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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Formulation for Simultaneous Aerodynamic Analysis and Design Optimization

An efficient approach for simultaneous aerodynamic analysis and design optimization is presented. This approach does not require the performance of many flow analyses at each design optimization step, which can be an expensive procedure. Thus, this approach brings us one step closer to meeting the challenge of incorporating computational fluid dynamic codes into gradient-based optimization techniques for aerodynamic design. An adjoint-variable method is introduced to nullify the effect of the increased number of design variables in the problem formulation. The method has been successfully tested on one-dimensional nozzle flow problems, including a sample problem with a normal shock. Implementations of the above algorithm are also presented that incorporate Newton iterations to secure a high-quality flow solution at the end of the design process. Implementations with iterative flow solvers are possible and will be required for large, multidimensional flow problems.

Hou, G. W.↗
NASA NTRS2001

Isolating Curvature Effects in Computing Wall-Bounded Turbulent Flows

The flow over the zero-pressure-gradient So-Mellor convex curved wall is simulated using the Navier-Stokes equations. An inviscid effective outer wall shape, undocumented in the experiment, is obtained by using an adjoint optimization method with the desired pressure distribution on the inner wall as the cost function. Using this wall shape with a Navier-Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient can be evaluated. The one-equation Spalart-Allmaras turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model possesses no heuristic functions or additional constants. It lowers slightly the computed skin friction coefficient and the turbulent stress levels for this case (in better agreement with experiment), but the effect on computed velocity profiles is very small.

Rumsey, Christopher L.↗
NASA NTRS2016

Challenges and Progress in Aerodynamic Design of Hybrid Wingbody Aircraft with Embedded Engines

We summarize the contributions to high-fidelity capabilities for analysis and design of hybrid wingbody (HWB) configurations considered by NASA. Specifically, we focus on the embedded propulsion concepts of the N2-B and N3-X configurations, some of the future concepts seriously investigated by the NASA Fixed Wing Project. The objective is to develop the capability to compute the integrated propulsion and airframe system realistically in geometry and accurately in flow physics. In particular, the propulsion system (including the entire engine core-compressor, combustor, and turbine stages) is vastly more difficult and costly to simulate with the same level of fidelity as the external aerodynamics. Hence, we develop an accurate modeling approach that retains important physical parameters relevant to aerodynamic and propulsion analyses for evaluating the HWB concepts. Having the analytical capabilities at our disposal, concerns and issues that were considered to be critical for the HWB concepts can now be assessed reliably and systematically; assumptions invoked by previous studies were found to have serious consequences in our study. During this task, we establish firmly that aerodynamic analysis of a HWB concept without including installation of the propulsion system is far from realistic and can be misleading. Challenges in delivering the often-cited advantages that belong to the HWB are the focus of our study and are emphasized in this report. We have attempted to address these challenges and have had successes, which are summarized here. Some can have broad implications, such as the concept of flow conditioning for reducing flow distortion and the modeling of fan stages. The design optimization capability developed for improving the aerodynamic characteristics of the baseline HWB configurations is general and can be employed for other applications. Further improvement of the N3-X configuration can be expected by expanding the design space. Finally, the support of the System Analysis and Integration Element under the NASA Fixed Wing Project has enabled the development and helped deployment of the capabilities shown in this report.

