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DOE OSTI2026

Optimized Tandem Catalyst Patterning for CO 2 Reduction Flow Reactors

Tandem catalysis involves two or more catalysts arranged in proximity within a single reaction vessel, with the aim of synergistically aligning the catalysts’ reaction pathways to maximize overall system performance. This study presents a proof of concept showing the integration of continuum transport modeling with design optimization in a simplified two-dimensional flow reactor setup for electrochemical CO 2 reduction. Ag catalysts provide the CO 2 ⟶ CO reaction capability, and Cu catalysts provide the CO ⟶ high-value products reaction capability. Given a set of input parameters, the optimization algorithm uses adjoint methods to modify the Ag/Cu surface patterning in order to maximize the current density toward high-value products, such as ethylene. The optimized designs yield significant performance enhancement especially at more negative applied voltages (i.e., stronger surface reactions) and for larger numbers of patterning sections. For an applied voltage of −1.7 V vs. SHE, the 12-section optimized design increases the current density toward ethylene by up to 65% compared to the unoptimized 2-section design. For the optimized cases, observed differences in the production and consumption of CO (the key intermediate species) and minimized zones of low CO reactant surface concentration on Cu sections explain the improved reactor performance.

CO2 reduction↗

NASA NTRSDate not supplied

Verification of Anisotropic Mesh Adaptation for Complex Aerospace Applications

The stabilized finite element solver, FUN3D-SFE, along with the grid mechanics package refine are verified for aerospace applications of laminar and turbulent flow simulations. The current verification exercise represents an extension of previous research using FUN3D-SFEwith adjoint-based mesh adaptation to generate highly anisotropic adapted meshes for inviscid problems. Adaptations are performed using a solution-based approach that controls the Lpnorm of Mach number interpolation error and an adjoint-based approach that controls the error in some output functional. Adaptive results are shown for laminar subsonic flow over a delta wing, laminar subsonic flow over ONERA M6 wing, inviscid supersonic flow over a sonic boom test case, and a turbulent flow over a high lift configuration (JAXA Standard Model). Mesh convergence results are also compared with results from FUN3D-FV (Finite Volume) whenever available. For all test cases considered, FUN3D-SFE gives significantly better accurate results than FUN3D-FV on coarse meshes.

Aravind Balan↗

NASA NTRS2002

Slat Cove Noise Modeling: A Posteriori Analysis of Unsteady RANS Simulations

A companion paper by Khorrami et al demonstrates the feasibility of simulating the (nominally) self-sustained, large-scale unsteadiness within the leading-edge slat-cove region of multi-element airfoils using unsteady Reynolds-Averaged Navier-Stokes (URANS) equations, provided that the turbulence production term in the underlying two-equation turbulence model is switched off within the cove region. In conjunction with a FfowesWilliams-Hawkings solver, the URANS computations were shown to capture the dominant portion of the acoustic spectrum attributed to slat noise, as well as reproducing the increased intensity of slat cove motions (and, correspondingly, far-field noise as well) at the lower angles of attack. This paper examines that simulation database, augmented by additional simulations, with the objective of transitioning this apparent success to aeroacoustic predictions in an engineering context. As a first step towards this goal, the simulated flow and acoustic fields are compared with experiment and simplified analytical model. Rather intense near-field fluctuations in the simulated flow are found to be associated with unsteady separation along the slat bottom surface, relatively close to the slat cusp. Accuracy of the laminar-cove simulations in this near-wall region is raised to be an open issue. The adjoint Green's function approach is also explored in an attempt to identify the most efficient noise source locations.

Choudhari, Meelan↗

NASA NTRS1992

Multidisciplinary analysis and sensitivity derivatives for isolated helicopter rotors in hover

A new method is presented for using Navier-Stokes results in the system analysis and sensitivity derivative computations for a helicopter rotor in hover. The system coupling includes the interactions between rotor performance, rotor structural properties and aerodynamics (i.e., airfoil shape). Emphasis is placed on the use of high fidelity Navier-Stokes algorithms for the aerodynamic problem. The present formulation is chosen to reduce the number of sensitivity derivative equations and their dimensions as much as possible. In addition, an alternative adjoint formulation is presented which dramatically reduces the computational requirement for disciplines in which there may be a large number of design variables (e.g., aerodynamics). The theoretical method makes use of a combination of derivatives from each discipline; the computation of these derivatives has already been shown to be feasible. Sample computations for the aerodynamic-rotor model coupling and an associated sensitivity derivative are also presented.

Jones, Henry E.↗

NASA NTRS2011

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

Mathur, Sanjay↗

NASA NTRS2016

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods.

