domain: spi phys

text:
Sebastien Defoort
email: sebastien.defoort@onera.fr

Michaël Méheut
email: michael.meheut@onera.fr

Bernard Paluch
email: bernard.paluch@onera.fr

Romain Liaboeuf
email: romain.liaboeuf@onera.fr

Raphaël Murray
email: raphael.murray@onera.fr

Daniel Mincu

Jean-Michel M David
email: jean-michel.david@onera.fr

D.-C Mincu

Conceptual design of disruptive aircraft configurations based on High-Fidelity OAD process

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Nomenclature

I. Introduction

The objective of the team work performed by ONERA in the frame of the Clean Sky2 -ITD Airframe European project is to design, within the so-called Techno-Stream A-1, four different innovative concepts (lifting fuselage, 3-surfaces, joined-wing and Blended Wing Body configurations) on two specific missions (A320-like and business-like). This work is performed in collaboration with DLR. As part of a down-selection process aimed at defining the most promising aircraft architectures for future air transport, this study shall provide enough accuracy in the performance evaluation to be able to compare the different concepts to the reference aircrafts evaluated with the same tools, and to rank and discriminate them with confidence.

The figure below illustrates the innovative architectures under study.

A320-like mission

Alternate BWB (illustration: Onera) Joined wing (illustration: Lockheed/NASA concept)

Business jet mission

Lifting Fuselage (illustration: Onera) 3-surface (illustration: Piaggio P180)

Initial view and objectives of the OAD process

The global scheme governing the new configuration studies is a progressive down-selection of interesting concepts with a simultaneous refinement of assessment level, from L0 (empirical, analytical based formulations) to L2 (detailed physics integrated on a true geometry). Rather than defining a new OAD process for each step of down selection, the approach chosen is to define a unique modular and evolutive multidisciplinary process. The logic defined as a long term vision of multidisciplinary coupling with L0 to L2 tools is illustrated on the figure below: A focus is made on the 3 main drivers for new airframe and engine integration concepts:

-Mass estimation including aeroelastic effects, -Cruise drag optimization with deformed shape, -Fuel consumption minimization taking into account coupled fan and core engine design and potential BLI effects.

Framework for integration: the MYSTIC tool

Integrated OAD activities have been running at ONERA for a long time, but the existing tool suites were either based on commercial integration softwares, or not sufficiently modular to perform MDO studies. Therefore in the frame of this project, and taking benefit of on-going internal studies on MDO, a large effort was undertaken to define a new, modular, evolutive tool to conduct the configuration studies, first at L0 level.

A first, simplified version of the tool called FAST (Fixed-wing Aircraft Sizing Tool) was initiated and is shared with ISAE. The description can be found in [START_REF] Schmollgruber | Use of a Certification Constraints Module for Aircraft Design Activities[END_REF]. An enhanced version calibrated and improved with ONERA internal knowledge has then been developed under the name of MYSTIC, and will be used in this study. -Loop 1: design of HTP and VTP surfaces upon trimmability and stability HQ criterions at take-off and in cruise, iterating on the CoG position, -Loop 2: iteration on the wing position to ensure a desired static margin, after calculation of aerodynamic center, -Loop 3: iteration on the maximum take-off weight (updated after OWE and mission fuel calculation) and wing size (to ensure required approach speed and accommodate the mission fuel). The logic of the study will be to progressively replace the L0 tools pre-existing in MYSTIC by the higher fidelity modules that will be described in the subsequent section B, and to tend to the process definition described in section A.1. In order to achieve this goal, a common input/output XML file is used, gathering the whole description of the aircraft through a dictionary of parameters. The geometrical parameterization is shared among all the modules and enables to generate an OpenVSP8 CAD model for visualization and disciplinary computation purposes.

Aerodynamics

For the evaluation of the aerodynamic performance of the different configurations, two specific aerodynamic modules have been developed. The first one aims at assessing the cruise performance and the second one, the maximum lift coefficient at low-speed conditions:

Cruise performance module (CANOE)

This module is based on Euler-CFD computations performed by the SU² [START_REF] Economon | SU2: An open-source suite for multiphysics simulation and design[END_REF] code and on the in-house ONERA far-field drag decomposition tools ffd [START_REF] Van Der Vooren | Drag/Thrust Analysis of a Jet-propelled Transonic Transport Aircraft; Definition of Physical Drag Components[END_REF]. This tool enables, from a CFD solution, to compute the different physical drag components (viscous, wave and induced) and eliminate the non-physical drag sources, called spurious drag. Thanks to this approach, the sensitivity of the total drag with respect to the mesh is drastically reduced compared to classical near-field integration methods. This aerodynamic module also provides the other aerodynamic coefficients (notably the lift and pitching moment coefficients). The surface meshes used for the Euler computations are created using OpenVSP [START_REF] Chaput | Vehicle Sketch Pad Structural Analysis Module Enhancements for Wing Design[END_REF] and the geometry defined by MYSTIC. The unstructured final volume meshes are generated using tetgen [START_REF] Si | TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator[END_REF].

To ensure an accurate and reliable evaluation of the total drag during the optimization process at OAD level, a detailed parametric study with respect to mesh parameters has been achieved and coupled with the postprocessing procedure using ffd (described above).

An example of results produced by the aerodynamic module is shown in Figure 6: surface pressure distributions, wave drag sources in the volume.

Low-speed-performance module

This module is based on a coupling between a VLM and 2.5D RANS computations performed by the ONERA in-house elsA code. The objective of this coupling ([6] and [START_REF] Parenteau | Aerodynamic optimization of aircraft wings using a coupled VLM-2.5D RANS approach[END_REF]) is to integrate in the VLM, the nonlinear effects captured by the 2.5D RANS computations (detached flows). Having 2.5D computations instead of purely 2D computations enables to take into account the transversal effects along the wing span and provides a more accurate prediction of the maximum lift coefficient (assuming that the 2.5D RANS computations are accurate).

The coupling algorithm (also detailed in Figure 7) proceeds as follows. For each spanwise section of the wing, A dedicated validation procedure has been set-up to evaluate the accuracy of the method and the results have been compared with full 3D RANS computations and experimental results.

