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DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

NASA NTRS1994

NASA Lewis Research Center Workshop on Forced Response in Turbomachinery

A summary of the NASA Lewis Research Center (LeRC) Workshop on Forced Response in Turbomachinery in August, 1993 is presented. It was sponsored by the following NASA organizations: Structures, Space Propulsion Technology, and Propulsion Systems Divisions of NASA LeRC and the Aeronautics and Advanced Concepts & Technology Offices of NASA Headquarters. In addition, the workshop was held in conjunction with the GUIde (Government/Industry/Universities) Consortium on Forced Response. The workshop was specifically designed to receive suggestions and comments from industry on current research at NASA LeRC in the area of forced vibratory response of turbomachinery blades which includes both computational and experimental approaches. There were eight presentations and a code demonstration. Major areas of research included aeroelastic response, steady and unsteady fluid dynamics, mistuning, and corresponding experimental work.

Stefko, George L.↗

NASA NTRS1999

Vortex Reconnection or Breakdown Subsequent to Perpendicular Collision With A Solid Body

This paper analytically examines the unsteady fluid dynamics of a vortex filament subsequent to a normal collision of the vortex with a solid body. In particular, the breakdown or reconnection phenomena, post-collision, for a vortex filament is studied. The paper does not investigate the collision dynamics process itself. The derived exact solution is based upon the laminar viscous form of the Helmholtz equations.

Young, Larry A.↗

NASA NTRS2011

Water Flow Testing and Unsteady Pressure Analysis of a Two-Bladed Liquid Oxidizer Pump Inducer

The unsteady fluid dynamic performance of a cavitating two-bladed oxidizer turbopump inducer was characterized through sub-scale water flow testing. While testing a novel inlet duct design that included a cavitation suppression groove, unusual high-frequency pressure oscillations were observed. With potential implications for inducer blade loads, these high-frequency components were analyzed extensively in order to understand their origins and impacts to blade loading. Water flow testing provides a technique to determine pump performance without the costs and hazards associated with handling cryogenic propellants. Water has a similar density and Reynolds number to liquid oxygen. In a 70%-scale water flow test, the inducer-only pump performance was evaluated. Over a range of flow rates, the pump inlet pressure was gradually reduced, causing the flow to cavitate near the pump inducer. A nominal, smooth inducer inlet was tested, followed by an inlet duct with a circumferential groove designed to suppress cavitation. A subsequent 52%-scale water flow test in another facility evaluated the combined inducer-impeller pump performance. With the nominal inlet design, the inducer showed traditional cavitation and surge characteristics. Significant bearing loads were created by large side loads on the inducer during synchronous cavitation. The grooved inlet successfully mitigated these loads by greatly reducing synchronous cavitation, however high-frequency pressure oscillations were observed over a range of frequencies. Analytical signal processing techniques showed these oscillations to be created by a rotating, multi-celled train of pressure pulses, and subsequent CFD analysis suggested that such pulses could be created by the interaction of rotating inducer blades with fluid trapped in a cavitation suppression groove. Despite their relatively low amplitude, these high-frequency pressure oscillations posed a design concern due to their sensitivity to flow conditions and test scale. The amplitude and frequency of oscillations varied considerably over the pump s operating space, making it difficult to predict blade loads.

Schwarz, Jordan B.↗

DOE OSTI2023

Design and Testing of the Vortex Ring Facility

This document summarizes the efforts of building an experimental test facility to study the evolution of the cloud following a nuclear detonation above ground level and support the development of numerical models to describe it. The experimental facility allows nonintrusive flow visualization and measurements of buoyant vortex ring formation and evolution using background-oriented Schlieren and particle image velocimetry techniques. In addition, 3D unsteady computational fluid dynamics simulations using unsteady Reynolds-averaged Navier–Stokes and volume-of-fluid numerical methods were performed to support the experimental design as well as to provide insight about the formation and evolution of the vortex ring.

