[en] Preliminary aircraft design is often carried out with the help of multidisciplinary optimization processes. Because there is a strong coupling between the flow and the structure of the aircraft, and because new composite materials have a unique capability of being designed for anisotropic directional stiffness and strength, these processes must model the aeroelastic behavior of the aircraft in order to be effective. Since many design variables are involved during the preliminary design stage, the optimization problems, formulated using high or medium fidelity models, can be solved using the adjoint method. Moreover, the level of fidelity of the fluid model and the associated simulation technique must also be selected with care, as they tend to be the main contributors to the computational cost. The novel contribution of the present work is twofold. Firstly, the discretized gradients of the full potential flow equation, which is a medium-fidelity model, are derived analytically so that they can be used in adjoint optimization problems. Moreover, the full potential flow solution and the computation of the gradients are implemented in an open-source and readily available finite element code. Secondly, aerodynamic shape and aerostructural optimization calculations are carried out on example wings to demonstrate the effectiveness and the computational efficiency of the proposed method. Overall, the results show that the newly implemented discrete adjoint nonlinear potential flow formulation is able to quickly optimize both the shape and the structural parameters of a typical wing. More specifically, the twist distribution along the wingspan is adapted to reduce the induced drag, the airfoils become more supercritical so that the shock strength and the associated wave drag are reduced, and the thickness of the structural elements is tailored to the loads to reduce the internal stresses. The present methodology is therefore able to deliver results at a low computational cost which are sufficiently accurate for the early design stages. Furthermore, the results obtained using the proposed methodology could be used as a starting point for the optimization calculations performed in later design stages.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Crovato, Adrien ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale
Prado, Alex Prado; Embraer S.A.
Cabral, Pedro Higino; Embraer S.A.
Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique
Terrapon, Vincent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Modélisation et contrôle des écoulements turbulents
Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale
Language :
English
Title :
A discrete adjoint full potential formulation for fast aerostructural optimization in preliminary aircraft design
Publication date :
April 2023
Journal title :
Aerospace Science and Technology
ISSN :
1270-9638
eISSN :
1626-3219
Publisher :
Elsevier BV
Volume :
138
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Shirk, M.H., Hertz, T.J., Aeroelastic tailoring - theory, practise and promise. J. Aircr. 23:1 (1986), 6–18.
Mura, G.L., Mesh Sensitivity Investigation in the Discrete Adjoint Framework. Ph.D. thesis, March 2017, University of Sheffield.
Yu, Y., Lyu, Z., Xu, Z., Martins, J.R., On the influence of optimization algorithm and initial design on wing aerodynamic shape optimization. Aerosp. Sci. Technol. 75 (2018), 183–199, 10.1016/j.ast.2018.01.016.
Martins, J.R.R.A., Hwang, J.T., Review and unification of methods for computing derivatives of multidisciplinary computational models. AIAA J. 51:11 (2013), 2582–2599.
Hwang, J.T., Martins, J.R.R.A., A computational architecture for coupling heterogeneous numerical models and computing coupled derivatives. ACM Trans. Math. Softw., 44(4), 2018, 37.
Shubin, G.R., Frank, P.D., A comparison of the implicit gradient approach and the variational approach to aerodynamic design optimization. Proceedings of the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences, 1991.
Brezillon, J., Gauger, N., 2d and 3d aerodynamic shape optimisation using the adjoint approach. Aerosp. Sci. Technol. 8:8 (2004), 715–727, 10.1016/j.ast.2004.07.006.
Burdette, D.A., Martins, J.R., Design of a transonic wing with an adaptive morphing trailing edge via aerostructural optimization. Aerosp. Sci. Technol. 81 (2018), 192–203, 10.1016/j.ast.2018.08.004.
Brooks, T.R., Kenway, G.K.W., Martins, J.R.R.A., Benchmark aerostructural models for the study of transonic aircraft wings. AIAA J. 56:7 (2018), 2840–2855.
Brooks, T., Martins, J.R.R.A., Kennedy, G.J., High-fidelity aerostructural optimization of tow-steered composite wings. J. Fluids Struct. 88 (2019), 122–147.
Bons, N.P., Martins, J.R.R.A., Aerostructural design exploration of a wing in transonic flow. Aerospace, 7(8), 2020, 118.
Hoogervorst, J.E., Elham, A., Wing aerostructural optimization using the individual discipline feasible architecture. Aerosp. Sci. Technol. 65 (2017), 90–99, 10.1016/j.ast.2017.02.012.
Li, M., Bai, J., Li, L., Meng, X., Liu, Q., Chen, B., A gradient-based aero-stealth optimization design method for flying wing aircraft. Aerosp. Sci. Technol. 92 (2019), 156–169, 10.1016/j.ast.2019.05.067.
Wright, J.R., Cooper, J.E., Static Aeroelasticity and Flutter. 2015, John Wiley and Sons, 475–480 Ch. 22.
