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At least 289 records · Page 16

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Abstract. Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIEADA (Artificial Intelligence Emulator-Assisted Data Assimilation).

58 GEOSCIENCES↗

Reduced Order Models for Liquid Hydrogen Pooling and Vaporization Supported by Experiments

In the event of a leak of liquid hydrogen, a pool can form that vaporizes, disperses, and eventually dilutes to a non-flammable mixture. In this work, we describe fast-running models for the pooling and vaporization of liquid hydrogen in a steady cross-wind. Several pooling models from the literature are compared to solve for the flow and extent of the pool. The size of the pool can serve as the source for a separate dispersion model, which builds upon the existing one-dimensional Gaussian plume model in HyRAM+. Additional terms for the effects of a cross-wind on momentum and entrainment were added so that the model could handle the effects of a cross-wind on a low-speed flow. The models are compared to experimental data on pooling extent and downwind dispersion for steady flow rates of liquid hydrogen in a steady cross-wind. In the two compared experiments, liquid flow rates of 15 and 45 g/s were spilled onto concrete in cross-winds of approximately 1.8 m/s. The rate of growth of the pool and the downwind concentration boundaries are compared to the models, showing good agreement, although additional tuning is needed. These models can contribute to the advancement of codes and standards for liquid hydrogen systems.

dispersion↗

An error bound for a discrete reduced order model of a linear multivariable system

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

Al-Saggaf, Ubaid M.↗

Reduced Order Modeling of SLS Liquid Hydrogen Pre-Valve Flow Guide to Enable Rapid Transient Analysis

NASA is developing a new launch vehicle, called the Space Launch System (SLS), which is intended on taking humans out of low earth orbit to destinations including the moon, asteroids, and Mars. The propulsion system for the core stage of this vehicle includes four RS-25 Liquid Hydrogen/Oxygen rocket engines. These engines are upgraded versions of the Space Shuttle Main Engines (SSME); the upgrades include higher power levels and affordability enhancements. As with any new vehicle, the Main Propulsion System (MPS), which include the feedlines and ancillary hardware connecting the engines to the fuel and oxidizer tanks, had to be redesigned (figure 1 - export clearance in progress), as the previous MPS for the SSME's was inherently part of the Space Shuttle System, which had a completely different overall configuration.

Brown, Andrew M.↗

High Fidelity Adaptively Refined CFD and Reduced Order Models of a High Aspect Ratio Aeroelastic Wing Wind Tunnel Model

Robust adaptive mesh refinement for transonic conditions is one of the most difficult challenges to advancing CFD usage for certification by analysis. Transonic fluid-structure interaction cases represent an even more difficult challenge for adaptive mesh refinement. Production aircraft furthermore have structural models that have gaps and discontinuities that make the interdomain transfer of loads and deflections difficult. This adds to the challenge of adaptive mesh refinement. An initial attempt to create an adaptive mesh refinement process that refines regions of high flow gradient based around the HeldenMesh software is presented. The method is applied to the Integrated Adaptive Wing Technology Maturation (IAWTM) configuration. That has developed an aspect ratio 13.5 wing aeroelastic wind-tunnel model for testing in the Transonic Dynamics Tunnel (TDT). The high levels of deformation of this wing make the adaptation of meshes for the static shape difficult and has necessitated some creativity in how to efficiently adapt meshes. A time-domain identification of the unsteady system based on flexible modes using the adapted meshes is performed.

Robert E. Bartels↗