42 ENGINEERING↗

NASA NTRS1980

Fluid dynamics of the unsteady two phase processes leading to DDT in granular solid propellants

Deflagration to Detonation (DDT) was predicted to occur in porous beds of high-energy solid propellants by solving the unsteady fluid mechanical convective heat transfer from hot gas products, obtained from the rapid burning at high pressures, provides the impetus to develop a narrow combustion zone and a resulting strong shock. A parametric study clearly indicates that DDT occurs only when a combination of the solids loading fraction, the burning rate constants, the propellant chemical energy, and the particle size provide for critical energy and gas release to support a detonation wave. Predictions for the run-up length to detonation as a function of these parameters are presented.

Krier, H.↗

NASA NTRS1991

FAST: A multi-processed environment for visualization of computational fluid dynamics

Three-dimensional, unsteady, multi-zoned fluid dynamics simulations over full scale aircraft are typical of the problems being investigated at NASA Ames' Numerical Aerodynamic Simulation (NAS) facility on CRAY2 and CRAY-YMP supercomputers. With multiple processor workstations available in the 10-30 Mflop range, we feel that these new developments in scientific computing warrant a new approach to the design and implementation of analysis tools. These larger, more complex problems create a need for new visualization techniques not possible with the existing software or systems available as of this writing. The visualization techniques will change as the supercomputing environment, and hence the scientific methods employed, evolves even further. The Flow Analysis Software Toolkit (FAST), an implementation of a software system for fluid mechanics analysis, is discussed.

Bancroft, Gordon V.↗

NASA NTRS2012

The Direction of Fluid Dynamics for Liquid Propulsion at NASA Marshall Space Flight Center

Marshall Space Flight Center (MSFC) is the National Aeronautics and Space Administration (NASA)-designated center for the development of space launch systems. MSFC is particularly known for propulsion system development. Many engineering skills and technical disciplines are needed to accomplish this mission. This presentation will focus on the work of the Fluid Dynamics Branch (ER42). ER42 resides in the Propulsion Systems Department at MSFC. The branch is responsible for all aspects of the discipline of fluid dynamics applied to propulsion or propulsion-induced loads and environments. This work begins with design trades and parametric studies, and continues through development, risk assessment, anomaly investigation and resolution, and failure investigations. Applications include the propellant delivery system including the main propulsion system (MPS) and turbomachinery; combustion devices for liquid engines and solid rocket motors; coupled systems; and launch environments. An advantage of the branch is that it is neither analysis nor test centric, but discipline centric. Fluid dynamics assessments are made by analysis, from lumped parameter modeling through unsteady computational fluid dynamics (CFD); testing, which can be cold flow or hot fire; or a combination of analysis and testing. Integration of all discipline methods into one branch enables efficient and accurate support to the projects. To accomplish this work, the branch currently employs approximately fifty engineers divided into four teams -- Propellant Delivery CFD, Combustion Driven Flows CFD, Unsteady and Experimental Flows, and Acoustics and Stability. This discussion will highlight some of the work performed in the branch and the direction in which the branch is headed.

Griffin, Lisa W.↗

NASA NTRS1976

Some current research in unsteady aerodynamics: A report from the Fluid Dynamics Panel

The highlights of a recent discussion by representatives of the fluid dynamics and structures and materials panels are reported with emphasis on the fundamental aspects of unsteady fluid mechanics. Topics include linearized potential flow theory, transonic flow calculations, unsteady boundary layers, dynamic stall, transonic buffet, and techniques for measuring unsteady pressures.