Structure

The mass and center of gravity position are two of the fundamental parameters governing aircraft performances. In most of the L0 level tools, these parameters are determined using statistical formulations depending only on a reduced number of significant variables (wing span, fuselage diameter,…). In this paper, the aircraft mass estimation (and associated data such as CoG position, tensor of inertia components,…) is done according to a method which combines the mass estimation coming from the sizing of the primary structure and that of the secondary structures obtained using analytical and/or statistical methods. The primary structure is the one which mainly supports the loads acting on the aircraft, while the secondary structures are attached to the primary structure, but do not contribute directly to its mechanical resistance. The whole of the components of the primary structure is mainly made up of the fuselage, the wing, the tail surfaces and the landing gear, the secondary structure gathers the various flaps, ailerons and equipment (cabin, instruments, etc…). In the approach adopted here, the fuselage and the airfoil are sized using finite elements methods in order to estimate their mass. The masses of the other components are estimated using statistical formulations for the remaining primary structures (control surfaces and landing gear) and for the secondary structures. However, for these last ones, the statistical formulations only allow to calculate their mass, and a special attention has been paid to spatially distribute these masses over the whole aircraft in order to obtain a better precision in the CoG position. This was done by refitting the existing formulations in order to take into account, in particular, the space distributions of the equipments.

Figure 8: example of V-N diagram

Concerning the wing sizing a finite elements (FE) code is used, with plate elements to represent the wing box mechanical behaviour with more accuracy. The wing boxes are delimited by the wing lower and upper surface skins, the leading and trailing edge spars on which the slats, flaps and ailerons are attached (their surface masses are estimated according to statistical formulations). The FE mesh is composed of only a few hundreds of elements to avoid high computation time. The V-N diagram (manoeuver and gust, Figure 8) for various sizing flight configurations allow to determine the wing loading cases. The wing is divided in a certain number of boxes, separated by ribs. For each box, a specific sizing procedure determines the wing skin thickness and stringer height to ensure rupture and skin buckling. The thicknesses and height distributions along wing boxes (Figure 9) allow to determine the wing mass by taking into account penalty factors such as connecting elements, the lightning devices, the box sealant for the fuel tanks, … It is possible to size the wing either with metallic or composite materials. In this last case, stacking sequences of each component (skins, ribs, stringers,…) are selected among existing pre-built families respecting a certain number of criteria (stacking sequence symmetry, defined angle plys,…).

Figure 9: thickness and height distribution along wing boxes

For the fuselage, the statistical formulation currently employed is gradually replaced by a more complete sizing procedure which can take into account large fuselages. The method employed being similar to that used in former studies [START_REF] Wiart | Development of NOVA Aircraft Configurations for Large Engine Integration Studies[END_REF]. The concatenation of the whole masses (primary and secondary structures) then gives the global aircraft masses (MTOW, MLW,…) which will be used for performance calculation.

Propulsion

Powering the system requires dedicated adjustments on various points of the flight envelope. The propulsion disciplinary module aims at providing thermodynamic conditions for a set type of turbomachine at specified operating conditions. This 0D modelling tool consists in applying the equations for the conventional Brayton thermodynamic cycle for gas turbine engines to the compression, combustion and expansion components. However, due to increasing demand in modularity, all the parts of the engines can be moved, duplicated or removed separately whilst keeping consistent and reliable thermodynamic modelling. This will allow for the description of advanced turbine based propulsion systems such as hybrid electric generators or multiple distributed power sources. Specific fuel consumption (SFC) and specific thrust (ST) are computed along with mass estimations using the expressions derived by Roux [START_REF] Schmollgruber | Use of a Certification Constraints Module for Aircraft Design Activities[END_REF] for turbofan engines, making the plane mass budget evaluation feasible.

Component pressure ratio, bypass ratio, pressure losses, polytropic efficiencies, or mixing conditions are set at the reference operating point of the engine when initializing the module. Bleed air can be taken where the user specifies. To adapt the engine to off design conditions, an iterative loop is run trying to adapt the pressure ratios, bypass ratios, and overall massflow to match the same conditions of reduced massflow as for the reference point design sections. This ensures that the physics solved matches the actual engine behavior. Efficiencies are adjusted in consequence. For a conventional non-mixing turbofan engine, 4 target sections are used: high pressure distributor outlet, low pressure distributor outlet, core-flow nozzle throat and bypass flow nozzle throat.

An engine can be iteratively defined with specified targets of SFC and thrust at different flight points. For this purpose, the loop would adapt the design parameters at reference point: pressure ratios, efficiencies, and massflow ratios to reach the desired engine design. This disciplinary module is in itself separated in submodules to enhance the level of modelling put into this design platform. More detailed submodules can include pollutant emission prediction, hybrid electric operation,…

Handling qualities

Unconventional configurations raise new questions on handling qualities (HQs) aspects. On the one side, having multiple control devices may enable actuators use optimization. On the other side, new configurations tend to be less stable or even unstable and such case can jeopardize aircraft safety unless an artificial stability is implemented through a flight control system. For such configurations HQs can even be a showstopper and thus must be included at early design stages.

To provide early design stages HQs assessment, a tool aiming at evaluating various aircraft configurations on a set of handling qualities criteria related to manoeuvers which occurs in aircraft operational life was designed. As HQs are related to center of gravity (CoG) position, each criterion is designed to compute the extremal CoG at which the manoeuver can be safely operated. Compared to the actual CoG range (given by mass analysis) a margin which can be used in an optimizing process is obtained. These criteria can be equilibrium computations, evaluating limit conditions on which the aircraft is trimmable; modal analysis, in order to verify is dynamic modes are stable enough (Dutch roll for instance); or dynamic manoeuvers where a time simulation is performed on either open or closed loop. Equilibriums and criteria are defined to be computed within scripts or via user console commands and are able to deal with multicontrol configurations via controls optimization for equilibriums and controls allocation for closed loop simulation.

In order to be able to deal with various configurations at any stage of aircraft development, this tool includes basic modeling for aerodynamics and propulsion, which can be customized taking into account aircraft specificities and design variables. These models are enriched while new data is provided from each domain experts to improve their fidelity, from L0 to L2.

