure field can be altered by means of nose piece attachments, gas ejection or energy deposition. The aero-jet-spike behaves similarly to physical spikes while in terms of reduction of overpressure the jet outperforms the physical spikes. However, the aero-jet- spikes increases drag substantially and raise additional issues concerning system integration and propellant supply of the retro-rocket but it offers a flexible adaptation of flow manipulation in flight so as to adapt to different flight conditions. In addition to physical spikes and aero jet spikes, volumetric energy deposition is utilized in order to numerically study the effect of sonic boom mitigation. In Figure 1.2.17 the pressure signature (Cp distribution) along the windward part of the line defined by the intersection of the symmetry plane and the exit plane of the computational domain is plotted. Here the pressure distribution resulting from the reference configuration without application of spikes or energy deposition is compared with the most efficient aero-jet-spike and one case utilizing energy deposition. The latter technique leads to a lower pressure distribution than the Figure 1.2.17 Near pressure field modifications by spikes, aero-jet-spikes and energy deposition. Left from top to bottom: energy deposition case B; energy deposition case B’, aero-jet-spike, 2nd generation spike. Right top: pressure signature. Right bottom: aerodynamic performances (DLR-AS)

24. 23 reference solution and the aero-jet-spike accompanied with a slight reduction in drag but a huge amount of energy (o[MW]) is required for this solution. It turns out that all investigated potential solutions do not produces the expected effects. As a matter of fact, the underlying theoretical work of Seebass and George is based on the linearized gas dynamic equations. Strictly, the theory is thus not applicable to hypersonic flight Mach numbers. Furthermore, no experimental data are available on hypersonic sonic boom mitigation based on these principles. Recent flight experiments have not exceeded a flight Mach number of 2.0 [19-20]. While the application of spikes to blunt bodies is a widely accepted and used method, no publications are available on the application of spikes to slender bodies. Also, no data are known on the behavior of spikes in a long sustained flight as envisioned here, particularly regarding heating and structural loads. Further, a complete optimized design of the whole airframe with respect to sonic boom mitigation is not planed in the frame of the present study but could be motivation for future researches. 1.2.6 Design Verification Since the final design of the airplane is based only on CFD results, an exhaustive CFD assessment exercise is being done by ESA-ESTEC taking advantage of the wind tunnel testing for similar configurations for which data is also available. Numerical solutions obtained with the CFD FASTRAN code of ESI GROUP for a HYCAT configuration are compared with available experimental data from literature [2], as is shown in Figure 1.2.18 where pressure contours are plotted on the vehicle- surface of the wind tunnel tests configuration (5° incidence, Mach 6). The signature of the vortex from the chine over the upper wing is apparent in the top figure and is evidenced by the low pressure region visible on the aft wing in the middle figure. The high pressure region in the nose, due to fuselage camber, drives the longitudinal pitch characteristics of the configuration. The on-going test matrix includes more than 100 computations, covering longitudinal and lateral coefficients as well as the assessment of the viscous effects. Figure 1.2.19 show pitching moment coefficients with three elevon settings from the wind tunnel cases. The value derived from the current CFD cases are over plotted for comparison. The wind tunnel data for 0° elevon deflection demonstrates significant differences from the Euler CFD prediction. No distributed pressure data from the wind tunnel tests exists, however; a working assumption is that the after-body flow is Figure 1.2.18 Computed surface pressure distribution for the HYCAT configuration. Left: leeward side. Right: windward side (ESA-ESTEC)