design optimization↗
NASA NTRS2017

Aerodynamic Design of the Hybrid Wing Body Propulsion-Airframe Integration

A hybrid wingbody (HWB) concept is being considered by NASA as a potential subsonic transport aircraft that meets aerodynamic, fuel, emission, and noise goals in the time frame of the 2030s. While the concept promises advantages over conventional wing-and-tube aircraft, it poses unknowns and risks, thus requiring in-depth and broad assessments. Specifically, the configuration entails a tight integration of the airframe and propulsion geometries; the aerodynamic impact has to be carefully evaluated. With the propulsion nacelle installed on the (upper) body, the lift and drag are affected by the mutual interference effects between the airframe and nacelle. The static margin for longitudinal stability is also adversely changed. We develop a design approach in which the integrated geometry of airframe (HWB) and propulsion is accounted for simultaneously in a simple algebraic manner, via parameterization of the planform and airfoils at control sections of the wingbody. In this paper, we present the design of a 300-passenger transport that employs distributed electric fans for propulsion. The trim for stability is achieved through the use of the wingtip twist angle. The geometric shape variables are determined through the adjoint optimization method by minimizing the drag while subject to lift, pitch moment, and geometry constraints. The design results clearly show the influence on the aerodynamic characteristics of the installed nacelle and trimming for stability. A drag minimization with the trim constraint yields a reduction of 10 counts in the drag coefficient.

hybrid wing↗
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

Goal-Oriented Discretization Error Control in Coupled Nearfield-Farfield Low-Boom Simulations

The method of adjoint weighted residuals is used to determine the level of discretization error in loudness predictions of sonic booms on the ground. We analyze the standard nearfied-farfield domain decomposition approach. In the nearfield domain, the three-dimensional Euler equations are solved to obtain a pressure signature generated by the aircraft. In the farfield, this waveform is propagated through the atmosphere to the ground by solving the augmented Burgers’ equation. Loudness is characterized using weighted sound-exposure-level metrics. We formulate discretization error estimates for the ground signature and loudness metrics for this one-way coupled system. Although the nearfield solution is independent of the farfield, the adjoint formulation for the coupled system provides feedback from the farfield to identify high-error regions in the nearfield. The results demonstrate that the discrete adjoint implementation is asymptotically consistent and provides reliable error estimates. Furthermore, we show how the error can be controlled through adaptive refinement of the nearfield mesh. The approach is evaluated on two- and three-dimensional problems, including the X-59 flight demonstration aircraft.

CST↗
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↗
DOE OSTI2022

Invertible Neural Networks for Airfoil Design

We report the airfoil design problem, in which an engineer seeks a shape with desired performance characteristics, is fundamental to aerodynamics. Design workflows traditionally rely on iterative optimization methods using low-fidelity integral boundary-layer methods as higher-fidelity adjoint-based computational fluid dynamics methods are computationally expensive. Surrogate-based approaches can accelerate the design process but still rely on some iterative inverse design procedure. In this work, we leverage emerging invertible neural network (INN) tools to enable the rapid inverse design of airfoil shapes for wind turbines. INNs are specialized deep-learning models with well-defined inverse mappings. When trained appropriately, INN surrogate models are capable of forward prediction of aerodynamic and structural quantities for a given airfoil shape as well as inverse recovery of airfoil shapes with specified aerodynamic and structural characteristics. The INN approach offers a roughly 100 times speed-up compared to adjoint-based methods for inverse design. We demonstrate the INN tool for inverse design on three test cases of 100 airfoils each that satisfy the performance characteristics close to those of airfoils used in wind-turbine blades. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of airfoils.

17 WIND ENERGY↗
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↗
NASA NTRSDate not supplied

Discretization Error Estimation and Control for Farfield Acoustic Signatures

We investigate the utility of adjoint-based error estimates for sonic boom farfield simulations governed by solutions of the augmented Burgers’ equation. Solution of this nonlinear system uses operator splitting with a second-order finite volume discretization in space and second-order Runge-Kutta time marching, while the absorption and molecular relaxation are solved using second-order central differencing. The discretization error in selected ground sonic boom cost functionals is estimated using the method of adjoint-weighted residuals. Key elements of the implementation process are emphasized with details provided on the practical aspects as appliedto the sonic boom farfield propagation. We establish the accuracy of the adjoint solutions usingcomplex step and finite difference approaches, and examine the accuracy of the error estimates using analytical N-wave solutions. We then apply it to a pressure waveform corresponding to the X-59 research aircraft. The investigations demonstrate that the method of adjoint-weighted residuals accurately predicts the level of discretization error present in sonic boom farfield simulations while offering insight into which features of the near field signal are the primary drivers of ground noise metrics. The numerical results indicate that at sampling frequencies as low as50kHz, discretization error in the propagation is under 0.01 dB[A] for realistically complex examples.