Acoustics

The aeroacoustics studies are performed using two levels of accuracy. The first one that aims to finally down select the less noisy aircraft takes into account all the scaled acoustic sources and their installation effects. These computations are performed using the in-house tools (i) BEMUSE 9 which evaluates the scattered field by the aircraft and (ii) CARMEN 10 which predicts the ground noise from an aircraft flyover. The second level is based on high fidelity calculations (hybrid CFD/CAA approach) on the final selected configuration.

Generally, the BEM codes are well suited for computing the acoustic scattered field around complex geometries in the presence of potential flows (low Mach numbers approximation). However, in this study, the objective is to compute the acoustical footprint for almost all the third octave bands (20 Hz-10 kHz) and for full size aircraft geometry. This is highly expensive, for higher frequencies, and unpractical for eventual optimization or refurbishing processes. 9 Rapid numerical methods (BEM) for solving Helmholtz equation in presence of arbitrary scattering geometries are based on mathematical approximations of an interaction matrix, representative of a perturbed linear system written on this surface. Onera's in-house code BEMUSE solves this system using either a Brakhage-Werner or a Burton-Miller integral formulation. Sommerfeld's radiation condition applies at infinity and the scattering surface defines the boundary conditions which can be, for instance, Neumann, Dirichlet or Robin conditions. These elements are coupled with an algebraic approach of the kernel approximation (inverse matrix) based on the Adaptive Cross Approximation (ACA) method. The implemented method is following the works of Grasedyck on asymptotically smooth kernel operators initially introduced by Bebendorf. It computes a low-rank approximation of appropriate matrix blocks, independent on the kernel operator. The size of the final matrix to be solved, within the above considerations, is largely diminished from an N2 to an N•log(N) order (where N denotes the number of grid points). 10 CARMEN is a tool to predict aircraft noise on the ground all along its trajectory during landing, take-off and cruise flyovers. It includes the acoustical source description, the installation effects and the sound propagation from the aircraft to the ground. The acoustic model CARMEN is connected with the engine module in order to provide, all along the trajectory, the inputs required for the propulsion noise sources, and also with the aircraft module to give the trajectory, the altitude of the aircraft, the high lift devices and the landing gear configurations. The aircraft and its fly mission being preliminary defined; CARMEN can predict the noise footprint around airport within a short CPU time, on existing and future aircraft. It describes the main acoustical phenomena encountered during aircraft flyover summarized by the sound pressure level prediction around the aircraft and also computes the propagation effects such as Doppler frequency shift, spreading loss and atmospheric attenuation. In Figure 12 two grid topologies are studied in order to drastically reduce the computational time for a given frequency. On the left side a common uniform 6 ppw (general rule) grid was generated for a business jet aircraft. After some geometrical approximations (like for example the trailing edges sharpening and some fuselage smoothing) the total grid accounts for 300 000 points. On the right side, all the surface gradients and small features (trailing edges) were preserved by densifying locally the grid up to about 40 ppw. The rest was mainly discretized with about 1 to 2 ppw. Figure 13, left, shows the results obtained for an acoustical source emitting at 1000Hz (aircraft length of about 20m) situated at the engine position over a surface parallel with the symmetry plane of the aircraft and passing through this source. The classical grid computation took about 3 CPU hours where the optimized grid needed only 15 CPU minutes. For validation purposes, these results were compared with CAA simulations performed using high order numerical code solving Euler equations in perturbed form (Figure 13, right). Besides the CAA stretching effect on the lateral computing zone, both approaches provide comparable results in terms of noise propagation. Based on these elements a final optimized grid will be derived and used for all the required sources and frequencies computations.

Aero-elasticity

Today the aeroelastic analysis does not enter directly into the OAD process set-up, it is a secondary module which allows to analyze the aeroelastic behavior of the pre-designed aircraft but the final objective is to include this module in the sizing loop. The aeroelastic analysis is mainly devoted to the structure optimization of the pre-designed aircraft under dimensioning loadings (defined by the flight domain) and consequently to the flutter analysis of the optimized aircraft. The analysis is based on the NASTRAN code which has all the required modules for an aeroelastic analysis of a complex structure. It has been coupled with the hybrid approach developed at ONERA. This method couples the classical DLM approach with 3D RANS CFD computations performed by the in-house elsA code [START_REF] Cambier | The Onera elsA CFD software: input from research and feedback from industry[END_REF] to consider the non-linear effects which are not taken into account with DLM (zero lift coefficient, camber, thickness, stall, shocks,…).

Performance

The performance analysis performed in MYSTIC consists in 3 different steps:

-The computation of a design mission using time step integration for all phases of the mission: take-off, climb at constant CAS, cruise with step climb, descent, landing, alternate mission of 200NM, holding pattern, landing. Taxi fuel consumption is also modelled.

C. Validation and sensitivities

In order to validate the disciplinary tools and their integration in the OAD process, sensitivities analysis were performed for classical wing planform parameters such as the Aspect Ratio (AR), the sweep angle, the taper ratio or the wing profile thickness. In the following sections, results of this validation procedure are detailed for the initial L0 OAD process, as well as the two main disciplines which are aerodynamics (cruise performance) and structure (mass breakdown).

OAD with L0 models

As a starting point, a sensitivity study to the AR is performed with the simplest models of the OAD process, before introducing higher fidelity for Aerodynamics and Structure. The sizing mode is used, which means that wing size and position as well as HTP and VTP sizes are re-estimated for each value of AR, in order to get the adequate aircraft for the design mission, as well as its associated MTOW, OWE and fuel burn.

The following results are obtained for the various figures of merit of the configuration, the TLAR being those of an A320-class aircraft.

Wing Area

Wing Weight Maximum L/D

OWE MTOW Mission Fuel Weight Figure 17: results of OAD sizing with L0 models

The following main observations can be made:

-First, the global tendencies expected for aerodynamics and structure are reproduced: increasing Aspect Ratio leads to better L/D (from 14 to 20) and heavier wing (from 6.5 to 13 tons). -Then, the simple L0 model used for structure leads to a linear behavior in wing weight estimation, and thus in OWE. Although consistent, this may lead to a low accuracy, especially for high aspect ratios. -With these models, the best compromise for MTOW is around AR=8, whereas for fuel consumption minimization, the highest possible AR should be chosen.