25. 24 significantly influenced by viscous effects missing from the Euler simulations. Confirmation on this point is partially given by the viscous CFD calculations where the deviation from the wind-tunnel results is reduced in comparison. Inclusion of additional parameters (e.g. differential elevon positions) may be foreseen in order to better characterize the respective configurations. The defined plan will allow a deeper understanding of the trim behavior and to a lesser extent the lateral stability characteristics of the chosen configuration. Care needs to be taken for the extrapolation to flight as some significant differences are present in the wind tunnel tests / CFD comparison. However the wind tunnel tests are far from fully representative in terms of Reynolds Number. The exercise is primarily to validate chosen CFD tool(s). Finally, a Cross validation (code-to-code) will be made with the DLR TAU code used in the MDO process in order to identify any major differences between the Euler methodology employed and the full viscous solutions. 1.2.7 Conclusions The present paper summarizes a conceptual study on the possibility to transport 200 passengers over a distance of about 7000km in a nominal point-to-point mission over the Atlantic (either London-New York or London-Rio) at a cruise Mach number of 6 and an altitude about 30km. The aim of the study is not to design a specific airplane but to explore today’s state of the art technology limits to realize such kind of concept, i.e. to identify if such a mission could succeed today. Because of the challenge the mission poses, it is being highly optimized regarding the major disciplines involving aerodynamics, flight-mechanics, propulsion-integration and structure by means of Multi- Disciplinary Optimization (MDO) tools. Two different MDO process, one for the airframe and one for the propulsion-integration are applied. The study includes a flexible structural model and provides engine parameters, internal layout (particularly tanks), mass distribution and trim considerations. The environmental impact is being analyzed in terms of the resulting sonic boom, while mitigating devices are evaluated. The study indicates that today the available technology provides with sufficient maturity to accomplish with the mission in areas like aerodynamic and thermal resistance materials but in others like sonic boom mitigation it is required a deeper insight in the physics. Finally while the present investigation clear identify that complex designs involving large amount of variables from different disciplines could be only possible via MDO/MDA strategies, today such processes still suffer on lack of robustness of the involved tools. Figure 1.2.19 Computed pitching moment coefficient vs. AoA for the HYCAT configuration (ESA-ESTEC)

26. 25 Acknowledgment This work is being performed within the ‘Aerodynamic and Thermal Load Interactions with Lightweight Advanced Materials for High Speed Flight’ project ATLLAS, coordinated by ESA-ESTEC and supported by the EU within the 6th Framework Program, Aeronautics and Space, Contract no.: AST5-CT-2006- 030729. 1.2.8 References [1] Morris, R.E., Brewer, G.D., Hypersonic Cruise Aircraft Propulsion Integration Study Volume I/II, NASA Contractor Report CR-158926-1, 1979. [2] Elison, J.C., Investigation of the Aerodynamic Characteristics of a Hypersonic Transport Model at Mach number to 6, NASA TN D-6191, 1971. [3] Dittrich, R., Longo, J., Preliminary Design of a Mach 6 Configuration using MDO Approach, Proceedings of the 16. DGLRFach-Symposium der STAB, Aachen, Germany, November 2008. [4] Schwamborn D., Gerhold, Th., Heinrich, R., The DLR TAU-Code: Recent Applications in Research and Industry, Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006. [5] Piegl, L., The NURBS Book, 2nd Edition, Springer, 1997. [6] CENTAUR Version 7.5 B1, CentaurSoft, www.centaursoft.com, 2007. [7] SynapsPointer Pro 2, Synaps Ingenieur-Gesellschaft mbH, Bremen, Germany, 2003. [8] Rowan, T., Functional Stability Analysis of Numerical Algorithms, Thesis, Department of Computer Sciences, University of Texas at Austin, USA, 1990. [9] Coquillart, S., Extended free-form deformation: a deformation sculpturing tool for 3D geometric modeling. Computer Graphics (SIGGRAPH ‘90) 24(4), 187-196 [10] Cambier, L. and M. Gazaix, M., elsA: An Efficient Object-Oriented Solution to CFD Complexity, 40th AIAA Aerospace Science Meeting and Exhibit, Reno, Jan. 2002. [11] Coulouvrat, F., Sonic boom in the shadow zone: A geometrical theory of diffraction, J. Acoust. Soc. Am. 111, 499-508, 2002 [12] Page, J., Plotkins, J., An efficient method for incorporating CFD into sonic boom prediction, AIAA paper AIAA-1991, 1991 [13] Zepler, E., Harel, F., The loudness of sonic booms and other impulsive sounds, J. Sound Vib. 2, 1965. [14] Blumrich, R., Coulouvrat, F. and Heimann, D., Meteorologically induced variability of sonic-boom characteristics of supersonic aircraft in cruising flight, J. Acoust. Soc. Am. 118, 707-722, 2005. [15] Lipkens, B., Blackstock, D, Model experiment to study sonic boom propagation through turbulence. Part I: General results, J. Acoust. Soc. Am. 103, 148-158, 1998. [16] Lipkens, B., Blackstock, T., Model experiment to study sonic boom propagation through turbulence. Part II: Effect of turbulence intensity and propagation distance through turbulence, J. Acoust. Soc. Am. 104, 1301-1309, 1998. [17] Ollivier, S., Blanc-Benon, P., Model experiments to study acoustic N-waves propagation through turbulent media, in 10th AIAA/CEAS Aeroacoustics Conference, 1355-1367 (American Institute of Aeronautics and Astronautics, Reston, VA), 2004. [18] Seebass, R., George, A., Sonic-boom minimization. Journal of the Acoustic Society of America, 51:686–694, 1972. [19] Haering, E., Murray, E., Purifoy, D., Graham, D., Meredith, K., Ashburn, C., Stucky, M., Airborne shaped sonic boom demonstration pressure measurements with computational fluid dynamics comparisons. Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2005-9, Reno, USA, 2005. [20] Howe, D., Improved sonic boom minimization with extendable nose spike. Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, USA, 2005.