Mccroskey, W. J.↗

NASA NTRS2001

Unsteady Flow in a Supersonic Turbine with Variable Specific Heats

Modern high-work turbines can be compact, transonic, supersonic, counter-rotating, or use a dense drive gas. The vast majority of modern rocket turbine designs fall into these Categories. These turbines usually have large temperature variations across a given stage, and are characterized by large amounts of flow unsteadiness. The flow unsteadiness can have a major impact on the turbine performance and durability. For example, the Space Transportation Main Engine (STME) fuel turbine, a high work, transonic design, was found to have an unsteady inter-row shock which reduced efficiency by 2 points and increased dynamic loading by 24 percent. The Revolutionary Reusable Technology Turbopump (RRTT), which uses full flow oxygen for its drive gas, was found to shed vortices with such energy as to raise serious blade durability concerns. In both cases, the sources of the problems were uncovered (before turbopump testing) with the application of validated, unsteady computational fluid dynamics (CFD) to the designs. In the case of the RRTT and the Alternate Turbopump Development (ATD) turbines, the unsteady CFD codes have been used not just to identify problems, but to guide designs which mitigate problems due to unsteadiness. Using unsteady flow analyses as a part of the design process has led to turbine designs with higher performance (which affects temperature and mass flow rate) and fewer dynamics problems. One of the many assumptions made during the design and analysis of supersonic turbine stages is that the values of the specific heats are constant. In some analyses the value is based on an average of the expected upstream and downstream temperatures. In stages where the temperature can vary by 300 to 500 K, however, the assumption of constant fluid properties may lead to erroneous performance and durability predictions. In this study the suitability of assuming constant specific heats has been investigated by performing three-dimensional unsteady Navier-Stokes simulations for a supersonic turbine stage.

Dorney, Daniel J.↗

NASA NTRS1999

Simulations of the Unsteady Flow through the Fastrac Supersonic Turbine

Analysis of the unsteady aerodynamic environment in the Fastrac supersonic turbine is presented. Modal analysis of the turbine blades indicated possible resonance in crucial operating ranges of the turbopump. Unsteady computational fluid dynamics (CFD) analysis was conducted to support the aerodynamic and structural dynamic assessments of the turbine. Before beginning the analysis, two major problems with current unsteady analytical capabilities had to be addressed: modeling a straight centerline nozzle with the turbine blades and exit guide vanes (EGVs), and reducing run times significantly while maintaining physical accuracy. Modifications were made to the CFD code used in this study to allow the coupled nozzle/blade/EGV analysis and to incorporate Message Passing Interface (MPI) software. Because unsteadiness is a key issue for the Fastrac turbine [and future rocket engine turbines such as for the Reusable Launch Vehicle (RI.V)], calculations were performed for two nozzle-to-blade axial gaps. Calculations were also performed for the nozzle alone, and the results were imposed as an inlet boundary condition for a blade/EGV calculation for the large gap case. These results are compared to the nozzle/blade/EGV results.

Griffin, Lisa W.↗

NASA NTRS1999

Overview of Current Turbine Aerodynamic Analysis and Testing at MSFC

An overview of the current turbine aerodynamic analysis and testing activities at NASA/Marshall Space Flight Center (MSFC) is presented. The presentation is divided into three areas. The first area is the three-dimensional (3D), unsteady Computational Fluid Dynamics (CFD) analysis of the Fastrac turbine. Results from a coupled nozzle, blade, and exit guide vane analysis and from an uncoupled nozzle and coupled blade and exit guide vane will be presented. Unsteady pressure distributions, frequencies, and exit profiles from each analysis will be compared and contrasted. The second area is the testing and analysis of the Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump (HPFTP) turbine with instrumented first stage blades. The SSME HPFTP turbine was tested in air at the MSFC Turbine Test Equipment (TTE). Pressure transducers were mounted on the first stage blades. Unsteady, 3D CFD analysis was performed for this geometry and flow conditions. A sampling of the results will be shown. The third area is a status of the Turbine Performance Optimization task. The objective of this task is to improve the efficiency of a turbine for potential use on a next generation launch vehicle. This task includes global optimization for the preliminary design, detailed optimization for blade shapes and spacing, and application of advanced CFD analysis. The final design will be tested in the MSFC TTE.

