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Isogeometric Analysis Methods for High Fidelity Mobility Applications



OBJECTIVE: To create a mathematical and numerical framework for the design, analysis, and optimization of performance of mobility system components that are subject to significant fluid-structure interaction effects. 

DESCRIPTION: The intent of this solicitation is to achieve superior accuracy and high-fidelity solutions in computational flow and fluid-structure interaction analysis for com-plex engineering applications, including military and commercial applications, through efficient conforming methods such as Isogeometric Analysis (IGA). Software objectives include extending CAD models to IGA models for high-fidelity computation on supercomputers, doing the required mesh generation automatically or without substantial user effort, and developing a good graphical user interface for conducting simulations and post-processing of results. IGA [1], because of its special higher-order nature, has several very desirable features in multiscale computation of flow and fluid-structure interaction (FSI) problems, including superior spatial and temporal accuracy in the flow solution and more accurate, sometimes exact, representation of the solid surfaces, in-cluding and especially those coming from CAD models. This plays a crucial role in many classes of problems. Compared to classical methods such as the finite differences and finite elements, it performs well even in computations with high-aspect-ratio elements; such elements are inevitable in real-world flow and FSI problems where accurate representation of boundary layers requires very small/thin elements near complex solid surfaces in internal flows and FSI prob-lems where contact between solid surfaces requires meshes in very narrow spaces. Also, for the same level of accuracy, it generally requires fewer un-knowns than classical methods, and so it has larger effective element sizes and therefore the computations can be done accurately with larger time-step sizes, resulting in substantial savings in computing time. Because it shifts the compu-tational burden from the number of unknowns to the number of floating-point operations per unknown, and because it does that without creating any compu-tational disadvantages, it is very suitable for efficient parallel computing. This makes IGA attractive in real-world flow and FSI analysis and is the reason this solicitation seeks to implement it in important mobility applications. IGA-based computation has been applied to FSI problems in turbomachinery [2], tire aerodynamics [3], ship hydrodynamics [4], and gas turbines [5-7]. However, mesh generation with IGA, such as in Nonuniform Rational B-Splines (NURBS) mesh generation, is not as established and straightforward as mesh generation in the classical methods such as the finite differences and finite elements. To make IGA-based flow and FSI computations even more powerful and practical, this solicitation seeks implementations that make the mesh generation more straightforward and automated, similar to current finite difference and finite ele-ment methods. It seeks easier adaptivity of solutions, such as creating thin lay-ers of elements near solid surfaces to accurately represent the boundary layers with less user effort. It seeks more user-friendly and dynamic mesh motion that matches the structure motion and deformation in an FSI computation, automati-cally maintaining the thin layers of elements created near solid surfaces. Basically, extending the CAD models to IGA models in terms of mesh generation, solution adaptivity and FSI mesh motion has to be more automated, embedded in a good graphical user interface (GUI). The product will enable IGA-based computation to play an expanded and significant role in enabling mobility design in military and commercial applications. 

PHASE I: a) Identify the most promising path(s) forward from existing methods and implementations of NURBS mesh generation in real-word mobility applications of interest, such as turbocharger turbines with exhaust manifolds, parachutes, and rotor-stator interactions in adaptive axial-flow or centrifugal turbomachinery with pitching blades/stator vanes. Identify typical applications and regimes of interest, and identify relevant geometries and parameters suitable to demonstrate the feasibility of IGA-enabled solutions. b) Develop and demonstrate the generation of a NURBS mesh made of patches, demonstrate recovery of the original model surfaces, and demonstrate the suitability of the recovered surface for accurate and robust fluid mechanical computations. c) Develop GUI implementation of the method. The focus will be on NURBS meshes. In problems with complex geometries, it may be necessary to use multiple NURBS patches; making that more user-friendly should be one of the GUI features. There should be two options for handling the joints be-tween patches: C0-continuity, or C-1-continuity (probably with discontinuous functions). d) Automate the mesh motion matching the structure motion and deformation in an FSI computation. The motion of the solid surfaces can be represented by using time-dependent NURBS basis functions as one of the possible feature choices in the GUI implementation. e) Implement the foregoing scheme numerically and conduct appropriate proof-of-concept computations. 

