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Projection-Based Reduced Order Modeling for Spacecraft Thermal Analysis

This paper presents a mathematically rigorous, subspace projection-based reduced order modeling (ROM) methodology and an integrated framework to automatically generate reduced order models for spacecraft thermal analysis. Two key steps in the reduced order modeling procedure are described: (1) the acquisition of a full-scale spacecraft model in the ordinary differential equation (ODE) and differential algebraic equation (DAE) form to resolve its dynamic thermal behavior; and (2) the ROM to markedly reduce the dimension of the full-scale model. Specifically, proper orthogonal decomposition (POD) in conjunction with discrete empirical interpolation method (DEIM) and trajectory piece-wise linear (TPWL) methods are developed to address the strong nonlinear thermal effects due to coupled conductive and radiative heat transfer in the spacecraft environment. Case studies using NASA-relevant satellite models are undertaken to verify the capability and to assess the computational performance of the ROM technique in terms of speed-up and error relative to the full-scale model. ROM exhibits excellent agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with salient computational acceleration (up to two orders of magnitude speed-up) over the full-scale analysis. These findings establish the feasibility of ROM to perform rational and computationally affordable thermal analysis, develop reliable thermal control strategies for spacecraft, and greatly reduce the development cycle times and costs.

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Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model

Reduced-Order Modeling and Parameter Identification of Wind Tunnel Measurement Systems

We present a method to develop a physics-based, reduced-order model of a wind tunnel measurement system (including a sting, strain gage force balance, and test article) that can be used to predict the dynamics of the system. This reduced-order model is combined with a simple finite element beam model of a sting to estimate the dynamics of the full assembly. We make comparisons between a full finite element model and the hybrid reduced-order model to show that this hybrid reduced-order model is capable of predicting the first six natural frequencies to within 10% error. This technique could be used to identify reduced-order parameters for a large number of balances and stings, which could then be used to estimate the dynamics of different measurement assemblies.

Reduced-order Modeling

Reduced-Order Modeling and Parameter Identification of Wind Tunnel Measurement Systems

We present a method to develop a physics-based, reduced-order model of a wind tunnel measurement system (including a sting, strain gage force balance, and test article) that can be used to predict the dynamics of the system. This reduced-order model is combined with a simple finite element beam model of a sting to estimate the dynamics of the full assembly. We make comparisons between a full finite element model and the hybrid reduced-order model to show that this hybrid reduced-order model is capable of predicting the first six natural frequencies to within 10% error. This technique could be used to identify reduced-order parameters for a large number of balances and stings, which could then be used to estimate the dynamics of different measurement assemblies.

Reduced-order Modeling

Reduced Order Model for Guided Wave Propagation on Gas Pipelines to Enable Real-Time Simulation

Reduced order model for simulation of Guided wave propagation is presented here. The utilization of reduced order models ensures efficient data generation for a variety of parameters where it takes huge computational effort to simulate, crucial for timely monitoring and decision-making. Autoencoder based reduced order models are proposed here, which are trained on simulated data from open-source finite element framework, Firedrake.

Bukka, Sandeep Reddy

Reduced Order Model for Guided Wave Propagation on Gas Pipelines to Enable Real-Time Simulation

Reduced order model for simulation of Guided wave propagation is presented here. The utilization of reduced order models ensures efficient data generation for a variety of parameters where it takes huge computational effort to simulate, crucial for timely monitoring and decision-making. Autoencoder based reduced order models are proposed here, which are trained on simulated data from open-source finite element framework, Firedrake.

Bukka, Sandeep Reddy

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING

A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations.

08 HYDROGEN

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction

Reduced-order model to approximate response matrices for filter stack spectrometers

We present a reduced-order model to calculate response matrices rapidly for filter stack spectrometers (FSSs). The reduced-order model allows response matrices to be built modularly from a set of pre-computed photon and electron transport and scattering calculations through various filter and detector materials. While these modular response matrices are not appropriate for high-fidelity analysis of experimental data, they encode sufficient physics to be used as a forward model in design optimization studies of FSSs, particularly for machine learning approaches that require sampling and testing a large number of FSS designs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Reduced-Order Modeling: New Approaches for Computational Physics

In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.

Beran, Philip S.

