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NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS2019

Computational Modeling for Non-Equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the large computational cost makes it impractical to support a real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube problem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computationally expensive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the established stagnation-line approach. Comparison with time-accurate simulations shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium.

Bensassi, Khalil↗

NASA NTRS2002

Efficient Reformulation of HOTFGM: Heat Conduction with Variable Thermal Conductivity

Functionally graded materials (FGMs) have become one of the major research topics in the mechanics of materials community during the past fifteen years. FGMs are heterogeneous materials, characterized by spatially variable microstructure, and thus spatially variable macroscopic properties, introduced to enhance material or structural performance. The spatially variable material properties make FGMs challenging to analyze. The review of the various techniques employed to analyze the thermodynamical response of FGMs reveals two distinct and fundamentally different computational strategies, called uncoupled macromechanical and coupled micromechanical approaches by some investigators. The uncoupled macromechanical approaches ignore the effect of microstructural gradation by employing specific spatial variations of material properties, which are either assumed or obtained by local homogenization, thereby resulting in erroneous results under certain circumstances. In contrast, the coupled approaches explicitly account for the micro-macrostructural interaction, albeit at a significantly higher computational cost. The higher-order theory for functionally graded materials (HOTFGM) developed by Aboudi et al. is representative of the coupled approach. However, despite its demonstrated utility in applications where micro-macrostructural coupling effects are important, the theory's full potential is yet to be realized because the original formulation of HOTFGM is computationally intensive. This, in turn, limits the size of problems that can be solved due to the large number of equations required to mimic realistic material microstructures. Therefore, a basis for an efficient reformulation of HOTFGM, referred to as user-friendly formulation, is developed herein, and subsequently employed in the construction of the efficient reformulation using the local/global conductivity matrix approach. In order to extend HOTFGM's range of applicability, spatially variable thermal conductivity capability at the local level is incorporated into the efficient reformulation. Analytical solutions to validate both the user-friendly and efficient reformulations am also developed. Volume discretization sensitivity and validation studies, as well as a practical application of the developed efficient reformulation are subsequently carried out. The presented results illustrate the accuracy and implementability of both the user-friendly formulation and the efficient reformulation of HOTFGM.

Zhong, Yi↗

NASA NTRS2026

Parametric-Based Heat Rejection Trade Study for Lunar and Martian Surface Operations

Establishing and maintaining a sustained presence on the lunar and/or Martian surfaces will require a diverse portfolio of surface elements (e.g., habitation, mobility, power generation, etc.). Many of these systems generate excess heat that must be rejected across a wide range of magnitudes, temperatures, and duty cycles and under variable environmental conditions. To identify the most promising heat rejection approaches for this diverse portfolio, a heat rejection trade study was conducted to evaluate the performance of different technology approaches across a spectrum of surface environments and heat-load requirements. The trade study consisted of three stages: (1) development of a parametric-based modeling framework, (2) creation of a database of heat rejection technologies, surface elements, and environmental conditions for the Moon and Mars, and (3) execution of a quantitative analysis of various heat rejection technologies across different operating conditions and surface elements. The modeling framework is developed in Python and Excel to prioritize small model size and hence low computational cost to enable large parametric sweeps while avoiding the reliance on proprietary software. Individual heat rejection processes are represented as simple Excel models, and a centralized Python script interfaces with the models to coordinate the parametric study. These simple sizing models were developed to take heat load requirements and environmental parameters as inputs and compute mass, power, and volume as outputs. Rather than assess each heat rejection technology separately for each surface element, a unified parametric space was developed to evaluate all technologies across all elements. This parametric space includes factors related to heat load (e.g., magnitude or temperature) and environment (e.g., surface temperature, sky temperature, solar flux). This effort generated a database containing information on over 60 heat rejection technologies and 30 surface elements. For each surface element, the expected heat rejection requirements were documented and analyzed to determine the most common needs shared across all elements. Environmental conditions at various lunar and Martian latitudes were also established for worst-case hot and worst-case cold scenarios. High-fidelity heat rejection models are currently under development. Preliminary trades between heat rejection technologies including radiators, venting technologies, convective coolers, and more have been conducted to identify promising options. This presentation will summarize the preliminary trade results and provide an overview and discussion of the expected heat loads and thermal environments for sustained surface operations on the Moon and Mars.

Heat Rejection↗

NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in A Mach 4.5 Boundary Layer

We use deep learning, an ensemble variationaltechnique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (Deep-ONets), which have the known ability to learn com-plex nonlinear operators within dynamical systems,are used for machine learning. For the baseline config-uration of a smooth flat plate, the second-mode wavesat the DNS inflow cause a quick nonlinear breakdownof the high-speed boundary layer within the computa-tional domain. Results reported in the present studyvalidate the ability of DeepONets to model the tran-sition delay via a given topography of the roughnesselement. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substan-tially lowered by the DeepONets-based reduced-ordermodel. In comparison to the baseline method of EnVaroptimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition pastthe outflow boundary of the computational domainwhile utilizing almost 5–6 times fewer DNS.