PHASE II: a) Expand the computational technique to basis functions other than NURBS, such as T-splines or others. By conducting numerical and automated tests, demonstrate that the selected linear combinations of basis functions optimally reconstruct a variety of surfaces. b) Explore methods for boundary layer refinement such as knot insertion, in-creasing the polynomial order, or particular combinations of the two (i.e., h,p,k refinement). Automate this refinement process. c) Demonstrate utility in a wide set of test mesh generations from CAD models for mobility applications. Use to evaluate the performance of the method and the GUI. d) Port the mesh generation module to parallel computing platforms and optimize performance on those platforms. e) The computational method shall be capable of performing dynamic transient flow simulations as fluid-structure interaction happens in adaptive or morphing structures interacting with fluid flows for both internal and external flows. The computational method shall be verified and validated by conducting required fluid flow experiments using a pitching annular turbomachinery cascade with articulating stator and rotor blade configuration. f) The computational technique will be tested, validated, and implemented as a documented software package that can be shared or marketed. g) Transition the developed methods and software, including documentation, to interested users in academia (e.g. CFD and Mobility Design research groups in the US and Europe), industry, and government (e.g. ARL-VTD, TARDEC) under appropriate licensing agreements. The software package will ultimately be integrated into the CREATE environment at HPCMP or at least be port-able to DoD HPC platform so that DoD and other government agencies and Universities can use the software within HPC environment. 

PHASE III: The uniquely capable analysis and numerical techniques developed under this topic will achieve superior accuracy and high-fidelity solutions in computational flows and fluid-structure interaction analysis involving flexible boundaries. This will in turn enable rapid, high quality solutions in a variety of complex engineering applications, especially those involving high velocity/high pressure flows over deforming elements, such as found in turbines, in highly deformable elements such as MAV rotors, and others. This will therefore make great progress in the design of a wide variety of both military and commercial applications, such as commercial and military aircraft turbines, commercial and military rotorcraft turbines, commercial and military MAV flexible rotors, etc. 


1: [1] T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement", Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4135-4195.

2:  [2] Y. Otoguro, K. Takizawa, T.E. Tezduyar, K. Nagaoka and S. Mei, "Turbo-charger Turbine and Exhaust Manifold Flow Computation with the Space-Time Variational Multiscale Method and Isogeometric Analysis", Computers & Fluids, published online, 10.1016/j.compfluid.2018.05.019 (May 2018).

3:  [3] T. Kuraishi, K. Takizawa and T.E. Tezduyar, "Space-Time Computational Analysis of Tire Aerodynamics with Actual Geometry, Road Contact and Tire De-formation", Chapter in a special volume to be published by Springer (2018).

4:  [4] I. Akkerman, Y. Bazilevs, D.J. Benson, M.F. Farthing, and C.E. Kees, "Free-Surface Flow and Fluid-Object Interaction Modeling with Emphasis on Ship Hy-drodynamics", Journal of Applied Mechanics, 79 (2012) 010905.

5:  [5] M.-C. Hsu, C. Wang, A.J. Herrema, D. Schillinger, A. Ghoshal, and Y. Ba-zilevs, An interactive geometry modeling and parametric design platform for isogeometric analysis, Computers & Mathematics with Applications, 70 (2015) 1481-1500.

6:  [6] F. Xu, G. Moutsanidis, D. Kamensky, M.-C. Hsu, M. Murugan, A. Ghoshal, and Y. Bazilevs, "Compressible flows on moving domains: Stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and applica-tion to gas-turbine modeling", Computers and Fluids, 158 (2017) 201-220.

7:  [7] M. Murugan, A. Ghoshal, F. Xu, M.-C. Hsu, Y. Bazilevs, L. Bravo, and K. Kerner, "Analytical study of articulating turbine rotor blade concept for improved off-design performance of gas turbine engines", Journal of Engineering for Gas Turbines and Power 139 (2017) 102601.

8:  [8] Y. Otoguro, K. Takizawa and T.E. Tezduyar, "A General-Purpose NURBS Mesh Generation Method for Complex Geometries", Springer (2018).

KEYWORDS: Isogeometric Analysis, Mobility, Fluid-structure Interaction 

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