Griffin, Lisa W.↗

NASA NTRS2015

Space Launch System Scale Model Acoustic Test Ignition Overpressure Testing

The overpressure phenomenon is a transient fluid dynamic event occurring during rocket propulsion system ignition. This phenomenon results from fluid compression of the accelerating plume gas, subsequent rarefaction, and subsequent propagation from the exhaust trench and duct holes. The high-amplitude unsteady fluid-dynamic perturbations can adversely affect the vehicle and surrounding structure. Commonly known as ignition overpressure (IOP), this is an important design-to environment for the Space Launch System (SLS) that NASA is currently developing. Subscale testing is useful in validating and verifying the IOP environment. This was one of the objectives of the Scale Model Acoustic Test, conducted at Marshall Space Flight Center. The test data quantifies the effectiveness of the SLS IOP suppression system and improves the analytical models used to predict the SLS IOP environments. The reduction and analysis of the data gathered during the SMAT IOP test series requires identification and characterization of multiple dynamic events and scaling of the event waveforms to provide the most accurate comparisons to determine the effectiveness of the IOP suppression systems. The identification and characterization of the overpressure events, the waveform scaling, the computation of the IOP suppression system knockdown factors, and preliminary comparisons to the analytical models are discussed.

Nance, Donald↗

NASA NTRS2015

Space Launch System Scale Model Acoustic Test Ignition Overpressure Testing

The overpressure phenomenon is a transient fluid dynamic event occurring during rocket propulsion system ignition. This phenomenon results from fluid compression of the accelerating plume gas, subsequent rarefaction, and subsequent propagation from the exhaust trench and duct holes. The high-amplitude unsteady fluid-dynamic perturbations can adversely affect the vehicle and surrounding structure. Commonly known as ignition overpressure (IOP), this is an important design-to environment for the Space Launch System (SLS) that NASA is currently developing. Subscale testing is useful in validating and verifying the IOP environment. This was one of the objectives of the Scale Model Acoustic Test (SMAT), conducted at Marshall Space Flight Center (MSFC). The test data quantifies the effectiveness of the SLS IOP suppression system and improves the analytical models used to predict the SLS IOP environments. The reduction and analysis of the data gathered during the SMAT IOP test series requires identification and characterization of multiple dynamic events and scaling of the event waveforms to provide the most accurate comparisons to determine the effectiveness of the IOP suppression systems. The identification and characterization of the overpressure events, the waveform scaling, the computation of the IOP suppression system knockdown factors, and preliminary comparisons to the analytical models are discussed.

Nance, Donald K.↗

NASA NTRS2004

Aeroacoustic Analysis of a Simplified Landing Gear

A hybrid approach is used to investigate the noise generated by a simplified landing gear without small scale parts such as hydraulic lines and fasteners. The Ffowcs Williams and Hawkings equation is used to predict the noise at far-field observer locations from flow data provided by an unsteady computational fluid dynamics calculation. A simulation with 13 million grid points has been completed, and comparisons are made between calculations with different turbulence models. Results indicate that the turbulence model has a profound effect on the levels and character of the unsteadiness. Flow data on solid surfaces and a set of permeable surfaces surrounding the gear have been collected. Noise predictions using the porous surfaces appear to be contaminated by errors caused by large wake fluctuations passing through the surfaces. However, comparisons between predictions using the solid surfaces with the near-field CFD solution are in good agreement giving confidence in the far-field results.

Lockard, David P.↗

NASA NTRS2017

Economical Unsteady High-Fidelity Aerodynamics for Structural Optimization with a Flutter Constraint

Structural optimization with a flutter constraint for a vehicle designed to fly in the transonic regime is a particularly difficult task. In this speed range, the flutter boundary is very sensitive to aerodynamic nonlinearities, typically requiring high-fidelity Navier-Stokes simulations. However, the repeated application of unsteady computational fluid dynamics to guide an aeroelastic optimization process is very computationally expensive. This expense has motivated the development of methods that incorporate aspects of the aerodynamic nonlinearity, classical tools of flutter analysis, and more recent methods of optimization. While it is possible to use doublet lattice method aerodynamics, this paper focuses on the use of an unsteady high-fidelity aerodynamic reduced order model combined with successive transformations that allows for an economical way of utilizing high-fidelity aerodynamics in the optimization process. This approach is applied to the common research model wing structural design. As might be expected, the high-fidelity aerodynamics produces a heavier wing than that optimized with doublet lattice aerodynamics. It is found that the optimized lower skin of the wing using high-fidelity aerodynamics differs significantly from that using doublet lattice aerodynamics.