Identification of Computational and Experimental Reduced-Order Models

The identification of computational and experimental reduced-order models (ROMs) for the analysis of unsteady aerodynamic responses and for efficient aeroelastic analyses is presented. For the identification of a computational aeroelastic ROM, the CFL3Dv6.0 computational fluid dynamics (CFD) code is used. Flutter results for the AGARD 445.6 Wing and for a Rigid Semispan Model (RSM) computed using CFL3Dv6.0 are presented, including discussion of associated computational costs. Modal impulse responses of the unsteady aerodynamic system are computed using the CFL3Dv6.0 code and transformed into state-space form. The unsteady aerodynamic state-space ROM is then combined with a state-space model of the structure to create an aeroelastic simulation using the MATLAB/SIMULINK environment. The MATLAB/SIMULINK ROM is then used to rapidly compute aeroelastic transients, including flutter. The ROM shows excellent agreement with the aeroelastic analyses computed using the CFL3Dv6.0 code directly. For the identification of experimental unsteady pressure ROMs, results are presented for two configurations: the RSM and a Benchmark Supercritical Wing (BSCW). Both models were used to acquire unsteady pressure data due to pitching oscillations on the Oscillating Turntable (OTT) system at the Transonic Dynamics Tunnel (TDT). A deconvolution scheme involving a step input in pitch and the resultant step response in pressure, for several pressure transducers, is used to identify the unsteady pressure impulse responses. The identified impulse responses are then used to predict the pressure responses due to pitching oscillations at several frequencies. Comparisons with the experimental data are then presented.

Silva, Walter A.

Reduced-Order Modeling: Cooperative Research and Development at the NASA Langley Research Center

Cooperative research and development activities at the NASA Langley Research Center (LaRC) involving reduced-order modeling (ROM) techniques are presented. Emphasis is given to reduced-order methods and analyses based on Volterra series representations, although some recent results using Proper Orthogonal Deco in position (POD) are discussed as well. Results are reported for a variety of computational and experimental nonlinear systems to provide clear examples of the use of reduced-order models, particularly within the field of computational aeroelasticity. The need for and the relative performance (speed, accuracy, and robustness) of reduced-order modeling strategies is documented. The development of unsteady aerodynamic state-space models directly from computational fluid dynamics analyses is presented in addition to analytical and experimental identifications of Volterra kernels. Finally, future directions for this research activity are summarized.

Silva, Walter A.

Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced-Order Modeling of S n Radiation Transport

Deterministic solutions to the Sn radiation transport equation can be computationally expensive to calculate. Reduced-order modeling enables efficient approximation of the full-order model (FOM) solution. We propose a novel method for constructing reduced-order models (ROMs) of the S n radiation transport equation, offline maximizing minimally invasive (OMMI) proper orthogonal decomposition (POD). POD uses the method of snapshots to create a reduced-order basis for constructing an ROM. Minimally invasive POD leverages the sweep infrastructure existing in deterministic transport codes to create a POD-based ROM, even when infeasible by traditional methods. Offline maximizing minimally invasive proper orthogonal decomposition (OMMI-POD) extends minimally invasive POD by performing sweeps offline, therefore maximizing the potential speedup. OMMI-POD does so by creating a library of reduced systems from a training set. This library of reduced systems is then interpolated to provide a rapid approximate solution of the S n radiation transport equation. The model is evaluated on a set of test problems, achieving a low error with a 466 times speedup over the FOM. Also presented is a study of the effect of sampling method on the performance of OMMI-POD, specifically comparing naive uniform sampling to the more accurate and computationally expensive greedy sampling.

97 MATHEMATICS AND COMPUTING

Reduced-Order Modeling of Hydrogen Releases from Vent Stacks and with Wind Effects

Here, the physical release behavior of hydrogen is important to understand from a safety and design perspective. The consequences of unignited pressurized gaseous hydrogen plumes exiting vent stacks were considered by extending and modifying existing general hydrogen plume models. Entrainment, vent stack backpressure, and the flow regime of hydrogen exiting the vent were found to be significant factors affecting plume shape and size, but further investigation and validation with unchoked, low-Froude-number flows is recommended to improve the model’s robustness. Additionally, models for the effects of wind on unignited plume momentum and entrainment were added to explore this behavior. Wind was assumed to increase mixing of hydrogen with the ambient air, and to affect the momentum of the released jet. Introducing wind into the plume model led to a shorter plume for all wind and jet directions. A high counter-flowing wind led to non-physical results and challenges in interpreting the visualization. The proposed jet plume wind sub-models (specifically entrainment coefficients) were fit and compared to experimental data of different releases of hydrogen into a wind tunnel, but the quantity of data available and experimental conditions were limited. Thus, collection of more empirical data and for a wider range of conditions is recommended for improvement of the proposed computational models. Developing reduced-order models for these physical phenomena can improve accessibility to predicted physical behavior and the rate at which hydrogen systems can be safely designed and deployed.

entrainment