Aerodynamics

For the assessment of the cruise aerodynamic performance, a simplified configuration based of the CeRas configuration was defined (see §III). This configuration is composed on the single trapezoidal wing (without kink) and fuselage. In order to evaluate the impact of the Aspect Ratio on the aerodynamic performance, several configurations (AR ranging from 6 to 20) keeping all other wing parameters constant (wing area, sweep angle, taper ratio, thickness and twist spanwise distributions) to obtain as much as possible a pure AR effect. The results are depicted Figure 18 and Figure 19 for C L =0.6. Figure 18 shows the influence of the Aspect Ratio on the wing pressure distributions and Figure 19 on the induced and wave drag components. Figure 18 highlights the wingspan increase with the AR as well as the decrease of the Mean Aerodynamic Chord (constant wing area). As expected for all configurations, the flow topology on the upper part of the wing remains identical (scaling effect) and the intensity of the shock wave consistent.

The evolutions of the induced and wave drag components with respect to the Aspect Ratio are shown in Figure 19 for C L =0.6. For the induced drag, the results are compared to the minimum induced drag values obtained for an elliptic wing distribution. For both components, the two curves correspond respectively to the results obtained without and with aircraft sizing (as detailed in §II). This means that for the sizing case, the wing area slightly evolves with the AR depending on the mass equilibrium. Consequently, the results in Figure 19 show that the impact of the sizing is relatively small but enable to demonstrate that:

• the aerodynamic module provides results consistent with the theory (constant wave drag and decrease of the induced drag similar to the theoretical minimum induced drag); • the correct integration of the aerodynamic module in the OAD process.

As an illustration, the overall sizing of the aircraft with this highfidelity model in the loop leads to the results shown on Figure 20 in terms of mass breakdown and fuel consumption. Compared to the L0 results, the optimal aspect ratios for MTOW and fuel consumption are shifted towards lower ones, but result are not directly comparable due to different wing planform (with and without kink).

Similar results were also obtained for other wing planform parameters (sweep angle, taper ratio, spanwise thickness and twist distributions). This exhibits that the OAD process coupled with the high-fidelity aerodynamic module can be used for wing planform optimization as wing planform parameter sensitivities are correctly captured.

Figure 20: masses of the resized aircraft 3. Structure Using the L0 modules of MYSTIC (especially for structure), it was observed that the dependency of wing weight to AR was fully linear, due to the very simple mass breakdown correlations used in this approach. Using the structure module described in B.2, one would expect a more realistic behavior, and in particular a stronger penalty for high AR wings, because of the finite element approach.

Therefore, a parametric study was conducted with respect to AR in order to compute the wing weight for an AR ranging from 6.0 to 16.0, and a wing planform with a kink. The geometries obtained as well as the sensitivity curve are presented below: -The global trend of wing weight evolution is closer to quadratic than linear, due to the more realistic modelling principles; this model can be expected to be more reliable when exploring wing shapes far away from the classical 2-section, AR=10 wing of current SMR aircrafts, -Some numerical artefacts can be observed on the parametric analysis: with only 6 points in the study, the effect of discretization and the discrete parameters such as the stacking sequence for composite materials lead to this behavior. When compared to the results observed with L0 models (see C.1), it can be seen that this new behavior of the structural model leads to a shift of the optimal Aspect Ratio for fuel consumption minimization to values around AR=14, due to higher weight penalty for high aspect ratios. Smaller MTOW is also observed because of a more optimistic absolute value of wing weight propagated by snowball effect.

III. Design of novel configurations

The use of this OAD process towards the assessment of new aircraft configurations has to follow a rigorous logic, our aim being to provide a comprehensive downselection of most interesting configurations. Therefore, the choice has been made to start from a single OAD tool and enrich it both to explore new configurations, and to assess them with higher and higher accuracy. This process is illustrated on the figure below.

Figure 24: overall approach for the design of novel configurations As a first step the reference configurations have been designed using L0 models. They will be refined using the more accurate high-fidelity modules to be compared to the new configurations. In parallel, new parameters and new sizing rules are introduced to be able to assess novel configurations such as joined wing, large fuselage, tri-surfaces or BWB.

A. Reference aircrafts

A-320-like mission

The TLARs of the aircraft are given by the configuration CSR-01 from the CeRAS open database of the University of Aachen 11 . The main features are recalled below: -Reverse engineering of the CeRAS configuration with the MYSTIC code, -Design of an A320-like aircraft with rear engine and T-tail features (to ease future innovative engine integration studies) -Design of the previous aircraft with more aggressive technology hypothesis (eg. SFC reduced by 20%, aerodynamic efficiency increased by 15%, airframe weights reduced by 10%) representative of a 2035 EIS.

Results and illustration of the configurations are given below: More specifically, it can be seen that the rear-engine option, after subsequent redesign of wing, HTP and VTP, provides an overall 1.5% penalty both on MTOW and on fuel burn, which is consistent with the experience of aircraft manufacturers. Figure 26 shows the detailed mass breakdown of this RE configuration compared to the CeRAS reference, with a small 3.5% penalty on airframe weight partially compensated by better aerodynamics. the aircraft is fully redesigned to match these requirements. For higher payloads, as the redesigned aircraft is lighter than the reference one, less fuel is available and the range performance is reduced. On the contrary, for lower payloads, as the aircraft performance is better, the range capability is increased. -The Joined wing configuration, for which a preliminary bibliography study [START_REF] Wolkovitch | The joined wing-An overview[END_REF] has been conducted, and the set of parameters to model this particular architecture has been chosen. The figures below illustrate these two aspects, estimation of wing weight at L0 level from bibliography, and new parameters introduced for the design. Challenges will be to provide a realistic mass breakdown, to quantify the gains in induced drag, and to handle the HQ issues induced by the absence of HTP (which role is played by the rear wing). -The BWB configuration: specific parameters and modelling approach will be derived from the internal Onera project CICAV, which is described in [START_REF] Gauvrit-Ledogar | Multidisciplinary Overall Aircraft Design Process Dedicated to Blended Wing Body Configurations[END_REF] 2

. Business-like mission

Two configurations are being studied for the business jet mission:

-The Large fuselage configuration: a new parameterization for the fuselage shape is introduced, and the CANOE tool will enable a proper estimate of the aerodynamic performance of this new configuration.