Adjoint↗

NASA NTRS2005

Computation of the Streamfunction and Velocity Potential for Limited and Irregular Domains

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, while the given velocity vectors can be accurately reconstructed from the computed streamfunction and velocity potential. Because the formulation of the minimization problem allows for circumventing the explicit specification of separate boundary conditions on the streamfunction and velocity potential, the algorithm is easily applicable to irregular domains. By using an advanced minimization algorithm with the use of adjoint techniques, the method is computationally efficient and suitable for problems with large dimensions. An example is presented for coastal oceans to illustrate the practical application of the algorithm.

velocity↗

DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗

DOE OSTI2025

Wind Turbine Rotor Design Using High-Fidelity Aerostructural Optimization

Large wind turbines yield more energy but demand careful aeroelastic blade design. Coupled multiphysics design strategies can reduce wind energy costs by exploiting fluid-structure interactions. This work presents the first high-fidelity aerostructural optimization study of a large wind turbine rotor. We use blade-resolved fluid dynamics and structural solvers in a monolithic gradient-based optimization framework to explore steady-state torque and blade mass tradeoffs. The coupled-adjoint approach computes gradients efficiently, enabling the optimization of over 100 structural and geometric parameters simultaneously. Our optimization study modifies a DTU 10 MW benchmark with a simplified structure and isotropic material properties. The tightly coupled optimizations increase torque by 14% while reducing rotor mass by 9% or reduce blade mass by 27% while maintaining torque. Blade-resolved models provide greater design freedom, enabling 5% higher mass reductions than conventional parameterizations at equal torque. This framework paves the way for more detailed high-fidelity optimization studies to complement conventional design approaches.

17 WIND ENERGY↗

DOE OSTI2024

Exploring gauge-fixing conditions with gradient-based optimization

Lattice gauge fixing is required to compute gauge-variant quantities, for example those used in RI-MOM renormalization schemes or as objects of comparison for model calculations. Recently, gauge-variant quantities have also been found to be more amenable to signal-to-noise optimization using contour deformations. These applications motivate systematic parameterization and exploration of gauge-fixing schemes. This work introduces a differentiable parameterization of gauge fixing which is broad enough to cover Landau gauge, Coulomb gauge, and maximal tree gauges. The adjoint state method allows gradient-based optimization to select gauge-fixing schemes that minimize an arbitrary target loss function.

Detmold, William↗

NASA NTRSDate not supplied

Design of a Distributed Propulsion Concept Using an Adjoint-Based Approach and Blade Element Theory to Minimize Power

The adjoint-based design capability in FUN3D is extended to allow efficient gradient-based optimization and design of concepts with highly integrated and distributed aero-propulsive systems. Previous work by the authors demonstrated the derivation and application of design sensitivities of flow power and vehicle forces with respect to design variables associated with actuator disk size, loading, and installation on the aircraft. In this work, calculations of propulsive power, shaft power, and propeller efficiency using blade element-based disk loading, along with sensitivity derivatives needed to perform adjoint-based design, have been implemented. This includes the derivation of additional design sensitivities for actuator disk variables with respect to the radial distributions of blade pitch angle and chord length. The blade element-based loading implementation allows us to tailor the actuator disk loading to provide greater design authority and calculate the torque imparted on the flow for the modeling of swirl effects. The design capability is demonstrated by the optimization of NASA's parallel hybrid electric PEGASUS aircraft concept. The optimization objective is the minimization of shaft power at the aerodynamic interface planes for the wing-mounted and tail-cone boundary layer ingestion propulsors, subject to vehicle performance and propulsive constraints.

Irian Ordaz↗

NASA NTRS2018

Aerodynamic Design and Optimization of Fan Stage for Boundary Layer Ingestion Propulsion System

The present paper addresses the process of preliminary design of a low-pressure fan and outlet guide vane (OGV) of a boundary layer ingestion (BLI) propulsion system. The tail-cone thruster systems of NASA's STARC_ABL (Single-aisle Turboelectric Aircraft with an Aft Boundary-Layer propulsor) adopts an axi-symmetric BLI type inlet as opposed to other embedded engine systems. Thus, the focus of the present work is placed on maximizing the efficiency of the fan and OGV stages under a significant radial distortion. A parameterization with B-spline function for camber line angles, metal chord, thickness distribution and stacking axis of blades is presented. The flowpath lines are also parameterized by B-spline function and aggregated in the design system of blades. The design optimization with evolutionary algorithm is performed with constraints of fan pressure ratio, OGV exit swirl angle and nozzle exit properties. The inlet conditions for the turbo-machinery CFD (Computational Fluid Dynamics) domain and the design goal of the fan stage are driven by a propulsion airframe integration (PAI) model that uses a 3-D unstructured RANS (Reynolds Average Navier Stokes) solver and actuator disk model. The expected power saving of the BLI propulsor is quantified via PAI analysis and the resulting preliminary design of the fan stages is compared with a clean-inlet flow propulsor.

