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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Sensitivity Analysis of Multidisciplinary Rotorcraft Simulations

A multidisciplinary sensitivity analysis of rotorcraft simulations involving tightly coupled high-fidelity computational fluid dynamics and comprehensive analysis solvers is presented and evaluated. An unstructured sensitivity-enabled Navier-Stokes solver, FUN3D, and a nonlinear flexible multibody dynamics solver, DYMORE, are coupled to predict the aerodynamic loads and structural responses of helicopter rotor blades. A discretely-consistent adjoint-based sensitivity analysis available in FUN3D provides sensitivities arising from unsteady turbulent flows and unstructured dynamic overset meshes, while a complex-variable approach is used to compute DYMORE structural sensitivities with respect to aerodynamic loads. The multidisciplinary sensitivity analysis is conducted through integrating the sensitivity components from each discipline of the coupled system. Numerical results verify accuracy of the FUN3D/DYMORE system by conducting simulations for a benchmark rotorcraft test model and comparing solutions with established analyses and experimental data. Complex-variable implementation of sensitivity analysis of DYMORE and the coupled FUN3D/DYMORE system is verified by comparing with real-valued analysis and sensitivities. Correctness of adjoint formulations for FUN3D/DYMORE interfaces is verified by comparing adjoint-based and complex-variable sensitivities. Finally, sensitivities of the lift and drag functions obtained by complex-variable FUN3D/DYMORE simulations are compared with sensitivities computed by the multidisciplinary sensitivity analysis, which couples adjoint-based flow and grid sensitivities of FUN3D and FUN3D/DYMORE interfaces with complex-variable sensitivities of DYMORE structural responses.

Wang, Li↗
DOE OSTI2016

Pn-FEM Method for Solving the First-Order Neutron Transport Equation

A deterministic method was investigated and developed for the photon-neutron transport calculation for fusion reactor blanket. Firstly, considering the fact that the second order transport equation cannot describe void region accurately due to the appearance of zero total cross section in the denominator, the first order equation was selected as the starting point of the solution. The angular discretization uses the spherical harmonics (Pn) method. Although discrete ordinates (Sn) method has been most commonly applied due to its efficiency, it suffers from the ray effect. To describe unstructured geometry, the finite element method was used to discrete spatial variable. It is well known that Bubnov-Galerkin discretization of the first-order equation is inappropriate which will create oscillations. To obtain robust solutions, Petrov- Galerkin methods have been developed such as the Streamline-Upwind Petrov-Galerkin (SUPG) method and the Generalized Least-Squares (GLS) method. These methods require a stabilization term added to its test functions, which will incur additional computational cost. Another finite element formulation that usually used for first order equation is the Discontinuous-Galerkin (DG) method. In this method, each element has a unique and separate set of basis function. Then the adjacent elements can be connected by using the in-coming flux. Its main drawback is the number of unknowns, much larger than Continuous-Galerkin (CG) method. The Sub-Grid Scale (SGS) finite element method combines the advantages of CG and DG methods together. It inserts the DG method in each element to correct the CG solution, and provides numerically stable solution of first-order equation without increasing the number of unknowns. The boundary conditions and interface conditions for Pn method is a hard nut to crack. We use Riemann method to deal with this problem. It decomposes the neutron angular flux into in-coming and out-going information through an interface, and applies boundary condition to the in-coming one. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2014

Towards Full Aircraft Airframe Noise Prediction: Detached Eddy Simulations

Results from a computational study on the aeroacoustic characteristics of an 18%-scale, semi-span Gulf-stream aircraft model are presented in this paper. NASA's FUN3D unstructured compressible Navier-Stokes solver was used to perform steady and unsteady simulations of the flow field associated with this high-fidelity aircraft model. Solutions were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg, with the main gear off and on (the two baseline configurations). Initially, the study focused on accurately predicting the prominent noise sources at both flap tips for the baseline configuration with deployed flap only. Building upon the experience gained from this initial effort, subsequent work involved the full landing configuration with both flap and main landing gear deployed. For the unsteady computations, we capitalized on the Detached Eddy Simulation capability of FUN3D to capture the complex time-dependent flow features associated with the flap and main gear. To resolve the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips and the region surrounding the gear. Extensive comparison of the computed steady and unsteady surface pressures with wind tunnel measurements showed good agreement for the global aerodynamic characteristics and the local flow field at the flap inboard tip. However, the computed pressure coefficients indicated that a zone of separated flow that forms in the vicinity of the outboard tip is larger in extent along the flap span and chord than measurements suggest. Computed farfield acoustic characteristics from a FW-H integral approach that used the simulated pressures on the model solid surface were in excellent agreement with corresponding measurements.