In parallel, a FEM structural parametric model is being developed, to assess the mass breakdown with sufficient accuracy. Redesign of HTP and VTP with shorter fuselage, and accommodation of high-lift devices will be the other challenges of this configuration.

IV. Conclusions

In the frame of the Clean Sky 2 -ITD Airframe, ONERA is conducting a design and downselection study on innovative aircraft architecture. In order to enable a fair comparison and a sufficient level of accuracy, the inhouse MYSTIC OAD process is used and enriched towards new configurations and higher fidelity. This paper has described the set of tools used to incorporate more high-fidelity in the OAD process, which proves to be challenging from an interface point of view on the one hand (set of data to be exchanges) and from a computational point of view on the other hand (robustness and calculation time of HF models). To improve the reliability of the overall process, a set of parametric studies have been conducted on the overall process, with respect to simple parameters such as aspect ratio. The results show the consistency of the designs and the improvement brought by L1 and L2 models with respect to the simple, empirical L0 process. A focus is then made on the set-up of reference configurations at L0 level for different missions and for different technology levels and architectures (current and 2035 technology, underwing or rear-engine) to set up a comparison point for further studies. Finally, the paper has introduced the challenges for the preliminary analysis of novel configurations, that will be investigated with high-fidelity tools in the near future, now that the enhanced process is fully available.

Figure 1 :

 1 Figure 1: innovative architectures under study II. Description of the OAD process A. Overall architecture and coupling between disciplines

Figure 2 :

 2 Figure 2: overall aircraft design process (long term vision)

Figure 3 :

 3 Figure 3: inputs and outputs of the MYSTIC tool This tool incorporates physical modules for the classical disciplines of Overall Aircraft Design: Propulsion, Aerodynamics, Mass breakdown and balance, Handling qualities, Trajectory and Performance. 3 sizing loops are implemented, allowing to design an aircraft upon its TLARs with iterations on the disciplinary modules:-Loop 1: design of HTP and VTP surfaces upon trimmability and stability HQ criterions at take-off and in cruise, iterating on the CoG position, -Loop 2: iteration on the wing position to ensure a desired static margin, after calculation of aerodynamic center, -Loop 3: iteration on the maximum take-off weight (updated after OWE and mission fuel calculation) and wing size (to ensure required approach speed and accommodate the mission fuel).

Figure 4 :

 4 Figure 4: sizing loops implemented in MYSTIC

Figure 5 :

 5 Figure 5: XML file, geometric parameters and OpenVSP visualization used in MYSTIC B. Disciplinary modules

Figure 6 :

 6 Figure 6: Euler-based CFD computations performed by SU² with far-field drag decomposition using ONERA ffd code.

4 .

 4 Correct the angle of attack given to the VLM by Δ (so each section will face a different angle of attack ); 5. Repeat these steps until + , with , -10 0 .

Figure 7 :

 7 Figure 7: VLM/2.5D RANS coupling for low-speed aerodynamic performance prediction

Figure 10 :

 10 Figure 10: Multi-actuator equilibrium by moving CoG for deferent elevator deflections

Figure 11 :

 11 Figure 11: time simulation with step on virtual rudder (dn) then virtual ailerons (dl) with feedback loop on virtual commands (left) and actual actuators evolution (right) with pseudo-inverse allocation

Figure 12 :

 12 Figure 12: business jet like fuselage surface grid for BEM studies; left -"classical grid", uniform 6 ppw; right -"optimized grid", stretched form 40 ppw to 1 ppw; ppw (point per wavelength)

Figure 13 :

 13 Figure 13: Scattered field for an acoustical source situated at the engine position; left: BEM comparisons between classical grid computation (the red lines) and the optimized one (flood/blue lines), right: comparison between the BEM optimized grid computation (black lines) and 3D CAA simulation (flood/red lines)

Figure 14 :

 14 Figure 14: example of sizing mission -The computation with the same principles as above of an operational mission of shorter range that can be the basis for direct operating cost estimation, and provides an overview of the aircraft performance on the most used routes.

Figure 15 :

 15 Figure 15: example of operational mission -The computation of the Payload-Range diagram which represents the aircraft performance with respect to its passenger loading.

Figure 16 :

 16 Figure 16: example of payload-range diagram

Figure 18 :Figure 19 :

 1819 Figure 18: Aerodynamic assessment -Influence of Aspect Ratio on the surface pressure distribution

Figure 21 :

 21 Structure assessment -evolution of wing weight with aspect ratioTwo main features can be observed in the sensitivity analysis:

  comparison of fidelity levelsTo confirm the effect of this new L1 Structure module, an additional parametric study was performed with the full OAD sizing process of MYSTIC, only replacing the L0 wing weight with its L1 estimation. Results are presented below:

Figure 23 :

 23 Figure 23: OAD sensitivities to the aspect ratio -evolution of MTOW (left) and fuel weight (right)

Figure 25 :

 25 Figure 25: Top Level Aircraft Requirements for A320-like mission A comparative study has been performed with the following steps:-Reverse engineering of the CeRAS configuration with the MYSTIC code, -Design of an A320-like aircraft with rear engine and T-tail features (to ease future innovative engine integration studies) -Design of the previous aircraft with more aggressive technology hypothesis (eg. SFC reduced by 20%, aerodynamic efficiency increased by 15%, airframe weights reduced by 10%) representative of a 2035 EIS.

Figure 26 :

 26 Figure 26: reference aircraft geometries (CeRAS, rear-engine, rear-engine 2035)This design of 3 reference configurations shows on the one hand the versatility of the MYSTIC OAD process, enabling to model several architecture options and technology effects with a minimal adaptation and a modelling consistency. On the other hand, it helps quantifying effects that are well-known and provides a strong basis for future comparison.

Figure 27 :

 27 Figure 27: Detailed mass breakdown of the RE configuration (A: airframe, B: propulsion, C: systems, D: cabin equipments) As further illustration, the Payload-Range diagram of the 2035 configuration is plotted on Figure27, and compared to the reference one. The design point (150 PAX, 2750 NM) is the intersection of the two curves, as the aircraft is fully redesigned to match these requirements. For higher payloads, as the redesigned aircraft is lighter than the reference one, less fuel is available and the range performance is reduced. On the contrary, for lower payloads, as the aircraft performance is better, the range capability is increased.