CST↗
DOE OSTI2023

Adjoint Waveform Tomography for Next Generation Seismic Analyses and Monitoring

The development of methods and capabilities to compute complete waveform simulations in three-dimensional (3D) Earth models along with adjoint methods for computing the fully 3D sensitivity kernels in the 2000's set the stage for new advances in seismic imaging. I believe that the full benefits of adjoint waveform tomography (AWT) are not yet fully realized and this will be an important direction for the future of seismic tomography.

58 GEOSCIENCES↗
NASA NTRS1984

Sensitivity analysis of discrete structural systems: A survey

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications addressed to structural analysis, but also includes a number of methods developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1986

Sensitivity analysis of discrete structural systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Photon detector response function methodology using MCNP and shift hybrid radiation transport code for wide-area contamination assay applications

Here, radiation transport modeling using the Monte Carlo N-Particle (MCNP) radiation transport code and Monte Carlo code, Shift, were employed to model detector responses for a variety of wide-area photon contamination scenarios. In this study, 2" × 2" and 3" × 3" cylindrical NaI(Tl) scintillation detector configurations at source detector-distances of 0.5 cm, 1 cm, 2.54 cm, 10 cm, and 30 cm were modeled. Media of soil, concrete, and steel were evaluated for contamination depths ranging from surface to a depth of an infinite thickness in each medium for photon energies ranging from 20 keV to 3 MeV, which correspond to the energies that current detectors can discern. Monoenergetic photon surface contamination detector responses for each of the media, source–detector distances, and detectors were estimated using MCNP v6.2. Shift was harnessed for improved variance reduction of particle transport in highly attenuating media to obtain average cell fluxes in the two MCNP NaI(Tl) scintillation detector configurations. Average cell flux values in Shift were coupled with detector responses from MCNP to convert average cell flux in a void to energy distribution of pulses in the NaI(Tl) scintillation detector crystal of interest. An optimized detector response function methodology was developed by coupling the MCNP radiation transport method with the Consistent Adjoint Driven Importance Sampling (CADIS) hybrid radiation transport method built into Shift to significantly decrease the runtime of thousands of MCNP pulse height simulations. The methodology may be utilized to quickly and accurately facilitate the assessment of a broad range of wide-area environmental contamination assay and decommissioning cleanup applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

GEAR-MC and Differential-Operator Methods Applied to Electron-Photon Transport in the Integrated TIGER Series

The sensitivity analysis algorithms that have been developed by the radiation transport community in multiple neutron transport codes, such as MCNP and SCALE, are extensively used by fields such as the nuclear criticality community. However, these techniques have seldom been considered for electron transport applications. In the past, the differential-operator method with the single scatter capability has been implemented in Sandia National Laboratories’ Integrated TIGER Series (ITS) coupled electron-photon transport code. This work is meant to extend the available sensitivity estimation techniques in ITS by implementing an adjoint-based sensitivity method, GEAR-MC, to strengthen its sensitivity analysis capabilities. To ensure the accuracy of this method being extended to coupled electron-photon transport, it is compared against the central-difference and differential-operator methodologies to estimate sensitivity coefficients for an experiment performed by McLaughlin and Hussman. Energy deposition sensitivities were calculated using all three methods, and the comparison between them has provided confidence in the accuracy of the newly implemented method. Unlike the current implementation of the differential-operator method in ITS, the GEAR-MC method was implemented with the option to calculate the energy-dependent energy deposition sensitivities, which are the sensitivity coefficients for energy deposition tallies to energy-dependent cross sections. The energy-dependent cross sections could be the cross sections for the material, elements in the material, or reactions of interest for the element. Further, these sensitivities were compared to the energy-integrated sensitivity coefficients and exhibited a maximum percentage difference of 2.15%.

42 ENGINEERING↗