27. 26 1.3 Case Study 3 - Aerodynamic Analysis of a Supersonic Transport Aircraft at Low and High Speed Flow Conditions Authors : Andrea Aprovitola , Oleksandr Dyblenko , Giuseppe Pezzella, and Antonio Viviani Affiliations : Engineering Department, Università della Campania “L.Vanvitelli”, Via Roma 29, I-81031 Aversa, CE, Italy; Citation : Citation: Aprovitola, A.; Dyblenko, O.; Pezzella, G.; Viviani, A. Aerodynamic Analysis of a Supersonic Transport Aircraft at Low and High Speed Flow Conditions. Aerospace 2022, 9, 411. Source : https://doi.org/10.3390/aerospace9080411 License : Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. 1.3.1 Abstract The recent improvement of technology readiness level in aeronautics and the renewed demand for faster transportation are driving the rebirth of supersonic flight for commercial aviation. However, the design of a future supersonic aircraft is still very challenging due to the complexity of several problems, such as static stability performance during the acceleration phase from subsonic speeds to supersonic speeds. Additionally, the interest of scientific community in open source numerical platform as a valid tool for a reliable and affordable aerodynamic design is considerably growing. In this framework, the present work addresses the aerodynamic performance of a Concorde like aero shape developed within the preliminary design of a high-speed civil transportation aircraft. Several flight conditions, ranging from subsonic to supersonic speeds, were investigated in detail by using Computational Fluid Dynamics. The aerodynamic force and moment coefficients are computed with fully three-dimensional and steady state Reynolds Average Navier-Stokes simulations, carried out in turbulent flow conditions. The effect of the Mach number variation on the shift of the aircraft aerodynamic center is detailed, by focusing on the aircraft pitching static stability. Flow field numerical simulations are performed with both commercial (Ansys-Fluent) tool and open-source SU2) code, which is also used extensively in multidisciplinary design procedures, for further comparisons. Particular attention is focused on the shift of the aero shape aerodynamic center to verify that the provided wing design allows the aircraft static margin to be within 5% of the reference length, both at low-speed and high-speed flight conditions. The computed positions of the aerodynamic center are in agreement with the aero shape surface pressure distributions and confirmed the literature results available for the Concorde aircraft. Therefore, in the view of future simulation campaigns for supersonic transportation aircraft, the present work aims to bridge the gap between previous aerodynamic design experiences, for instance matured on Concorde, and those carried out with modern CFD tools on full-scale aircraft, and on time-scales compatible with conceptual design practice. Finally, as the difference between the computed aerodynamic coefficients reflected mainly on drag computation performed with SU2, a special focus on numerical diffusion effect of the solver is also given and compared with a commercial certified CFD tool. This adds a unique further contribution to the SU2 community for aeronautics application. Keywords: supersonic aircraft; aircraft aerodynamics; Mach tuck;; longitudinal static stability; CFD; SU2 1.3.2 Introduction Recent studies performed by aerospace industries demonstrated that faster aircrafts improves both business and international relationships while reducing time connections [1]. Regular market of business-class fare gives special attention to time spent during flight. Therefore, companies like Boom and Boeing are focusing on this peculiar aspect by relying on a wider demand of faster flights [2–7]. Several U.S. companies are currently proposing new Supersonic Aircraft (SA) prototypes,