Turbo-machinery↗

NASA NTRSDate not supplied

Towards Aerodynamic Shape Optimization Using an Immersed Boundary Overset Grid Method

Traditional Reynolds-averaged Navier-Stokes grid methods applied to aerodynamic shapeoptimization can struggle with the deformation of surface and volume grids at componentintersections, such as at wing-fuselage junctions. To overcome this, we propose an approachwhich utilizes curvilinear overset grids for the discretization of the domain, with the presenceof the body modeled using an immersed boundary method. This approach handles complexgeometries without the need for their explicit integration into the grid. The goal of this approachis to reduce grid generation time and allow for greater geometric freedom for component-basedaerodynamic shape optimization. Two different methods are presented: a source-term-basedand a ghost-node-based immersed boundary method. Flow analyses and adjoint solutionsobtained using the proposed methods show promising comparisons with standard body-fittedgrid methods. Preliminary aerodynamic shape optimization results obtained using one of theimmersed boundary methods are also presented.

TTT↗

DOE OSTI2025

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗

NASA NTRSDate not supplied

Influence of the Perception Constraint, Installation Effects, and Broadband SelfNoise on Low-Fidelity, Multi-point, UAM Vehicle Perception-Influenced-Design(PID) Optimization

UAM vehicles represent a unique challenge in acoustics because there are a limited number of full-scale datasets that can be used to calibrate and validate prediction models. In addition, acoustics is considered more often in the early design loop as a higher priority concern in UAM vehicle design, whereas with traditional vehicles, acoustics is typically addressed with post-design constraints. This paper will present an approach in design optimization of a proprotor in two flight conditions, hover, and forward flight, with several acoustic objective functions that simulate community response. An adjoint-capable vortex-lattice method (VLM), implemented in VSPAERO, will be used to compute the blade forces and inflow properties required to compute tonal and broadband noise using the second-generation Aircraft NOise Prediction Program (ANOPP2). In addition, a wing is placed near the proprotor to simulate installation effects on a vehicle’s wing. The influence of rotation rate, chord distribution, twist angle, and sweep on installation, broadband noise, and choice of perception constraint from the design optimization will be shown.

acoustics↗

NASA NTRS2004

Sensitivity Equation Derivation for Transient Heat Transfer Problems

The focus of the paper is on the derivation of sensitivity equations for transient heat transfer problems modeled by different discretization processes. Two examples will be used in this study to facilitate the discussion. The first example is a coupled, transient heat transfer problem that simulates the press molding process in fabrication of composite laminates. These state equations are discretized into standard h-version finite elements and solved by a multiple step, predictor-corrector scheme. The sensitivity analysis results based upon the direct and adjoint variable approaches will be presented. The second example is a nonlinear transient heat transfer problem solved by a p-version time-discontinuous Galerkin's Method. The resulting matrix equation of the state equation is simply in the form of Ax = b, representing a single step, time marching scheme. A direct differentiation approach will be used to compute the thermal sensitivities of a sample 2D problem.

Hou, Gene↗

NASA NTRS2019

High-fidelity Multidisciplinary Sensitivity Analysis and Design Optimization for Rotorcraft Applications

A multidisciplinary sensitivity analysis of rotorcraft simulations involving tightly coupled high-fidelity computational fluid dynamics and comprehensive analysis solvers is presented and evaluated. A sensitivity-enabled fluid dynamics solver and a nonlinear flexible multibody dynamics solver are coupled to predict aerodynamic loads and structural responses of helicopter rotor blades. A discretely consistent adjoint-based sensitivity analysis available in the fluid dynamics solver provides sensitivities arising from unsteady turbulent flows and unstructured dynamic overset meshes, while a complex-variable approach is used to compute 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. Accuracy of the coupled system is validated by conducting simulations for a benchmark rotorcraft model and comparing solutions with established analyses and experimental data. Sensitivities of lift computed by the multidisciplinary sensitivity analysis are verified by comparison with the sensitivities obtained by complex-variable simulations. Finally the multidisciplinary sensitivity analysis is applied to a constrained gradient-based design optimization for a HART-II rotorcraft configuration.

Wang, Li↗

NASA NTRS2003

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Nielsen, Eric J.↗