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DOE OSTI2026

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗

NASA NTRS1993

Frequency distributions and correlations of solar X-ray flare parameters

Frequency distributions of flare parameters are determined from over 12,000 solar flares. The flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons are among the parameters studied. Linear regression fits, as well as the slopes of the frequency distributions, are used to determine the correlations between these parameters. The relationship between the variations of the frequency distributions and the solar activity cycle is also investigated. Theoretical models for the frequency distribution of flare parameters are dependent on the probability of flaring and the temporal evolution of the flare energy build-up. The results of this study are consistent with stochastic flaring and exponential energy build-up. The average build-up time constant is found to be 0.5 times the mean time between flares.

Crosby, Norma B.↗

NASA NTRS2003

Analysis of Combustion Systems

As part of the NASA High-Speed Research Program, low emission combustors are being studied and demonstrated. One combustor concept that is currently being studied and evaluated is the Rich burn-Quick mix-Lean burn (RQL) combustor. The quick-mix zone of the RQL combustor is extremely important in reducing NO(x) emissions; rapid mixing of the bypass airflow with rich-born effluent is essential. The basic challenge can be described as rapid jet-in-crossflow mixing. Although jet-in-crossflow mixing is not new, this RQL application is unique in that the jet-to-mainstream mass-flow ratios are higher than studied previously (approx. 3 in RQL applications versus approx. 0.5 in dilution zone studies), plus the emphasis is on reducing NO(x) emissions (i.e. good mixing might not necessarily produce low emissions). This five-years project focused on identifying quick-mix method that would reduce NO(x) emissions in RQL combustor. The work included study of mixing concepts, and the development of design methodology. Three dimension CFD analysis was the primary tool used in assessing concept and developing design methodology for low emission. Isothermal and reacting CFD calculations were performed on cylindrical, rectangular, and annular generic geometries. Systematic parameters studies were performed to isolate key design parameters and their influence on mixing and emissions.

Daniel B. Bain↗

NASA NTRS2022

Impact of 3D Structure on Magnetic Reconnection

Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was performed. An initially simple 1D equilibrium was used, consisting of a modified force-free current sheet, with periodic boundary conditions in all directions. In all cases, the linear and nonlinear evolution led to a primary current sheet between two large flux ropes. The global reconnection rate during this later stage was analyzed in all simulations. It was found that in 2.5D the primary current sheet fragmented owing to plasmoids, and as expected, the global reconnection rate, calculated using multiple methods, increases with the strength of the reconnecting field owing to a stronger Alfvén speed. In 3D, the presence of interacting oblique modes of the tearing instability complicates the simple 2.5D picture, entangling the magnetic field of the inflow and introducing a negative effect on the reconnection rate. The two competing effects of stronger Alfvén speed and entangling, which both increase with the strength of the reconnecting field, resulted in a decrease in the reconnection rate with increasing reconnecting field. For all simulations, the 3D rates were less than in 2.5D but suggest that as one goes to weak reconnecting field (or strong guide field) the system becomes more 2.5D-like and the 2.5D and 3D rates converge. These results have relevance to situations like nanoflare heating and flare current sheets in the corona.

Lars K S Daldorff↗

NASA NTRS2022

The Role of Reconnection in the Onset of Solar Eruptions

Solar eruptive events such as coronal mass ejections and eruptive flares are frequently associated with the emergence of magnetic flux from the convection zone into the corona. We use three-dimensional magnetohydrodynamic numerical simulations to study the interaction of coronal magnetic fields with emerging flux and determine the conditions that lead to eruptive activity. A simple parameter study is performed, varying the relative angle between emerging magnetic flux and a preexisting coronal dipole field. We find that in all cases the emergence results in a sheared magnetic arcade that transitions to a twisted coronal flux rope via low-lying magnetic reconnection. This structure, however, is constrained by its own outer field and so is noneruptive in the absence of reconnection with the overlying coronal field. The amount of this overlying reconnection is determined by the relative angle between the emerged and preexisting fields. The reconnection between emerging and preexisting fields is necessary to generate sufficient expansion of the emerging structure so that flare-like reconnection below the coronal flux rope becomes strong enough to trigger its release. Our results imply that the relative angle is the key parameter in determining whether the resultant active regions exhibit eruptive behavior and is thus a potentially useful candidate for predicting eruptions in newly emerging active regions. More generally, our results demonstrate that the detailed interaction between the convection zone/photosphere and the corona must be calculated self-consistently in order to model solar eruptions accurately.

James E Leake↗

NASA NTRS1997

12 Inch Fan Acoustic Research

There were three general purposes of this research; first, to investigate fundamental fan acoustic processes, second, to produce high quality data for the validation of aeroacoustic codes and, third, to investigate candidate noise control concepts. These were all to be investigated using the NASA built and supplied 12 inch fan which is a 0.1 scale model of a modem ultra high bypass fan. NASA also supplied the test environments, wind tunnel entries in the 14 by 22 Foot Subsonic Wind Tunnel and the Anechoic Noise Research Facility. To fulfill the purposes of the grant, investigations were performed in several general topics. In the area of fundamental fan studies, some of the topics involved were azimuthal directivity and tip clearance effects. In the area of high quality validation data significant parameter studies in the wind tunnel tests were performed. And in the area of noise control concepts, heated air injection was studied. The principal investigator performed the work on this grant by leading the concept development, design, planning, data analysis and reporting of the areas studied. The final report for this grant consists of a listing, which follows, of all reports, presentations, and publications that were made for the work done during the performance period.