Bartels, Robert E.↗

NASA NTRS2003

Investigation of the Flow Physics Driving Stall-Side Flutter in Advanced Forward Swept Fan Designs

Flutter-free operation of advanced transonic fan designs continues to be a challenging task for the designers of aircraft engines. In order to meet the demands of increased performance and lighter weight, these modern fan designs usually feature low-aspect ratio shroudless rotor blade designs that make the task of achieving adequate flutter margin even more challenging for the aeroelastician. This is especially true for advanced forward swept designs that encompass an entirely new design space compared to previous experience. Fortunately, advances in unsteady computational fluid dynamic (CFD) techniques over the past decade now provide an analysis capability that can be used to quantitatively assess the aeroelastic characteristics of these next generation fans during the design cycle. For aeroelastic applications, Mississippi State University and NASA Glenn Research Center have developed the CFD code TURBO-AE. This code is a time-accurate three-dimensional Euler/Navier-Stokes unsteady flow solver developed for axial-flow turbomachinery that can model multiple blade rows undergoing harmonic oscillations with arbitrary interblade phase angles, i.e., nodal diameter patterns. Details of the code can be found in Chen et al. (1993, 1994), Bakhle et al. (1997, 1998), and Srivastava et al. (1999). To assess aeroelastic stability, the work-per-cycle from TURBO-AE is converted to the critical damping ratio since this value is more physically meaningful, with both the unsteady normal pressure and viscous shear forces included in the work-per-cycle calculation. If the total damping (aerodynamic plus mechanical) is negative, then the blade is unstable since it extracts energy from the flow field over the vibration cycle. TURBO-AE is an integral part of an aeroelastic design system being developed at Honeywell Engines, Systems & Services for flutter and forced response predictions, with test cases from development rig and engine tests being used to validate its predictive capability. A recent experimental program (Sanders et al., 2002) was aimed at providing the necessary unsteady aerodynamic and vibratory response data needed to validate TURBO-AE for fan flutter predictions. A comparison of numerical TURBO-AE simulations with the benchmark flutter data is given in Sanders et al. (2003), with the data used to guide the validation of the code and define best practices for performing accurate unsteady simulations. The agreement between the analyses and the predictions was quite remarkable, demonstrating the ability of the analysis to accurately model the unsteady flow processes driving stall-side flutter.

Sanders, Albert J.↗

DOE OSTI2021

Experimental Investigation of Innovative Cooling Schemes on an Additively Manufactured Engine Scale Turbine Nozzle Guide Vane

This study includes the design, validation, and fabrication via direct metal laser sintering (DMLS) of a gas turbine nozzle guide vanes (NGV) that incorporates three innovative cooling schemes specifically enabled by additive manufacturing. The novel NGV design is the culmination of an extensive research and development effort over a period of 4 years that included low- and high-speed cascade testing coupled with unsteady computational fluid dynamics for numerous candidate innovative cooling architectures. The final vane design (SJ-vane) consists of sweeping jet (SJ) film cooling holes on the suction surface (SS), sweeping jet impingement holes at the leading edge and double-wall partial length triangular pin-fin with impinging jet at the trailing edge. For comparison purposes, a second DMLS enabled vane (777-vane) was designed and fabricated with prototypical cooling circuits to serve as a baseline. This vane consists of a shaped film cooling holes on the suction surface, circular impingement holes at the leading edge, and full-length cylindrical pin-fins at the trailing edge. Experiments with the two DMLS enabled vanes were performed at the Ohio State University Turbine Reacting Flow Rig (TuRFR) at engine-relevant temperature (1375 K) and Mach number conditions. Infrared (IR) thermography was utilized to measure the wall temperature of the pressure and suction surface at several coolant mass flowrates to estimate the overall cooling effectiveness (&straightphi;). Results showed improved cooling performance for the advanced cooling schemes (sweeping jet film cooling, impingement cooling, and triangular pin-fin cooling) compared with the baseline cooling schemes.

Engineering↗