Equation-based

Equation-based reduced order modeling, i.e., model order reduction (MOR) is applicable when physics-governing equations are available in the discretized form. The large equation set is projected onto a low-dimensional subspace, resulting in a reduced set for fast simulation. A significant amount of effort in MOR focuses on identifying the best-performed subspace yielding the lowest dimension without noticeable compromise in model fidelity. Specific MOR methods studied by iMSEL include Krylove subspace (moment matching), singular value decomposition-based (proper orthogonal decomposition, truncated balanced truncation, and dynamic model decomposition), and their combinations
First five proper orthogonal decomposition (POD) modes of the streamwise velocity extracted from unsteady simulation of a delta wing with a large AoA = 24 deg. The iso-surfaces colored in red and blue, respectively, denote the values with opposite signs in the mode. The leading mode represents flow structures with large spatial scales and high kinetic energy, while the higher-order model indicates the flow structure with small spatial scales and low kinetic energy. Twisted flow structures are clearly observed in the high-order modes.

Spacecraft Thermal Analysis

Computational models and analysis are increasingly used to support the engineering of spacecraft at every stage of the development. Every single element in the spacecraft needs to be thermally interrogated to ensure that its temperature, thermal distortion and stability remain in the pre-defined operating envelope and in-orbit performance requirements are met during all mission phases. iMSEL has developed POD-based thermal ROMs for NASA's Laser Interferometer Space Antenna (LISA), a constellation mission spacecraft to detect and observe gravitational waves in the 0.1 mHz to 0.1 Hz frequency band. ROMs has been used to accelerate the heat transfer analysis (involving conduction and radiation) for a large number of orbits with different parameters to evaluate the quasi-steady-state and drifting behavior. In contrast to the full-scale LISA model ~200X speed with relative error less than 1%. Software to automate ROM generation and computation has been developed and delivered to NASA for testing.

High-speed Vehicle Thermal Analysis

There is a clear and unmet need for an integrated simulation tool for accurate, in-line, real-time analysis of closed-loop digital simulation. The key member in iMSEL has developed thermal ROMs and a real-time thermal history prediction tool for accurate analysis of complex 3D high-speed vehicles/targets with multi-layered materials and paint coatings in a broad spectrum of environments. Excellent agreement between the full CFD model and ROM with a relative error <1% and orders-of-magnitude (~100X) speedup for nonlinear heat transfer of the 3D whole target have been achieved. Integrated ROM simulation framework for model generation, computation, and verification has also been established.

X-56A MUTT (Flexible Aircraft) Aeroservoelasticity

Design of a modern flexible aircraft with a safe and acceptable flight envelope demands detailed modeling and high fidelity simulations of aeroservoelastic (ASE) systems prior to flight tests in order to investigate the source of potential aeroelastic (AE) failures. While full-order models coupled the nonlinear aerodynamics with structural models are capable of accurate prediction of underlying AE phenomena and onset, their prohibitive computational cost, low speed, nonlinear nature, as well as difficulty to deploy controllers with high-state-order models render it impractical for integration in the design environment involving concurrent ASE analysis and control synthesis and design. IMSEL has developed a model order reduction (MOR) framework to construct linear parameter-varying (LPV) reduced order models (ROM) of flexible aircrafts for aeroservoelasticity (ASE) analysis and control synthesis in broad 2D flight parameter space. The framework includes two key elements: (1) Genetic algorithms (GAs) to automatically determine physical states for reduction and generate ROMs at grid points within parameter space while minimizing the trial-and-error process; and (2) balanced truncation for unstable systems in conjunction with the congruence transformation technique to achieve locally optimal realization and “weak” fulfillment of state consistency across the entire parameter space. Therefore ASE ROM at any flight condition can be obtained simply through model interpolation. The methodology has been demonstrated using the pitch-plant model of X-56A MUTT currently being tested at NASA/AFRC for flutter suppression and gust load alleviation: more than 12X reduction in the number of states relative to the original model while preserving model and synthesis accuracy. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.

Heat Transfer, Species Transport & Kinetics in Microfluidics

In many microfluidic lab on chip (LoC) applications, thermal environments need to be precisely controlled for proper execution of biochemical and cellular assays, such as PCR, high-through kinetics analysis, among others. Thermal analysis in microfluidics poses formidable challenges to the chip design as heat propagates in the entire chip domain rather than only in the fluidic channels, leading to more substantial model sizes and slower thermal diffusion process. Both factors contribute to the prohibitively computational cost associated with whole-chip thermal analysis, rendering it ill-suited for concept evaluation, operational optimization, as well as closed-loop thermal control and management, where rapid (near real-time) iterative simulation capability is strongly desired for fast turnaround times. iMSEL has developed a Krylov subspace projection-based Reduced Order Model (ROM) for whole microfluidic chip thermal analysis, including conjugate heat transfer. Case studies using practically relevant thermal microfluidic chip demonstrate that the ROM matches the full-scale model very well in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with over three orders-of-magnitude acceleration in computational speed. The salient model reusability and real-time simulation capability renders it amenable for operational optimization and in-line thermal control and management of microfluidic systems and devices. The Krylov MOR framework has been extended to species transport and surface kinetics in both the 2D and 3D microfluidic channels (below).