28. 27 which represent the future for business class routes [1,8]. Supersonic aircraft concepts, namely AS2, S-512, and Overture, are the ongoing development carried on by Aerion, Spike Aerospace, and Boom aircraft companies, respectively [9–11]. While the AS2 and the S-512 concepts belong to the business jet segment, Overture is a larger Mach 2.2 High Speed Civil Transportation (HSCT) aircraft, having transport capability of about fifty passengers and a range of nearly 5000 nm [1,11]. In this scenario, aircraft designers are facing two challenging problems i.e., the environmental effects due to supersonic aviation and noise emission due to sonic boom, which actually represents the strongest barriers to supersonic flight [8,12]. The environmental focus is related to the lowering of greenhouse gas and pollutant emissions and demands to implement strategies to comply with the sustainability standard of International Civil Aviation Organization (ICAO). The objective is set to a 50% reduction of aviation emissions related to CO2 and NOx in the next future[13]. Additionally, a significant attention of designers is also focused on sonic boom mitigation. Actually, since Concorde last flight, sonic-boom is still the main design concern for commercial SA due to prohibition of supersonic overland flight [8, 13–16]. Aside from the environmental issues related to sonic boom mitigation and reduction of fuel emissions, physics of supersonic flows is completely different from the one featuring the sub-transonic regime [17,18]. Many design criteria of SA are different from those adopted for low-speed regime. Specifically, longitudinal stability requirement of SA relates to peculiar aerodynamic phenomena characterizing the supersonic regimes. As matter of fact, aerodynamic characteristics radically change when aircraft accelerate from subsonic to supersonic speeds [19]. Among the most relevant changes, it is worth noting that the lift-to-drag ratio (L/D) strongly decreases and the aircraft Centre of Pressure (CoP) shifts backward, by affecting vehicle performance, static stability, and trim ability. The rearward movement of CoP determines a marked nose pitch-down tendency, known as Mach tuck phenomenon. Moreover, a marked rearward shift of CoP at M∞ > 1 (i.e., increased distance between the CoP and the Center of Gravity (CoG) ) determines a lower maneuverability and a large elevon deflection to trim the aircraft which, in turn, leads to an unacceptable large trim drag. Recall that stability considerations are, however, performed with reference to the Aerodynamic Center (AC) of the aircraft, also known as the vehicle neutral point. Differently to CoP, in fact, the pitching moment coefficient evaluated with respect to the AC does not depend on the AoA. Previously mentioned design concerns are even more challenging considering that for a SA the longitudinal stability requirement must be prescribed over a wide range of Mach numbers. Aircraft longitudinal stability is investigated in literature by formulating mathematical problems which resume by MDO (Multidisciplinary Design Optimization) procedures [20]. Specifically, low- speed stability for SA is related to the peculiar slender-shaped wing planform, as discussed in the papers of Seraj et al. and Gursul et al. [21,22]. Seraj et al. [21] performed an optimization study by minimizing the drag at supersonic cruise and considering the static margin as a stability constraint at low-speed. Authors found that pitch stability at subsonic speeds was enforced by increasing the leading edge thickness at the expense of a larger wave drag. Gursul et al. [22,23] studied and related the stability behavior of delta shaped wings to flow separation which was dependent on the leading edge radius. Furthermore, the aircraft behavior consequent to vortex breakdown was analyzed, and it was found that breakdown favored the longitudinal instability. Longitudinal stability condition for SA was also studied at high speed by Mangano et al. [20], who considered a multipoint design optimization over a two-dimensional supersonic profile and over an ideal supersonic concept the Aerion AS2 in several flow regimes. The highspeed stability constraint was formulated in term of trim condition by constraining the pitching moment coefficient. Fukurawa et al. [16] studied a civil SA concept with sonic boom mitigation at supersonic speed. The stability condition in supersonic regime was used as objective function. Therefore, the absolute value of the static margin and the CoG was minimized.