Thomas, R. H.↗

NASA NTRS1989

Failure modes and damage accumulation in laminated composites with free edges

The influence of fiber orientation, stacking sequence, material properties and edge effects on the accumulation of damage and modes of failure in angle-ply and quasi-isotropic composite laminates are studied. Experimental results are presented for graphite-epoxy and graphite-polyimide coupons subjected to tensile load. It is shown that all the parameters studied can have a significant influence on the behavior of the composite.

Herakovich, Carl T.↗

NASA NTRS1988

Basic and applied research related to the technology of space energy conversion systems

The first six months' research effort on the Liquid Droplet Radiator (LDR) focussed on experimental and theoretical studies of radiation by an LDR droplet cloud. Improvements in the diagnostics for the radiation facility have been made which have permitted an accurate experimental test of theoretical predictions of LDR radiation over a wide range of optical depths, using a cloud of Dow silicone oil droplets. In conjunction with these measurements an analysis was made of the evolution of the cylindrical droplet cloud generated by a 2300-hole orifice plate. This analysis indicates that a considerable degree of agglomeration of droplets occurs over the first meter of travel. Theoretical studies have centered on developments of an efficient means of computing the angular scattering distribution from droplets in an LDR droplet cloud, so that a parameter study can be carried out for LDR radiative performance vs fluid optical properties and cloud geometry.

Hertzberg, A.↗

NASA NTRS1989

Parametric study of power absorption from electromagnetic waves by small ferrite spheres

Algebraic expressions in terms of elementary mathematical functions are derived for power absorption and dissipation by eddy currents and magnetic hysteresis in ferrite spheres. Skin depth is determined by using a variable inner radius in descriptive integral equations. Numerical results are presented for sphere diameters less than one wavelength. A generalized power absorption parameter for both eddy currents and hysteresis is expressed in terms of the independent parameters involving wave frequency, sphere radius, resistivity, and complex permeability. In general, the hysteresis phenomenon has a greater sensitivity to these independent parameters than do eddy currents over the ranges of independent parameters studied herein. Working curves are presented for obtaining power losses from input to the independent parameters.

Englert, Gerald W.↗

NASA NTRS1972

Scatter factor and reliability of aircraft structures

The concept of time to first failure is utilized to perform a parameter study of scatter factors of aircraft structures. The Weibull distribution is used for estimation of characteristic and certifiable lives. Scatter factors for various Weibull-shaped parameters, fleet sizes and level of reliabilities are calculated. It is concluded that the currently used range of scatter factors (2 through 4) is too narrow for the estimation of a safe life and that a safe and economical design for structural materials with shape parameters less than 2 does not seem feasible except for very small fleet sizes and low levels of reliability.

Schueller, G. I.↗

NASA NTRS1991

Tunable far infrared studies of molecular parameters in support of stratospheric measurements

Lab studies were made in support of far infrared spectroscopy of the stratosphere using the Tunable Far InfraRed (TuFIR) method of ultrahigh resolution spectroscopy and, more recently, spectroscopic and retrieval calculations performed in support of satellite-based atmospheric measurement programs: the Global Ozone Monitoring Experiment (GOME), and the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY).

Chance, Kelly V.↗

NASA NTRS1992

Atmospheric measurements using the LAMP lidar during the LADIMAS campaign

The results of the LAtitudinal DIstribution of Middle Atmosphere Structure (LADIMAS) experiment have provided a unique data set to improve our understanding of the middle atmosphere. The project included shipboard and rocket range coordinated measurements between 70 deg N to 65 deg S to study the structure, dynamics, and chemistry of the atmosphere. Results on important dynamical processes, such as gravity waves, tidal components, as well as the formation of the layers of meteoric ion and neutral species, were obtained with lidar, digisonde, microwave radiometer, and spectrometers. The cooperative study of the atmosphere was undertaken by researchers from several laboratories, including Penn State University (PSU), University Bonn, University Wuppertal, Lowell University, and others. Several of the parameters studied have never been measured before over such a wide range of latitudes. Instruments were assembled aboard the German research vessel RV POLARSTERN while this vessel was sailing from the Arctic to the Antarctic seas between 8 Oct. 1991 - 2 Jan. 1992. This paper presents an introduction to the data gathered by the PSU investigation with the Lidar Atmospheric Measurements Program (LAMP) lidar.