Khorrami, Mehdi R.↗
DOE OSTI2017

Extreme scale unstructured adaptive CFD for aerodynamic flow control

Understanding the flow of fluid, either liquid or gas, through and around solid bodies has challenged man since the dawn of scientific inquiry. Many of the great minds of science and mathematics have progressively built up a hierarchy of fluid models since fluid flow impacts our lives in so many fundamental ways - from the early days of flow of water in viaducts to cities, to today's flight of planes. This chapter is concerned with the computational modeling of turbulent flow around aerodynamic bodies such as planes and wind turbines. In this case, viscous effects near the solid bodies create very thin boundary layers that yield highly anisotropic (gradients normal to the surface may be 10 6 larger than gradients along the surface) solutions to the governing non-linear partial differential equations (PDE); the Navier-Stokes equations. Furthermore, turbulent flows develop extremely broad ranges of length and time scales motivating the use of discretization methods capable of employing adaptivity and implicit time integration. The combination of these features - non-linear, anisotropy, adaptivity, and implicit - dramatically raise the complexity of the discretization, posing large challenges to efficient scalable parallel implementation. However, through careful design, the more complex algorithms can provide great reductions in computational cost relative to simpler methods (e.g., Cartesian grids with explicit time integration) that are easier to mate efficiently to hardware. In this chapter, we not only describe our approach but we also address the fact that while complex algorithms may never be as efficient flop-for-flop as simple methods, in the important measure of science-per-core-hour, they can still win big by making complex features like adaptivity and implicit methods as efficient and scalable as possible.

42 ENGINEERING↗
DOE OSTI2019

Development of a Novel Accelerator for Neutron Transport Solution Using the Galerkin Spectral Element Methods (Final Report)

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to develop and implement advanced acceleration schemes for the DOE NEAMS neutronics code PROTEUSSN. The project team included the University of Massachusetts Lowell, The Ohio State University, University of Michigan, and Argonne National Laboratory. The PROTEUS code is a high-fidelity capable deterministic neutron transport code based on unstructured finite element meshes, which solves the steady-state and transient neutron transport problem using the 2nd-order discrete ordinate method (SN2ND), the method of characteristics (MOC), and the advanced nodal transport method (NODAL). The DSA scheme has been implemented in PROTEUS to speed up SN transport calculations. The existing DSA scheme employs a consistent finite element formulation on the same fine mesh structure as the SN solution While the use of consistent discretizations makes the DSA method effective, it does not necessarily make it efficient because the numerical solution of a discretized elliptic diffusion problem itself can be costly, particularly when the problem size becomes large. We developed a new discontinuous Galerkin (DG) discretization of the diffusion equation, called DG-DSA, which can effectively and efficiently accelerate the SN transport iterations. As compared with the previous work, the novelty of our method is that the diffusion equation is solved on a coarse-mesh grid using the DG methods, and the DG diffusion discretization incorporates local hp adaptation, i.e., local adaptation of mesh size and/or polynomial degree, based on local total cross section (or optical thickness). Therefore, the resulting number of degrees of freedom (DOF) of the DG discretization is much less than the conventional consistent DSA discretizations, and thus DG-DSA can achieve significant improvement in computational efficiency. We implemented this scheme in PROTEUS-SN. In addition, we developed a new stabilization scheme named linear prolongation CMFD (lpCMFD). A novel feature of this scheme is that the conventional flat flux ratio–based scaling approach is replaced with a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the neutron transport and CMFD calculations. Fourier convergence analysis and numerical results show that lpCMFD is unconditionally stable and more effective than other CMFD based on acceleration schemes such as pCMFD, odCMFD. We also developed a new nonlinear diffusion acceleration scheme for solving neutron transport equations. This scheme, called LR-NDA, employs a local refinement approach on the framework of CMFD by solving a local boundary value problem of the scalar flux on the coarse-mesh structure to replace the piecewise constant scalar flux obtained by CMFD. The refined flux is then used to update the scalar flux in the neutron transport source iteration. It has been demonstrated that that LR-NDA is much more effective and stable than CMFD for a wide range of optical thicknesses. LR-NDA is a local adaptive method, which means LR-NDA does not necessarily require local refinement for all the coarse-mesh cells on the problem domain, i.e., it can be used only for relatively optically thick regions where the standard CMFD scheme would encounter the convergence problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