Machine Learning↗

NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the mutlifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Thomas K. West IV↗

NASA NTRSDate not supplied

DeepONet-Assisted Optimization of Surface Topography for Transition Delay in a Mach 4.5 Boundary Layer

We use deep learning, an ensemble variational technique (EnVar), and direct numerical simulations(DNS) to design an optimal topography for a two-dimensional roughness element that delays the on-set of laminar-turbulent transition in a Mach 4.5 flat-plate boundary layer. Deep operator networks (DeepONets), which have the known ability to learn complex nonlinear operators within dynamical systems, are used for machine learning. For the baseline configuration of a smooth flat plate, the second-mode waves at the DNS inflow cause a quick nonlinear breakdown of the high-speed boundary layer within the computational domain. Results reported in the present study validate the ability of DeepONets to model the transition delay via a given topography of the roughness element. The computing cost to optimize the rough-ness element for minimal skin-friction drag is substantially lowered by the DeepONets-based reduced-order model. In comparison to the baseline method of EnVar optimization based on DNS alone, the DeepONets-based EnVar optimizer is able to delay transition past the outflow boundary of the computational domain while utilizing almost 5–6 times fewer DNS.

Machine Learning↗

NASA NTRSDate not supplied

High-precision predictions of properties of chemically disordered crystals

Multiple scattering theory (MST) combined with density functional theory (DFT) allows to predict properties of chemically disordered materials from the first principles. However, such predictions often suffer from the systematic errors, which depend on crystal geometry. Each computed property of a particular crystal structure typically has a relatively small random error and a larger systematic error. Cancellation of systematic errors allows more accurate predictions. We propose a computational methodology based on the subtraction of the systematic errors in MST. To exemplify it, we apply it to the precipitated alloys. Considering precipitation strengthening in Ni superalloys, we compute the relative enthalpies of the competing Ni3(Al,Ti)1 crystal structures with a chemical disorder on the Al+Ti sublattice. Such predicted composition-structure-property dependencies are useful for the guided design of the next-generation alloys with improved strength. Our predictions are validated by comparison with the results of other DFT methods (having a higher computational cost) and with experiment. We acknowledge funding of the guided design of stronger superalloys for airspace by NASA Aeronautics Research Mission Directorate (ARMD) via Transformational Tools and Technologies (TTT) Project.

Computational↗

NASA NTRS1991

An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2

The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.

Rendell, Alistair P.↗

NASA NTRS1998

Modeling Macro- and Micro-Scale Turbulent Mixing and Chemistry in Engine Exhaust Plumes

Simulation of turbulent mixing and chemical processes in the near-field plume and plume-vortex regimes has been successfully carried out recently using a reduced gas phase kinetics mechanism which substantially decreased the computational cost. A detailed mechanism including gas phase HOx, NOx, and SOx chemistry between the aircraft exhaust and the ambient air in near-field aircraft plumes is compiled. A reduced mechanism capturing the major chemical pathways is developed. Predictions by the reduced mechanism are found to be in good agreement with those by the detailed mechanism. With the reduced chemistry, the computer CPU time is saved by a factor of more than 3.5 for the near-field plume modeling. Distributions of major chemical species are obtained and analyzed. The computed sensitivities of major species with respect to reaction step are deduced for identification of the dominant gas phase kinetic reaction pathways in the jet plume. Both the near field plume and the plume-vortex regimes were investigated using advanced mixing models. In the near field, a stand-alone mixing model was used to investigate the impact of turbulent mixing on the micro- and macro-scale mixing processes using a reduced reaction kinetics model. The plume-vortex regime was simulated using a large-eddy simulation model. Vortex plume behind Boeing 737 and 747 aircraft was simulated along with relevant kinetics. Many features of the computed flow field show reasonable agreement with data. The entrainment of the engine plumes into the wing tip vortices and also the partial detrainment of the plume were numerically captured. The impact of fluid mechanics on the chemical processes was also studied. Results show that there are significant differences between spatial and temporal simulations especially in the predicted SO3 concentrations. This has important implications for the prediction of sulfuric acid aerosols in the wake and may partly explain the discrepancy between past numerical studies (that employed parabolic or temporal approximations) and the measured data. Finally to address the major uncertainty in the near-field plume modeling related to the plume processing of sulfur compounds and advanced model was developed to evaluate its impact on the chemical processes in the near wake. A comprehensive aerosol model is developed and it is coupled with chemical kinetics and the axisymmetric turbulent jet flow models. The integrated model is used to simulate microphysical processes in the near-field jet plume, including sulfuric acid and water binary homogeneous nucleation, coagulation, non-equilibrium heteromolecular condensation, and sulfur-induced soot activation. The formation and evolution of aerosols are computed and analyzed. The computed results show that a large number of ultra-fine (0.3--0.6 nm in radius) volatile HSO4 - HO embryos are generated in the near-field plume. These embryos further grow in size by self coagulation and condensation. Soot particles can be activated by both heterogeneous nucleation and scavenging of H2SO4-H2O aerosols. These activated soot particles can serve as water condensation nuclei for contrail formation. Conditions under which ice contrails can form behind aircrafts are studied. The sensitivities of the threshold temperature for contrail formation with respect to aircraft propulsion efficiency, relative humidity, and ambient pressure are evaluated. The computed aerosol properties for different extent of fuel sulfur conversion to S(VI) (SO3 and H2SO4) in engine are examined and the results are found to be sensitive to this conversion fraction.