29. 28 Because of the significant variation of pitching moment and drag coefficients a supersonic aircraft has to withstand during flight, its aero shape must be accurately designed. With this in mind, aircraft architectures made by appropriately combining slender low aspect ratio Delta wings (DW) and the Sears-Haack body fuselage represent the right design option. In fact, Sears- Haack bodies and DW are able to alleviate the wave drag at supersonic speeds. In addition, DW also at low-speed conditions provide interesting aerodynamic characteristics, namely the vortex lift phenomenon. At high Angle of Attack (AoA), DW promotes the creation of leading edge vortices which originate from the leading edge separation, and consequent roll up of the oncoming airstream [24,25]. This vortex system increases the aerodynamic lift, according to the well-known vortex lift phenomenon. Additionally, DW have the further advantage to limit the excursion of the CoP towards aircraft tail. It is shown in Ref. [26] that the Concorde ogee wing was designed to constraint the CoP displacement within a fixed range of the chord length at the wing root. Within this framework, the present research effort addresses the aerodynamic analysis of a SA featuring a Concorde-like aero shape by means of steady state, fully turbulent, and three-dimensional Reynolds Average Navier-Stokes (RANS) simulations, carried out in subsonic, transonic, and supersonic flow conditions. The aerodynamic force and moment coefficients are computed for different angles of attack and for longitudinal flight conditions only. The shift of the aero shape AC is assessed in a wide range of Mach number, and results are compared with literature data [26]. Flow field numerical simulations are performed with both commercial Ansys-Fluent and open-source SU2 tools for further comparisons. The shift of the aircraft AC is related to the different pressure distributions predicted by CFD simulations both at low speed and high speed flight conditions. The computed positions of the AC are in agreement with the aero shape surface pressure distributions and confirmed the literature results, available for the Concorde aircraft [26]. 1.3.3 Aircraft Static Stability The static stability and the trim ability of an aircraft is commonly formalized by evaluating the static margin of the vehicle defined as the distance between the CoG and the AC of the aircraft: SM = X ̅CoG − X ̅AC Eq. 1.3.1 where ⎺XCoG and ⎺XAC are the longitudinal dimensionless position (i.e., ⎺Xi = Xi/Lref ) of the CoG and AC, respectively. The aircraft static stability is indeed resumed by the following relationship: ∂CM ∂CL = X ̅CoG − X ̅AC < 0 Eq. 1.3.2 when ⎺XCoG < ⎺XAC the aircraft is considered statically stable (i.e., CMa < 0). Otherwise, for ⎺XCoG > ⎺XAC the aircraft is statically unstable (i.e., CMa > 0). Stability of SA becomes problematic during the transition between the subsonic and the supersonic regime. In fact, while flow physics imposes to the AS to move backward during the acceleration phase, there are no natural reasons that determine changes in CoG position. So that, when the SA accelerates to supersonic speed the ⎺XCoG remains unchanged while the AC moves [27]. As a result, the shift of the AC is one among the major concern for a reliable SA design. If the aircraft is designed to have CoG by allowing a proper SM at subsonic speeds, the SM eventually becomes unacceptably large at supersonic speeds. In addition, if aircraft design provides a CoG located to achieve a proper SM at supersonic speeds, the subsonic SM most likely would be negative (i.e., AC ahead of the CoG), hence making the aircraft unstable in subsonic

30. 29 flight. Thus, two different solutions to overcome the stability and maneuverability issues can be Figure 1.3.1 The aircraft configuration with dimensions.