Figure 28 :Figure 29 :

 2829 Figure 28: Payload-Range diagram for the EIS 2035 improved aircraft2. Business jet missionA set of requirements representative of a classical business jet mission was chosen to perform the sizing studies. They are summarized below:

Figure 30 :

 30 Figure 30: result of business jet reference aircraft sizing D. Towards the design and analysis of the 4 disruptive concepts 1. A-320-like mission Two configurations are being studied for the SMR mission:

Figure 31 :

 31 Figure 31: joined wing bibligraphy survey ([10] -left) and main parameters (right)

Figure 32 :

 32 Figure 32: parameterization of the large fuselage and extraction of transverse sections -The tri-surface configuration: the HQ module described above will be extensively used to find the best compromise of the aerodynamic surfaces and controls allocation.

Table 1 :

 1 synthesis of reference aircrafts resizing results

www.openvsp.org

https://ceras.ilr.rwth-aachen.de/

Acknowledgments

The authors would like to specially thank:

-The European Commission and the Clean Sky 2 Joint Undertaking for the financial support in the frame of Clean Sky 2 Airframe ITD; -Peter Schmollgruber and Alessandro Sgueglia (ONERA Information Processing and Systems Department) for their contribution to the MYSTIC tool development. -Alexandre Sapet and Jean-Luc Hantrais-Gervois (ONERA Aerodynamics, Aero-Acoustics and Aero-elasticity Department), developers of the CANOE tool suite. -Maxime Vergez (ONERA Aerodynamics, Aero-Acoustics and Aero-elasticity Department), developer of the VLM/2.5D RANS coupling strategy.

-Laurent Sanders (ONERA Aerodynamics, Aero-Acoustics and Aero-elasticity Department) for his contribution to the aeroacoustics studies.


David ) Chen
email: z.chen@dal.ca

Michel M Ney
email: michel.ney@enst-bretagne.fr

Method of Moments: A General Framework for Frequency-and Time-domain Numerical Methods

Keywords: Method of Moments, frequency domain, time-domain, spectral domain method, finite-difference method, finite-element method, integral equation method, and pseudo-spectral time-domain method

Many numerical methods have been derived and developed in the past five decades for solving electromagnetic structure problems. They can be categorized into frequency-and time-domain methods. Among them are frequency-and time-domain spectral domain methods, finite difference based methods, finite element FEM) methods and integral equation methods. These methods have been studied extensively and become mature enough such that a number of software packages based on them have been developed commercially. However, all these methods appear to have been unrelated and formulated on different mathematical bases. In this paper, we show that all these methods can be derived directly with the Method of Moments (MoM). The differences among them are (1) the equations and quantities to be solved and (2) the expansion and weighting functions used. The work presented here opens a new horizon for developing other new methods under a unifying framework of MoM without considering which methods they belong to.

I. INTRODUCTION

T OSOLVE electromagnetic structure problems, two types of numerical methods have been developed so far: frequency-domain and time-domain methods. Thanks to significant advancements in high-speed computer technology, both types of the methods become increasingly effective in computing complex electromagnetic structures used in electronic circuits, communication systems, and sensor networks and applications. While frequency-domain methods are efficient in simulation of narr ow band signals, time domain methods becomes increasingly popular due to their capability of solving wide-band signals. Typically among the frequency-domain methods are the finite difference frequency-domain methods [l], frequency domain finite-element method [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF], spectral domain method [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF], mode matching [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF] and transverse-resonance method [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF]. Among the time-domain techniques are the time-domain finite-element methods [START_REF] Lee | Time-domain finite-element methods[END_REF], time-domain integral-equation methods [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF][4] and the finite-difference time-domain based methods (e.g. FDTD and TLM) [START_REF] Taflove | Computational Electrodynamics: The Finite-Dif f erence Time-Domain Method, 2 00[END_REF] [START_REF] Hoefer | The transmission-line-matrix method -theory and applications[END_REF].

As the results of research advances on these methods, simulators have been developed worldwide and have been made commercially available (e.g. HFSS by Ansoft [7] and XFDTD by Remcom [8]).

In the numerical methods, the continuous system of Maxwell's equations is replaced with a discrete system or a system of approximations whose solutions are accurate enough with certain parametric constraints. So far, different numerical methods have been developed through different mathematical processes. They appear to be unrelated to each other. For instance, the finite-element (FEM) method was based on numerical solutions or functional minimization for a generalized wave equation [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF]. The integral equation (IE) methods came about with applying the method of moments (MoM) to an integral equation in spatial domain and finite-difference in time domain if needed [START_REF] Pisharody | Robust solution of time-domain integral equations using loop-tree decomposition and band limited extrapolation[END_REF]. The widely used finite-difference frequency-domain and time-domain methods were formulated by direct finite-differencing the frequency domain and time-domain Maxwell's equations, respectively [1] [START_REF] Taflove | Computational Electrodynamics: The Finite-Dif f erence Time-Domain Method, 2 00[END_REF]. The TLM method was derived with the utilization of transmission line networks [START_REF] Hoefer | The transmission-line-matrix method -theory and applications[END_REF]. Even the classical mode matching was simply application of the boundary conditions with mode expansions.

In this paper, all these numerical methods are shown to be derivable from the well-known Method of Moment (MoM) [START_REF] Harrington | Field Computations by Moment Methods[END_REF]. In other words, all these numerical methods can be obtained by first expanding solutions in terms of sets of basis functions and then minimizing the associated residual errors with sets of weighting functions. Differences among the different methods are simply the uses of different expansion and weighting functions as well as solutions of different equations. Consequently, different numerical methods are generalized under a unifying framework. Numerical issues such as numerical stability and dispersions can be directly related to the convergence of the expansions and the measure of the errors in frequency and spectral domain. In other words, the work presented in this paper provides a general theoretical framework under which a common procedure for developing a numerical technique (i ncluding a potentially new one) is defined.

The paper is organized in the following manner. First, a general MoM is reviewed. Then the MoM derivations of the frequency-and time-domain finite-difference based methods, spectral domain methods, finite-element methods, and integral equation method are derived. Finally, conclusions and discussions are made.

