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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1995

Galactic oscillator symmetry

Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

Rosensteel, George↗

NASA NTRS2014

Recent Updates to the GEOS-5 Linear Model

Global Modeling and Assimilation Office (GMAO) is close to having a working 4DVAR system and has developed a linearized version of GEOS-5.This talk outlines a series of improvements made to the linearized dynamics, physics and trajectory.Of particular interest is the development of linearized cloud microphysics, which provides the framework for 'all-sky' data assimilation.

Adjoint↗

NASA NTRS1991

On the accuracy of shape sensitivity

The calculation of sensitivity of the response of a structure modeled by finite elements to shape variation is known to be subject to numerical difficulties. The accuracy of a given method is typically measured against the yard stick of finite-difference sensitivity calculation. The present paper demonstrates with a simple example that this approach may be flawed because of discretization errors associated with the finite element mesh. Seven methods for calculating sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the mesh is refined, displacement sensitivity derivatives converge more slowly than the displacements. Six of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer rather than reduced accuracy. Additionally, it is observed that small derivatives are particularly prone to accuracy problems.

Haftka, R. T.↗

NASA NTRS2001

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗

NASA NTRS2016

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

Propulsion↗

NASA NTRS2017

Viscous Aerodynamic Shape Optimization with Installed Propulsion Effects

Aerodynamic shape optimization is demonstrated to tailor the under-track pressure signature of a conceptual low-boom supersonic aircraft. Primarily, the optimization reduces nearfield pressure waveforms induced by propulsion integration effects. For computational efficiency, gradient-based optimization is used and coupled to the discrete adjoint formulation of the Reynolds-averaged Navier Stokes equations. The engine outer nacelle, nozzle, and vertical tail fairing are axi-symmetrically parameterized, while the horizontal tail is shaped using a wing-based parameterization. Overall, 48 design variables are coupled to the geometry and used to deform the outer mold line. During the design process, an inequality drag constraint is enforced to avoid major compromise in aerodynamic performance. Linear elastic mesh morphing is used to deform volume grids between design iterations. The optimization is performed at Mach 1.6 cruise, assuming standard day altitude conditions at 51,707-ft. To reduce uncertainty, a coupled thermodynamic engine cycle model is employed that captures installed inlet performance effects on engine operation.

computational fluid dynamics↗

NASA NTRS2015

Aerodynamic Shape Optimization Benchmarks with Error Control and Automatic Parameterization

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the nest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

Anderson, George R.↗

NASA NTRS2014

Aerostructural Level Set Topology Optimization for a Common Research Model Wing

The purpose of this work is to use level set topology optimization to improve the design of a representative wing box structure for the NASA common research model. The objective is to minimize the total compliance of the structure under aerodynamic and body force loading, where the aerodynamic loading is coupled to the structural deformation. A taxi bump case was also considered, where only body force loads were applied. The trim condition that aerodynamic lift must balance the total weight of the aircraft is enforced by allowing the root angle of attack to change. The level set optimization method is implemented on an unstructured three-dimensional grid, so that the method can optimize a wing box with arbitrary geometry. Fast matching and upwind schemes are developed for an unstructured grid, which make the level set method robust and efficient. The adjoint method is used to obtain the coupled shape sensitivities required to perform aerostructural optimization of the wing box structure.

Dunning, Peter D.↗

NASA NTRS2020

Global Environmental Impact of Supersonic Cruise Aircraft in the Stratosphere

We analyze the climate and ozone impacts of commercial supersonic aircraft using state-of-the-science modeling capabilities ranging from plume to global scale. A scenario-based approach captures variability and uncertainty in the impacts with market adoption, aircraft design choices and regulatory scenarios, focusing on different overland flight restrictions. We find that the notional aircraft considered could attract a market of up to 2.5% of year-2035 seat-kilometers. Overland flight restrictions reduce this market by 80–100%. In comparison to subsonic aircraft, contrails are found to be∼10 times less likely to form behind supersonic jets. A Mach 1.6 jet cruising at 17 km altitude causes 0.85 mDU of depletion per billion seat-km, with 54% of this impact attributable to sulfur emissions and 35% to NOx emissions. Asa result, we find a net non-CO2, non-contrail radiative forcing of−0.020 mW m−2per billion seat-km. Long-term adjoint simulations show that net ozone-neutral cruise can be achieved by flying near 14 km, subject to fuel sulfur content and NOx emissions index.