Crovato, A., Almeida, H.S., Vio, G., Silva, G.H., Prado, A.P., Breviglieri, C., Güner, H., Cabral, P.H., Boman, R., Terrapon, V.E., Dimitriadis, G., Effect of levels of fidelity on steady aerodynamic and static aeroelastic computations. Aerospace, 7(4), 2020, 42, 10.3390/aerospace7040042.
Crovato, A., Boman, R., Güner, H., Dimitriadis, G., Terrapon, V., Almeida, H., Prado, A., Breviglieri, C., Cabral, P., Silva, G., A full potential static aeroelastic solver for preliminary aircraft design. Proceedings of the 18th International Forum on Aeroelasticity and Structural Dynamics, 2019.
Crovato, A., Steady Transonic Aerodynamic and Aeroelastic Modeling for Preliminary Aircraft Design. Ph.D. thesis, October 2020, University of Liège http://hdl.handle.net/2268/251906.
Angrand, F., Optimum design for potential flows. Int. J. Numer. Methods Fluids 3 (1983), 265–282.
Jameson, A., Aerodynamic design via control theory. J. Sci. Comput. 3:3 (1988), 233–260.
Jameson, A., Automatic design of transonic airfoils to reduce the shock induced pressure drag. 31st Israel Annual Conference on Aviation and Aeronautics, 1990, 5–17.
Reuter, J., Jameson, A., Control theory based airfoil design for potential flow and a finite volume discretization. Proceedings of the 32nd Aerospace Sciences Meeting and Exhibit, 1994, 10.2514/6.1994-499.
De Castro Santos, L. Carlos, An adjoint formulation for the non-linear potential flow equation. Appl. Math. Comput. 108:1 (2000), 11–21, 10.1016/S0096-3003(98)10137-6.
Galbraith, M.C., Allmaras, S.R., Haimes, R., Full potential revisited: a medium fidelity aerodynamic analysis tool. Proceedings of the 55th AIAA Aerospace Sciences Meeting, 2017, 10.2514/6.2017-0290.
Parrinello, A., Mantegazza, P., Independent two-fields solution for full-potential unsteady transonic flows. AIAA J., 48(7), July 2010, 10.2514/1.J050013.
Parrinello, A., Mantegazza, P., Improvements and extensions to a full-potential formulation based on independent fields. AIAA J., 50(3), March 2012, 10.2514/1.J051270.
Galbraith, M.C., Allmaras, S., Darmofal, D.L., A verification driven process for rapid development of CFD software. Proceedings of the 53rd AIAA Aerospace Sciences Meeting, 2015, 10.2514/6.2015-0818.
Davari, M., Rossi, R., Dadvand, P., Lopez, I., Wuchner, R., A cut finite element method for the solution of the full potential equation with an embedded wake. Comput. Mech. 63:5 (2018), 821–833.
Núñez, M., López, I., Baiges, J., Rossi, R., An embedded approach for the solution of the full potential equation with finite elements. Comput. Methods Appl. Mech. Eng., 388, 2022, 114244.
Dadvand, P., Rossi, R., Onate, E., An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch. Comput. Methods Eng. 17:3 (2010), 253–297.
Johnson, F., Samant, S.S., Bieterman, M., Melvin, R., Young, D., Bussoletti, J., Hilmes, C., Tranair: A Full-Potential, Solution-Adaptive, Rectangular Grid-Code for Predicting Subsonic, Transonic, and Supersonic Flows About Arbitrary Configurations. Tech. Rep., 1992, NASA.
W. Huffman, R. Melvin, D. Young, F. Johnson, J. Bussoletti, Practical Design and Optimization in Computational Fluid Dynamics, AIAA paper.
D. Young, W. Huffman, R. Melvin, M. Bieterman, C. Hilmes, F. Johnson, Inexactness and Global Convergence in Design Optimization, AIAA paper.
Melvin, R., Huffman, W., Young, D., Johnson, F., Hilmes, C., Bieterman, M., Recent progress in aerodynamic design and optimization. Int. J. Numer. Methods Fluids 30 (1999), 205–216.
Young, D., Huffman, W., Melvin, R., Hilmes, C., Johnson, F., Nonlinear elimination in aerodynamic analysis and design optimization. Large-Scale PDE-constrained Optimization Lecture Notes in Computational Science and Engineering, 2004, Springer Verlag, 17–44.
Crovato, A., DARTFlo - Discrete Adjoint for Rapid Transonic Flows. October 2021, University of Liège.
Farhat, C., Lesoinne, M., Maman, N., Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int. J. Numer. Methods Fluids 21:10 (1995), 807–835, 10.1002/fld.1650211004.
Maute, K., Nikbay, M., Farhat, C., Sensitivity analysis and design optimization of three-dimensional non-linear aeroelastic systems by the adjoint method. Int. J. Numer. Methods Eng. 56:6 (2003), 911–933, 10.1002/nme.599.
Steger, J.L., Baldwin, B.S., Shock waves and drag in the numerical calculation of isentropic transonic flows. Tech. Rep., 1972, NASA.
Eberle, A., A finite volume method for calculating transonic potential flow around wings from the pressure minimum integral., 1978, NASA https://ntrs.nasa.gov/citations/19780019138.