31. 30 adopted for SA. On one hand, the CoP can be maintained at the CoG location by trimming the aircraft using a suitable elevon deflection. However, this solution requires an additional elevon oversizing with a consequent increase of trim drag. On the other hand, the XCoG could be moved backward (i.e., CoG control) in order to limit the increase of the aircraft SM. For instance, this was the design solution adopted for the Concorde aircraft. In that case, the shift of the CoG was performed with a fuel pumping system which transferred the fuel from fore to the aft tank of the aircraft, namely rear trim tank [26]. When crossing the sound barrier, Concorde uses afterburners. Therefore, during the acceleration to Mach 2, the fuel is pushed towards the tail producing an additional retraction of the CoG [26]. Conversely, during the deceleration, fuel is pumped forward to compensate the forward shift of the AC, thus establish the static equilibrium at subsonic condition [26]. In addition, in order to further limit the aircraft SM, the wing planform of Concorde was opportunely chosen, by adopting an ogee delta wing. In fact, the Concorde ogee-planform wing, helped to constraint the shift of AC in cruise conditions within about 62% of the length of the wing root chord. Finally, it is worth noting that another advantage in moving the CoG of the aircraft consisted in the possibility of using the internal elevons of the Concorde to trim the aircraft to a certain attitude. In fact, without shifting the CoG high elevon deflections were required, which were impossible due to the Concorde operating range in cruising conditions (i.e., M∞ = 2.02) [26]. 1.3.4 Aerodynamic Analysis Aircraft aerodynamics and static stability in longitudinal flight conditions are addressed in the current sections for the whole flight scenario of the vehicle. The shift of the AC (i.e., the aircraft neutral point) expected during the acceleration phase from subsonic to supersonic speeds is also discussed in detail. Flow modelling and simulations procedures are detailed hereinafter. 1.3.4.1 Aircraft Configuration Generally speaking, a SA aero shape essentially blends two different airplanes concepts. SA is optimized for the supersonic cruise, but at the same time optimal shapes are also designed to efficiently cover some segments of their trajectory at subsonic speeds (e.g., takeoff and landing). With this in mind, the aircraft configuration under investigation is shown in Figure 1.3.1. As one can see, it features a Concorde-like aero shape with a low mounted thin delta wing, seamlessly integrated within a Sears-Haack body fuselage, and a tailless configuration, as used for the Concorde and the Tupolev Tu-144 airplanes. The configuration also features a quite constant cross section fuselage with considerable nose overhang relative to an ogee wing. This aero shape was obtained starting from high-level requirements of 80–100 passengers, a supersonic cruise up to Mach 1.5–2.0 (1590– 2120 km/h; 859–1145 kn) at an altitude of 60,000 ft (18.3 km), and a range of 4000–4500 nmi (7400–8334 km). To cope with these requirements, an aircraft architecture with a tailless and a narrow fuselage integrated with a low aspect ratio delta wing with cropped wingtips was chosen, like those adopted for the Concorde and Boom Overture aircraft. Therefore, the planform view features a long, slim fuselage and a slender delta wing with its distinctive ogee leading edge, long root chord and short span. In particular, design requirements lead to a first instance aircraft 65 m long and with 27 m as wingspan. These dimensions were refined while design matured, as shown in Figure 1.3.1. The slender high fineness ratio fuselage (i.e., needle-like shape) was obtained starting from a Sears-Haack body, which also satisfied the area rule, to limit drag at high-speed conditions. In fact, the fuselage design depends on the wave drag coefficient (CDw) which increases rapidly as the fuselage volume (V) increases:

32. 31 CDW = 24 V L3 Smax Sref = 9π2 2 ( Rmax L ) Smax Sref = 4.69 4 [( Rmax 2lN ) 2 + ( Rmax 2lT ) 2 ] Smax Sref Eq. 1.3.3 where Rmax is the body maximum radius, Smax and L are its maximum cross-section area and length, respectively. Sref is the aircraft aerodynamic reference surface, lN and lT are the lengths of nose and tail parts of the aircraft (see Figure 1.3.2) [19,28]. A double-bubble cross-sectional layout was considered to separate areas for cabin and cargo. The wing and the tail were designed in order to provide the aircraft with a suitable aerodynamic performance throughout the flight envelope, especially at high-speed conditions. In fact, according to Ref. [19], their wave drag coefficient reads: CDW = 512 π (vps)2 K0(βs) Swet,each 2Sref Eq. 1.3.4 where s is the slenderness ratio of the part; for the wing: s = b 2lW Eq. 1.3.5 p is the planform parameter of the part; for the wing: p = Sref blW Eq. 1.3.6 v is the volume parameter of the part; for the wing: Figure 1.3.2 Design parameters of the aircraft configuration

33. 32 v = V (Sref)3/2 Eq. 1.3.7 being V the volume of the part; in addition β = √M2 − 1 Eq. 1.3.8 K0 is an empirical coefficient for wave drag due to volume and Swet,each is the wetted area of each part. A NACA 64A series airfoil was chosen with a thickness ranging from 3% at root up to about 2% at tip; the wingspan was determined according to the Mach’s cone semi aperture angle at cruise speed (i.e., the wing leading edge remains behind the shock cone created by the leading-edge root); the ogival delta wing was compound-rounded into the shape of a smooth ogee equal to that of the Concorde wing. Therefore, the high sweptback leading-edge and low thickness/chord ratio improved wave drag. Furthermore, the high leading-edge sweep at the root (i.e., wing strakes) determines, at low speed, strong controlled counter-rotating vortices on the leeside at high angles of attack. Such vortices lower the local air pressure andcause high-lift (i.e., vortex-lift phenomenon), thus improving aircraft low speed performance, such as take-off and landing speeds. A detailed description of the vortex lift phenomenon that takes place over this ogee wing at very low speeds can be found in Ref. [24]. Figure 1.3.3 The Concorde flight envelope in the altitude-airspeed plane with iso-Mach lines [26,29]