Philbrick, C. R.↗

NASA NTRS2001

Electrical Transmission on the Lunar Surface: DC Transmission - Part 1

This report summarizes a portion of the results from a grant at Auburn University to study the electrical and thermal energy management for lunar facilities. Over the past year (June 1989 to May 1990) the following topics have been investigated: June 1989 to November 1989 - Literature survey, assessment of lunar power needs, and overview study of the requirements of a lunar power system; November 1989 to April 1990 - Develop models for the study of dc electrical power transmission lines for the lunar surface; March 1990 to May 1990 - Develop models for the study of ac electrical power transmission lines for the lunar surface. Because of the large amount of information in the model development and application to a wide parameter space this report is being bound separately. This report specifically contains the model development and parameter study for dc electrical power transmission lines. The end of the funding year (May 1990) will conclude with an annual report including the literature survey, the overview of the requirements of a lunar power system, and summaries of the dc and ac models of electrical transmission lines.

Gordon, Lloyd B.↗

NASA NTRS1994

Dense molecular shocks and accretion onto protostellar disks

We have examined the physical and chemical processes which accompany the propagation of a J-type shock through molecular astrophysical gas of density 10(exp 7.5) - 10(exp 12) H nuclei per cu cm. Our study is primarily relevant to the high-density accretion shocks which are associated with the supersonic infall of material during the collapse of a molecular cloud core to form a protostar. We have carried out a general parameter study to determine the characteristic infrared emission spectrum of dense molecular shocks and the extent of grain destruction within such shocks as a function of relevant shock parameters. Accretion shocks with mass accretion rates approximately greater than 10(exp -5) solar masses per y are plausible sources of the CO v = 2-0 vibrational band emission observed in many protostars, at least for sources of moderate CO v = 2-0 luminosity (approximately less than few x 10(exp 23) W). Rovibrational emissions from H2O and OH are also predicted to be luminous in dense molecular accretion shocks. Vaporization is the dominant mechanism of grain destruction within dense molecular shocks, leading to the efficient removal of those grains which are heated to their vaporization temperature by the combined effects of radiative heating, drag heating, and thermal heating by the hot postshock gas. The criteria for grain vaporization are obtained for grains composed of several different materials: metallic iron, silicate, troilite, refractory organic materials, volatile organic materials, and water ice.

Neufeld, David A.↗

DOE OSTI2026

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗

NASA NTRS2003

Computational Study of Porous Treatment for Altering Flap Side-Edge Flowfield

Reynolds-averaged Navier-Stokes calculations are used to investigate porous side-edge treatment as a passive means for flap noise reduction. Steady-state simulations are used to infer effects of the treatment on acoustically relevant features of the mean flow near the flap side edge. Application of the porous treatment over a miniscule fraction of the wetted flap area (scaling with the flap thickness) results in significantly weaker side-edge vortex structures via modification of the vortex initiation and roll-up processes. At high flap deflections, the region of axial flow reversal associated with the breakdown of the side-edge vortex is also eliminated, indicating an absence of vortex bursting in the presence of the treatment. Potential ramifications of the mean-flow modifications for flap-noise reduction are examined in the light of lessons learned from recent studies on flap noise. Computations confirm that any noise reduction benefit via the porous treatment would be achieved without compromising the aerodynamic effectiveness of the flap. Results of the parameter study contribute additional insight into the measured data from the 7x10 wind tunnel at NASA Ames and provide preliminary guidance for specifying optimal treatment characteristics in terms of treatment location, spatial extent, and flow resistance of the porous skin.

Choudhari, Meelan↗

NASA NTRS1987

Influence of torsional-lateral coupling on stability behavior of geared rotor systems

In high-performance turbomachinery trouble often arises because of unstable nonsynchronous lateral vibrations. The instabilities are mostly caused by oil-film bearings, clearance excitation, internal damping, annular pressure seals in pumps, or labyrinth seals in turbocompressors. In recent times the coupling between torsional and lateral vibrations has been considered as an additional influence. This coupling is of practical importance in geared rotor systems. The literature describes some field problems in geared drive trains where unstable lateral vibrations occurred together with torsional oscillations. This paper studies the influence of the torsional-lateral coupling on the stability behavior of a simple geared system supported by oil-film bearings. The coupling effect is investigated by parameter studies and a sensitivity analysis for the uncoupled and coupled systems.

Schwibinger, P.↗

NASA NTRS1985

CELSS Transportation Analysis

Regenerative life support systems based on the use of biological material was considered for inclusion in manned spacecraft. Biological life support systems are developed in the controlled ecological life support system (CELSS) program. Because of the progress achieved in the CELSS program, it is determined which space missions may profit from use of the developing technology. Potential transportation cost savings by using CELSS technology for selected future manned space missions was evaluated. Six representative missions were selected which ranged from a low Earth orbit mission to those associated with asteroids and a Mars sortie. The crew sizes considered varied from four persons to five thousand. Other study parameters included mission duration and life support closure percentages, with the latter ranging from complete resupply of consumable life support materials to 97% closure of the life support system. The analytical study approach and the missions and systems considered, together with the benefits derived from CELSS when applicable are described.

Olson, R. L.↗