RICH: OPEN-SOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH

We present here RICH, a state-of-the-art two-dimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time-advancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time-advancement scheme is more accurate and robust than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than a Eulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoi-based moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the change in the area of a cell. Our code is publicly available as open source and designed in an object-oriented, user-friendly way that facilitates incorporation of new algorithms and physical processes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Anti-soiling and highly transparent coatings with multi-scale features

We report that soiling of optical surfaces due to sand and dust accumulation is the main cause for decreased efficiency of concentrating solar power and photovoltaic installations in desert areas. Nanostructured coatings with tailored surface roughness can reduce the rate of soil accumulation and maintain the high optical performance of the solar mirrors and cover glass. Here, we investigate the correlation between the size and structure of the surface features of the coating and its anti-soiling and optical properties. To control the morphology of the surface features we developed two types of coating: (1) based on small size (30–50 nm) silica particles with nanostructured surface and (2) based on unstructured nanoparticles with bimodal size distribution (80 and 35 nm). We tailored the surface features of the coatings to achieve synergistic improvements over different length-scales and thus decrease the adhesion force between the soil particles and the surface. Adhesion force measurements were performed using atomic force microscopy. The adhesion force and energy required to separate a silica particle from the surface of coated solar glass was significantly lower than the respective values from the surface of uncoated solar glass. A falling sand abrasion test, modeled after the procedure in ASTM D968, was performed. The optical properties of coated and uncoated solar glass were measured before and after the soiling test. Coated solar mirror samples were tested in the field. The results of the field test provided evidence that the anti-soiling coating is effective at reducing soiling and improving the specular reflectances of the coated mirrors. Finally, the use of the developed anti-soiling coating can be extended to other power-grid applications where reducing the soil accumulation is valuable.

14 SOLAR ENERGY↗
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗
NASA NTRSDate not supplied

Implementation and Verification of the SST-𝜸 and SA-AFT Transition Models in FUN3D

The transition modeling capability in the NASA unstructured FUN3D suite of codes has been augmented by incorporating two additional transport-equation-based transition models, namely, the 𝜸 transition model coupled with Menter’s 2003 Shear-Stress Transport (SST) turbulence model and Coder’s Amplification Factor Transport (AFT) transition model combined with the Spalart-Allmaras (SA) turbulence model. Both of these models, SST-𝜸 and SA-AFT, are used to compute transition characteristics of several test cases from the literature. The selected test cases cover a range of transition scenarios including bypass transition over a flat plate (ERCOFTAC T3A and T3A- flow configurations), transition in the presence of separation bubbles (NLF-0416 airfoil at selected angles of attack), and natural transition due to Tollmien-Schlichting instabilities (flat-plate experiment by Schubauer and Klebanoff). To address the urgent need for model verification as highlighted in recent workshops on transition modeling, the drag, lift, surface pressure, and skin-friction coefficients from the FUN3D solutions for a sequence of meshes are compared with the results obtained with the same models implemented in the NASA structured grid flow solver OVERFLOW. Comparisons between the local and global surface coefficients from the FUN3D and OVERFLOW solvers for all test cases resulted in good agreement for the finest meshes.

Verification↗