II. THE METHOD OF MOMENTS

The Method of Moments (MoM) was developed and reported decades ago; [START_REF] Harrington | Field Computations by Moment Methods[END_REF] is an excellent classical reference on the method. In the method, the general equation to be solved is expressed as:

Lf-g=O (1)
where L is a mathematical operator that can be of either differential, integral or mixed differential and integral; it can be in space, in time or in mixed time and space. f is the unknown function to be solved. G is the known source function.

The MoM solution involves two computing steps: solution expansion and residual (error) minimization.

In the solution expansion step, a pre-selected set of known basis functions in both space and time is first chosen and then used to expand f Denote the basis functions as cp1 andj as the index for each basis function (which has to be independent of each other). Then, f is approximated by a trial function f in terms of weighted sum of the basis functions:

N f "" ] = "'f. a //Jj (2)
m=l where aj is the expansion coefficient that are to be found.

In the second step ofMoM, the residual error of placing (2) in (1) is evaluated as:

R=Lf-g (3)
Forcing R to be exact zero in the whole solution domain is equivalent to finding exact solutions, a difficult task in general. In the context of MoM, it is made to be zero in a weighted and averaged sense with a pre-selected set of known weighting functions, denoted as w; . In a mathematical term, this means that R is forced to be null in terms of its inner product with the weighting functions:

< R,w; >=0 i=l,2, .... M (4)
The inner product usually refers to an integral over the solution domain defined in a particular function space, for instance the Hilbert space [START_REF] Mate | Hilbert Space Methods in Science and Engineering[END_REF]. Both the basis and weighting functions have to be members of a complete set defined in the function space. In addition, the trial function f has to satisfy the essential boundary condition.

When the weighting functions are chosen to be the same as the expansion functions, w; = <P; the MoM becomes the Galerkin's method [START_REF] Harrington | Field Computations by Moment Methods[END_REF]. It has been shown that Galerkin's method is equivalent to minimizing inner product of R to itself, i.e. <R, R>.

( 4) is essentially a system of equations for the unknown expansion coefficient aj . It is normally solvable, some times in a recursive fashion. Once aj is found, the approximating solution f is obtained.

III. DERIVATIONS OF THE FINITE-DIFFERENCE BASED METHODS WITH MoM

The finite-differenced based methods are perhaps most straightforward methods where differential operators in electromagnetic equations are simply replaced with their finite-difference counterparts. The resulting equations are usually algebraic formulations that can be solved relatively easily. The time-domain finite-difference methods have become popular these days while the frequency-domain finite-difference methods are still effective and efficient for narrow band computation.

The time-domain finite-difference based methods include finite-difference time-domain (FDTD) method, transmission-line-matrix (TLM) method, multi-resolution time-domain (MRTD) method, Crank-Nicolson FDTD, alternating-direction-implicit (ADI) FDTD and unconditionally stable FDTD using weighted Laguerre polynomials. Their MoM derivations were presented in [START_REF] Chen | Generalization of the finite-difference based time-domain methods using the method of moments[END_REF]. Therefore, the derivations are not repeated here.

In the following paragraphs, we focus on the MoM derivation of the frequency-domain finite-difference method (FDFD). Before the derivation, a rooftop function is introduced below: Its graphical representation is shown in Fig. 1.

Then, consider one of the frequency-domain Maxwell's equations:

This is exactly the same as the finite-difference frequency domain formulations derived from Maxwell's equations by applying the finite differences directly.

IV. DERIVATIONS OF THE FREQUENCY-DOMAIN AND TIME-DOMAIN SPECTRAL DOMAIN METHOD WITH MoM

The frequency-domain spectral-domain method developed so far is a specialized numerical method designed effectively for the transmission line structures of planar types, such as microstrip lines [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF]. In it, based on the frequency-domain Maxwell's equations, an integral equation was first derived where current densities or charges on the metal strips are the unknown solutions to be found. Then, the MoM technique is applied and a system of linear equations is obtained for the expansion coefficients. The core of the spectral-domain method is that the elements of the coefficient matrix of the system of the linear equations are efficiently found with the use of the Green's functions in the spectral (or spatial frequency) domain (rather than directly in the spatial domain). An excellent MoM derivation of the frequency-domain spectral domain method is presented in [START_REF] Davison | An introduction to spectral domain method-of-moments formulations[END_REF].

The time-domain spectral domain method that has been more comprehensively developed so far is the pseudo spectral time-domain (PSTD) method [START_REF] Liu | The pseudospectral time-domain (PSTD) method: a new algorithm for solutions of Maxwell's equations[END_REF]. In the original development of PSTD, the Fourier transforms (or other transforms) were applied to field components in spatial domain. However, in the context ofMoM, this process can be shown to amount to expansion and residual minimization as described below. First, field quantities are expanded as:

T(t,nlit,At) H a = N � N L [ L X y z Jx ,Jy ,Jz ,n ix ,iy ,iz 1 T[t, (n +-)At, At] 2 a=x,y,z (10)
Substitution of (10) into Maxwell's equation in the Cartesian coordinates, and residual minimization of the resulting equations

[� [� (, _ _ [� ( )o(x-ixAx) with 1 o(y-i y Ay)o(z -iz&)O[t-(n + 2
)At]dx�dzdt lead to, for instance, [START_REF] Chen | Generalization of the finite-difference based time-domain methods using the method of moments[END_REF] is exactly the same as the original PSTD equation presented in [START_REF] Liu | The pseudospectral time-domain (PSTD) method: a new algorithm for solutions of Maxwell's equations[END_REF]. Therefore, the PSTD formulations can be derived by applying the MoM procedures with particular sets of expansion functions that related to the Fourier transforms.