supersonic, Stratosphere, environment↗

NASA NTRS2021

Global Environmental Impact of Supersonic Cruise Aircraft in the Stratosphere

We analyze the climate and ozone impacts of commercial supersonic aircraft using state-of-the-science modeling capabilities ranging from plume to global scale. A scenario-based approach captures variability and uncertainty in the impacts with market adoption, aircraft design choices and regulatory scenarios, focusing on different overland flight restrictions. We find that the notional aircraft considered could attract a market of up to 2.5% of year-2035 seat-kilometers. Overland flight restrictions reduce this market by 80–100%. In comparison to subsonic aircraft, contrails are found to be ∼ 10 times less likely to form behind supersonic jets. A Mach 1.6 jet cruising at 17 km altitude causes 0.85 mDU of depletion per billion seat-km, with 54% of this impact attributable to sulfur emissions and 35% to NOx emissions. As a result, we find a net non-CO2, non-contrail radiative forcing of −0.020mWm−2 per billion seat-km. Long-term adjoint simulations show that net ozone-neutral cruise can be achieved by flying near 14 km, subject to fuel sulfur content and NOx emissions index.

Raymond L Speth↗

NASA NTRS1994

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Webb, G. M.↗

NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗

NASA NTRS2011

Multidisciplinary Modeling Software for Analysis, Design, and Optimization of HRRLS Vehicles

The concept for Highly Reliable Reusable Launch Systems (HRRLS) under the NASA Hypersonics project is a two-stage-to-orbit, horizontal-take-off / horizontal-landing, (HTHL) architecture with an air-breathing first stage. The first stage vehicle is a slender body with an air-breathing propulsion system that is highly integrated with the airframe. The light weight slender body will deflect significantly during flight. This global deflection affects the flow over the vehicle and into the engine and thus the loads and moments on the vehicle. High-fidelity multi-disciplinary analyses that accounts for these fluid-structures-thermal interactions are required to accurately predict the vehicle loads and resultant response. These predictions of vehicle response to multi physics loads, calculated with fluid-structural-thermal interaction, are required in order to optimize the vehicle design over its full operating range. This contract with ResearchSouth addresses one of the primary objectives of the Vehicle Technology Integration (VTI) discipline: the development of high-fidelity multi-disciplinary analysis and optimization methods and tools for HRRLS vehicles. The primary goal of this effort is the development of an integrated software system that can be used for full-vehicle optimization. This goal was accomplished by: 1) integrating the master code, FEMAP, into the multidiscipline software network to direct the coupling to assure accurate fluid-structure-thermal interaction solutions; 2) loosely-coupling the Euler flow solver FEFLO to the available and proven aeroelasticity and large deformation (FEAP) code; 3) providing a coupled Euler-boundary layer capability for rapid viscous flow simulation; 4) developing and implementing improved Euler/RANS algorithms into the FEFLO CFD code to provide accurate shock capturing, skin friction, and heat-transfer predictions for HRRLS vehicles in hypersonic flow, 5) performing a Reynolds-averaged Navier-Stokes computation on an HRRLS configuration; 6) integrating the RANS solver with the FEAP code for coupled fluid-structure-thermal capability; and 7) integrating the existing NASA SRGULL propulsion flow path prediction software with the FEFLO software for quasi-3D propulsion flow path predictions, 8) improving and integrating into the network, an existing adjoint-based design optimization code.

Spradley, Lawrence W.↗

NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