34. 33 According to the Concorde design, the ogee wing planform helps in reducing the amount of control force required to pitch trim the aircraft. In fact, the movement of the aerodynamic center between low speed and supersonic cruise conditions is reduced (i.e., low static margin both at low speed and in supersonic cruise). This way, the trim of the aircraft in cruise for minimum drag was accomplished by means of fuel transfer to adjust the center of gravity in supersonic flight and with a proper camber and twist of the wing. Finally, the pitch down tendency of the sweptback wing is counterbalanced by four engines placed beneath the wing and on the rear part of it. This arrangement has also the advantage to determine a lighter wing since allows the engine weight to counteract the wing lift, thus reducing the wing root bending moment. 1.3.4.2 Flight Envelope The Concorde flight envelope (FE), shown in Figure 1.3.3 and reported in Ref. [27], was assumed as reference for this aerodynamic study [26,29]. As shown, iso-Mach curves are also drawn to appreciate the Mach number variation expected during flight. The Concorde FE is limited in terms of speed; the maximum operating speed limits (Vmo) is set at about 530 knots IAS at 43,750 ft, where Mach number equals 2.04. Another limit set at 300 knots is represented by the lowest speed limit achievable. In addition, it is worth noting that the aircraft is characterized by an extended FE Table 1.3.1 CFD Test Matrix

35. 34 subjected to significantly different design requirements (with a wide range of airspeed while altitudes extend up to about 18 km (60 kft), which adds further complications to the design of SA [26,29]. 1.3.4.3 CFD Test Matrix Aircraft aerodynamics and static stability in longitudinal flight conditions are addressed by means of CFD simulations which are performed at several Mach numbers from M∞ = 0.24 to M∞ = 2.0, according to the FE in Figure 1.3.3. Eleven control points along with the flight profile were considered to perform aircraft aerodynamic analysis. The selected flight conditions refer to M∞ = 0.24, 0.5, 0.8, 0.9, 0.95, 1.02, 1.1, 1.2, 1.5, 1.8, and 2.0. For each Mach number, CFD simulations were carried out at different angles of attack, according to the CFD test matrix in Table 1.3.1. For the sake of simplicity, only low values of the AoA have been considered, namely α = 0, 3, 5, and 10 deg, since the focus is on the shift in the position of the aero shape aerodynamic center which, as is well known, does not depend on a. Each simulated Mach number corresponds to a fixed height and cruise speed (i.e., Re∞, M∞) of the FE. Therefore, aircraft aerodynamics and static stability in longitudinal flight conditions are addressed by means of twenty seven steady state, three-dimensional, and fully turbulent Navier- Stokes (NS) CFD simulations. 1.3.4.4 Grid Generation Flow field simulations were carried out on several quite different grids, according to the different free-stream Mach numbers summarized in the CFD test matrix (see Table 1.3.1). All grids are unstructured hybrid mesh with hexagonal or polyhedral cells in the flow field domain, prisms in the boundary layer and triangular elements on the surface of the aircraft. In particular, two computational domains were generated for the CFD simulations: one for subsonic simulations and the other one for supersonic computations. The fluid domain for the subsonic case is a prismatic brick with dimensions of length, width, and depth equal to fifty times the body-length of the aircraft. The subsonic computational domain is shown in Figure 1.3.4 where the mesh on the aircraft wall and symmetry plane is also provided. Figure 1.3.4 Subsonic computational domain with mesh on the aircraft wall and symmetry plane