I I FFr ' [jk Y FFT(H: + 2 )]-FFr ' [jk z FFT(H; + 2 )] ( 11
) I n+- + J I 2 =0 X lx,ly,lz (

III. DERIVATIONS OF THE FREQUENCY-DOMAIN AND TIME-DOMAIN FEM WITH MoM

In the frequency-domain FEM formulations known so far, either an integral equation or a functional (that correspond to weak forms of the wave equations) was first established [START_REF] Ltoh | Numerical Techniques for Microwave and Millimeter wave Passive Structures[END_REF] [START_REF] Lee | Time-domain finite-element methods[END_REF]. Then the function expansion and residual minimization were applied in spatial domain. Or, the expansion was performed in spatial domain and the expansion coefficients were obtained through the residual minimization. In the time-domain FEM method, the expansion and residual minimization were carried out exactly in the same way as that for the frequency-domain FEM in the spatial domain. In the time domain, however, the finite-differencing was applied to replace temporal derivatives. For instance, as described in [START_REF] Lee | Time-domain finite-element methods[END_REF], the second order derivative in time is replaced with the central finite difference operator (i.e. equation ( 26) of [START_REF] Lee | Time-domain finite-element methods[END_REF]). However, by careful examinations, it can be shown that such a replacement actually amounts to expansion and residual weighting with a high-order temporal function and a Dirac impulse function, respectively.

III. DERIVATIONS OF INTEGRAL EQUATION METHODS WITH MoM

Integral equations methods have been of interest to electromagnetic modeling community for more than 30 years. Many different integral equations have been developed from Maxwell's equations such as the electric field integral equation (EFIE) [START_REF] Pisharody | Robust solution of time-domain integral equations using loop-tree decomposition and band limited extrapolation[END_REF]. They have been solved by following the solution steps of MoM, expansion of E and H and minimization of residual errors, in both frequency-and time-domains. For example, in [START_REF] Pisharody | Robust solution of time-domain integral equations using loop-tree decomposition and band limited extrapolation[END_REF], the expansion function used in space is the divergence conforming basis functions on curvilinear triangles and expansion function used in time is the Knab's bandlimited interpolation function [START_REF] Pisharody | Robust solution of time-domain integral equations using loop-tree decomposition and band limited extrapolation[END_REF]:

sin{ a /(_ t ) 2 -1} sin(smt) V NA.t T(t)= 0 (12) SOJ 0 t � t 2 sinh( a) (-) -1 NA.t
The use of ( 12) is to control late-time instability that has crippled the wide applications of time-domain integral equation methods.

In all, integral equation techniques have been derived so far with an application of the MoM in space and in time (if needed) for electromagnetic problems. They naturally fall within the frame work ofMoM.

V. DISCUSSIONS AND CONCLUSIONS

In this paper, frequency-and time-domain numerical methods, such as frequency-and time-domain finite difference methods, frequency-and time-domain spectral domain methods, frequency-and time-domain finite-element methods, and frequency-and time-domain integral equation methods have been derived with MoM. The differences among the different methods are shown to be the uses of different expansion and weighting functions as well as the equations and quantities to be solved. In other words, numerical methods can be generalized under the framework of MoM. New methods, particularly effective and efficient for specific structures, can now be developed with the MoM framework. One of such applications was reported in [START_REF] Chung | Solution of time domain electric field integral equation using the Laguerre polynomials[END_REF] where an unconditionally stable time-domain integral equations was developed by using the weighted Laguerre polynomials as the expansion and weighting functions in time.

In our other publication such as [START_REF] Chen | Generalization of the finite-difference based time-domain methods using the method of moments[END_REF], we have shown numerical issues associated with numerical methods can be easily understood with the MoM framework. For instance, numerical stability of a time-domain numerical methods is associated with the convergence of the expansion coefficients as t � oo , while numerical dispersion is a measure of the residual errors in the spectral domain due to the expansion.

]Fig. 1

 1 Fig. 1 Illustration of function T(.;, .;0 , A.;) With the rooftop function defined, the field components are expanded as follows:


Lack of research on the Urdu language

Ø Very few authentic research on the Urdu language, on its origin and the linguistic aspect of Urdu Ø No concept of teaching mother tongue -Maulvi Abdul Haque Ø Learning of Arabic and Persian = Informal learning of Urdu Ø High illiteracy until 21st century Ø Many books on Urdu History are documenting falsely based on ideology or false assumptions -Shamsur Rahman Faruqi

Some different names of Urdu

Hindvi (13th-19th century) Hindi (13th-19th century) Musulmani zubaan (13th -15th century)

Dehlavi (13th-14th century) Gujri (15th century) Rekhtah (13th-19th century) Dakhini (15th-18th century)

Indostan (17th century) Hindustani (18th-20th century)

Some different forms of Urdu -Premchand

During the Muslim period, there must have been three forms of Hindi :

one the pure, unmixed with loan-words, written in the Nagari script, and called Bhasha, or Nagari ; the other, Urdu, that is, Hindi, mixed with Persian, and written in the Persian script, and the third, Braj Bhasha.

Meaning & word origin of Urdu

• Urdu means "military camps" , "army" ?

• Urdu word originated from Altai region of Mongolia (Jaffar & Chand)

• Yousuf Khaas Hajib gave the meaning of Urdu as town or palace (1072).

• Mohammad Al-Kashgari wrote the meaning of Urdu as "the town where the king resides" (11 th century, cited by Jaffar & Chand) • For Shamsur Rahman Faruqi, first reference of Urdu was in the term "zaban-eurdu-e mu'alla-e shahjanabad (the language of the exalted city / Court of Shahjanabad, Delhi) • Till the 18 th century, Urdu meant the "city of Delhi".

Tracing the origins of Urdu -I

From 11th century till 13th century

• Prakarit was spoken in most part of India.

• Several varieties of Parkarait all over India.

• Hindi, Urdu and Punjabi find roots in Shourseni & Aphbransh

• After attack of Mahmud Ghaznavi during the first half of 12th century, varieties of Prakarit language have had an impact from these invasions. • Usage of Khari Boli in Northern India from Delhi to East.

• Muslim invaders began to call the languages of India as Hindvi.

■ The region of invasion was the northern India and particulary the Punjab region.

■ Impact of Punjab in the development of Urdu language (Shirani 1928) ■ We may say that Urdu might have begun as koiné (kind of common language between invaders and local people). The main koiné was the Khari Boli (though its name came in 18th century), from which Hindi and Urdu offshooted.

• The Muslims began to employ heavily the words of Arabic, Persian and Turkish in the local language spoken near Delhi & Punjab region.

• First known Urdu literary product from Deccan

• Long masnavi of more than 400 lines.

• No Sufi influence, the poem is incomplete.

• Only one known copy is preserved in the Library of Karachi, Anjuman Taraqqi Urdu, Pakistan