Hafez, M., South, J., Murman, E., Artificial compressibility methods for numerical solutions of transonic full potential equation. AIAA J. 17:8 (1979), 838–844, 10.2514/3.61235.
Nielsen, E.J., Park, M.A., Using an adjoint approach to eliminate mesh sensitivities in computational design. AIAA J. 44:5 (2006), 948–953, 10.2514/1.16052.
Dwight, R.P., Robust mesh deformation using the linear elasticity equations. J. Comput. Fluid Dyn. 12 (2009), 401–406.
Widhalm, M., Brezillon, J., Ilic, C., Leicht, T., Investigation on adjoint based gradient computations for realistic 3d aero-optimization. Proceedings of the 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, 2010, 10.2514/6.2010-9129.
Guennebaud, G., Jacob, B., et al. Eigen v3. http://eigen.tuxfamily.org, 2010.
Beazley, D.M., SWIG: an easy to use tool for integrating scripting languages with C and C++. Proceedings of the 4th Conference on USENIX Tcl/Tk Workshop, Monterey, California, USA, 1996, 15.
Gray, J.S., Hwang, J.T., Martins, J.R.R.A., Moore, K.T., Naylor, B.A., OpenMDAO: an open-source framework for multidisciplinary design, analysis, and optimization. Struct. Multidiscip. Optim. 59:4 (2019), 1075–1104.
Thomas, D., Cerquaglia, M., Boman, R., Economon, T., Alonso, J., Dimitriadis, G., Terrapon, V., CUPyDO - an integrated Python environment for coupled fluid-structure simulations. Adv. Eng. Softw. 128 (2019), 69–85, 10.1016/j.advengsoft.2018.05.007.
Cerquaglia, M., Thomas, D., Boman, R., Terrapon, V., Ponthot, J.-P., A fully partitioned lagrangian framework for fsi problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects. Comput. Methods Appl. Mech. Eng. 348 (2019), 409–442, 10.1016/j.cma.2019.01.021.
Bank, R.E., Rose, D.J., Global approximate Newton methods. Numer. Math. 37:2 (1981), 279–295, 10.1007/BF01398257.
Kraft, D., A Software Package for Sequential Quadratic Programming. Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln: Forschungsbericht, 1988, Wiss. Berichtswesen d. DFVLR.
Nocedal, J., Stephen, J.W., Sequential Quadratic Programming. 2006, Springer New York, New York, NY, 529–562.
Geuzaine, C., Remacle, J.-F., Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79 (2009), 1309–1331.
Kenway, G.K.W., Kennedy, G.J., Martins, J.R.R.A., A CAD-free approach to high-fidelity aerostructural optimization. Proceedings of the 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Fort Worth, TX, 2010 AIAA 2010-9231.
Boopathy, K., Kennedy, G.J., Parallel finite element framework for rotorcraft multibody dynamics and discrete adjoint sensitivities. AIAA J. 57:8 (2019), 3159–3172.
Kiviaho, J.F., Kennedy, G.J., Efficient and robust load and displacement transfer scheme using weighted least squares. AIAA J. 57:5 (2019), 2237–2243.
V. Schmitt, F. Charpin, Pressure distributions on the ONERA-M6-wing at transonic Mach numbers, Experimental data base for computer program assessment 4.
Lyu, Z., Kenway, G.K., Paige, C., Martins, J.R.R.A., Automatic differentiation adjoint of the Reynolds-averaged Navier-Stokes equations with a turbulence model. 21st AIAA Computational Fluid Dynamics Conference, 2013, 10.2514/6.2013-2581.
Kreisselmeier, G., Steinhauser, R., Systematische Auslegung von Reglern durch Optimierung eines vektoriellen Gütekriteriums. Automatisierungstechnik 27:1–12 (1979), 76–79.
Kenway, G.K., Martins, J.R.R.A., Multi-point high-fidelity aerostructural optimization of a transport aircraft configuration. J. Aircr. 51:1 (2014), 144–160.
Bons, N., Martins, J.R.R.A., Odaguil, F., Cuco, A.P.C., Aerostructural wing optimization of a regional jet considering mission fuel burn. ASME Open J. Eng., 1, 2022, 011046.
Drela, M., Giles, M., Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25:10 (1987), 1347–1355.
Bilocq, A., Implementation of a viscous-inviscid interaction scheme in a finite element full potential solver. Master's thesis, June 2020, University of Liège https://orbi.uliege.be/handle/2268/252195.
Dechamps, P., Improvement of the viscous-inviscid interaction method implemented in DARTFlo. Master's thesis, January 2022, University of Liège.
Dechamps, P., Bilocq, A., Crovato, A., Dimitriadis, G., Terrapon, V., Pseudo unsteady quasi-simultaneous integral boundary layer methodology for preliminary aircraft design. J. Aircr., 2023 in preparation for submission.
Lambe, A., Martins, J.R.R.A., Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes. Struct. Multidiscip. Optim. 46 (2012), 273–284, 10.1007/s00158-012-0763-y.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.