36. 35 On the other hand, for the supersonic case, the computational domain is different with respect to the subsonic one. In fact, due to the hyperbolic nature of the supersonic flow field equations it features a paraboloid-like domain. To carry out simulations with Mach number ranging from 1.1 up to 2.0, the lowest Mach value was chosen for the paraboloid semi-aperture angle. The supersonic computational domain is shown in Figure 1.3.6 where the mesh on the aircraft wall and symmetry plane is also provided. To facilitate a correct transition in the growth of the size of adjacent tetrahedral cells, density boxes have been defined at the nose, at the leading edge of the wing, at the engine, and at the wing tip. The boundary layer region has been discretized by exploiting prismatic inflation layers. The grid featured a minimum wall spacing equal to 10-6 m to allow for y+ = O(1) and to describe the viscous sublayer. The prismatic layers of a typical mesh is shown in Figure 1.3.5 where the mesh on the aircraft wall and symmetry plane is also provided. Finally, the half-body subsonic grid consisted of about 6 x 106 cells meanwhile the supersonic grid consisted of about 5 x 106 cells, according to a grid independence study performed on three subsequent levels of mesh refinement. Figure 1.3.6 Supersonic computational domain with mesh on the aircraft wall and symmetry plane Figure 1.3.5 Typical boundary layer prismatic cells with mesh on the aircraft wall and symmetry plane

37. 36 1.3.4.5 CFD Modeling and Numerical Discretization Steady-state RANS simulations are performed with ANSYS-FLUENT and SU2 solvers. Air is modelled according to the perfect gas model, with specific heat at constant pressure equal to cp = 1006 J/kgK and viscosity provided by the Sutherland law. Air thermal conductivity was assumed constant, k = 0.0242 W/mK. RANS closure is performed using the shear–stress transport (SST) κ-ω model. In the current computation, pressure far field and pressure outlet boundary conditions are used at the domain inlet and outlet, respectively. While adiabatic wall boundary condition is applied at the aircraft surface. Finally, tool settings adopted for both ANSYS-FLUENT and SU2 solvers are detailed described hereinafter. They were validated against theoretical and experimental data in several numerical investigations carried out by authors in previous works, as detailed discussed in Refs. [24,30–32]. 1.3.4.5.1 The FLUENT Solver As the Mach number significantly varies within the investigated flow conditions, compressibility effects on the aircraft aerodynamic performance were taken into account by means of the pressure- based solver and the density-based solver, available in ANSYS FLUENT. The SIMPLE solver is used for subsonic speeds, although the adopted version is also applicable for a wide range of flow regimes, from low-speed incompressible to high-speed compressible flows [33]. Spatial discretization of inviscid terms in NS equation is performed using second-order upwind scheme, while gradients of solution variables at cell centers are obtained by using the Least-Squares Cell-Based (LSCB) method [33]. The supersonic simulations were performed by using the density-based solver with the implicit formulation. To correctly track the discontinuities which arise at supersonic speeds, an approximate Riemann solver implemented in the ROE-FDS scheme available in ANSYS-FLUENT is adopted for inviscid flux computation. As far as solution procedure is concerned, it is worth noting that the solution steering algorithm in FLUENT was considered. It determined the Courant number (CN) during the simulations which affects the solution speed and stability. During solution startup, a CN equal to 1 is considered as changes in the flow field solution are highly nonlinear. But as solution progresses, solution steering automatically changes some solver parameters and progressively increases the CN in order to ensure a steady-state-converged solution. In particular, solution steering allows the solver to not exceed the assigned maximum CN and to use a CN less than the initial value if the solution diverges. In addition, full multi grid initialization is also adopted which computes a quick, simplified solution based on a number of coarse sub-grids. This helps to get a stable and better starting field for the main calculation [33]. Under-relaxation factors for the uncoupled parameters are keep at the default values. Finally, at each selected test matrix flight conditions the overall mass, momentum, energy, and scalar balances are verified to address convergence of solution. Residuals are verified to have a decrease at least of three order of magnitude; while the scaled energy residual should decrease to 10-6. 1.3.4.5.2 The SU2 Solver The open source multi-physics CFD toolkit SU2 is based on a finite volume discretization of a PDE performed on an edge based dual grid using a finite volume approach [34]. In the current computations, a second order backward scheme is used for time integration and spatial gradients are computed with a Green-Gauss approach averaged at the cell faces for viscous fluxes computation. SU2 has been extensively validated with respect to experimental data [34]. However, aerodynamic analysis of complete aircraft configurations, like SST aircrafts demands CFD simulations for a wide range of Mach numbers. At very low-Mach numbers, pressure disturbances travel at the speed of sound which at the incompressible limit, becomes infinite and drives to numerical instability. At high Mach numbers, shock-waves create strong gradients in flow properties eventually driving to

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