Menon, Suresh↗

NASA NTRSDate not supplied

Modeling of Cavity Residence Time via Modeled Lagrangian Particle Tracking

One of the critical components in a scramjet is the cavity flame holder. In evaluating the sizing of this component, the residence time of the fuel in the cavity is a common parameter used. However, to obtain the residence time via CFD is an expensive undertaking. One method is to perform an LES simulation of the cavity and use Lagrangian particle tracking to obtain both the mean and probability density function of the time that the particles remain in the cavity. While this method affords a significant amount of information, it is very costly in CPU run time. A simpler method involves performing a time accurate RANS simulation of the cavity, and when converged, overlay a traceable scalar in the cavity region, and then record the decay of this scalar’s flux at a downstream location. The time scale of the decay rate can then be estimated and a residence time inferred. This method is less computationally expensive than the LES approach, but still requires a time-accurate solution while only providing a mean cavity residence time evaluation. In this paper a method of determining the mean cavity residence time as well as the Probability Density Function (PDF) of the residence time is proposed and demonstrated. This method is based on Lagrangian particle tracking modeled by the Generalized Langevin Equation and is implemented as a post-processing step for a steady RANS solution. Computational cost is on the order of minutes and the results are in agreement with values obtained by the LES and scalar decay methods.

Langevin↗

NASA NTRS2005

A Reduced-frequency Approach for Calculating Dynamic Derivatives

Computational Fluid Dynamics (CFD) is increasingly being used to both augment and create an aerodynamic performance database for aircraft configurations. This aerodynamic database contains the response of the aircraft to varying flight conditions and control surface deflections. The current work presents a novel method for calculating dynamic stability derivatives which reduces the computational cost over traditional unsteady CFD approaches by an order of magnitude, while still being applicable to arbitrarily complex geometries over a wide range of flow regimes. The primary thesis of this work is that the response to a forced motion can often be represented with a small, predictable number of frequency components without loss of accuracy. By resolving only those frequencies of interest, the computational effort is significantly reduced so that the routine calculation of dynamic derivatives becomes practical. The current implementation uses this same non-linear, frequency-domain approach and extends the application to the 3-D Euler equations. The current work uses a Cartesian, embedded-boundary method to automate the generation of dynamic stability derivatives.

Murman, Scott M.↗

NASA NTRS2007

Numerical Strip-Yield Calculation of CTOD

Many existing methods to calculate CTOD can be costly and complicated, or apply only to particular configurations. A new numerical method for calculating CTOD was investigated. NASGRO's Boundary Element module NASBEM was adapted to calculate displacements at any point on the crack. Demonstrated for a number of crack configurations: a) finite and infinite domains; b) center and edge cracks; and c) complex cases with several cracks and holes. Great accuracy at minimal computational cost.

Beek, Joachim↗

NASA NTRS2020

Flutter Analysis with Stabilized Finite Elements Based on the Linearized Frequency-Domain Approach

When designing and certifying aircraft, engineers must take into consideration aeroelastic effects such as flutter. Design and certification of a vehicle may require analysis of thousands of aeroelastic responses. Standard tools in the aerospace industry are based on linear aerodynamic models such as the doublet-lattice method, but these methods can be nonconservative in certain situations such as in the transonic regime. While computational fluid dynamics (CFD) is a higher fidelity alternative, the time-marching approach has a drastically increased computational cost compared to the linear aerodynamic methods. By taking advantage of the periodic nature of flutter, frequency-domain methods offer a more efficient alternative to time-marching CFD. In this work, a linearized frequency-domain method is implemented and verified in the stabilized finite-element solver in FUN3D. The linearized frequency-domain method is demonstrated and compared to other methods for traditional benchmark cases for computational aeroelasticity: the AGARD 445.6 wing, the Benchmark Supercritical Wing, and the Benchmark NACA 0012Wing.

Kevin E Jacobson↗

NASA NTRS1991

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in a high gradient region or the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational costs. A detailed description is given of the enrichment and coarsening procedures and comparisons with alternative results and experimental data are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Rausch, Russ D.↗

NASA NTRS1991

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper gives a detailed description of the enrichment and coarsening procedures and presents comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Rausch, Russ D.↗

NASA NTRS2017

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Aguilo, Miguel A.↗