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Equilibrium velocities of a planetesimal population

The random velocities of planetesimal populations specified by maximum and minimum masses and a power-law number density are calculated iteratively. The calculation is based on two different physical models involving ratios of rates: (1) excitation of kinetic energy by gravitational perturbation and elastic collision equal to damping of kinetic energy by inelastic collisions; and (2) excitation of kinetic energy a ratio b (about 3 usually) to doubling of mass. Both physical models are developed approximately and then more precisely. The approximate model (2) agrees with results of Safronov (1972). Both precise models are applied to populations approximating those generated by the calculations of Greenberg et al. (1978), Cox and Lewis (1979), and Wetherill (1979).

Kaula, W. M.↗

Computation of eigenpairs of Ax = lambda Bx for vibrations of spinning deformable bodies

It is shown that, when linear theory is used, the general eigenvalue problem related with the free vibrations of spinning deformable bodies is of the type AX = lambda Bx, where A is Hermitian, and B is real positive definite. Since the order n of the matrices may be large, and A and B are banded or block banded, due to the economics of the numerical solution, one is interested in obtaining only those eigenvalues which fall within the frequency band of interest of the problem. The paper extends the well known method of bisections and iteration of R to the n power to n dimensional complex spaces, i.e., to C to the n power, so that it can be applied to the present problem.

Utku, S.↗

Feature Extraction of Event-Related Potentials Using Wavelets: An Application to Human Performance Monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many f ree parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation,-, algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

Trejo, Leonard J.↗

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance. Copyright 1999 Academic Press.

Evoked Potentials↗

System Modeling of a Lunar Molten Regolith Electrolysis Plant

In-Situ Resource Utilization (ISRU) is the process of extracting local resources to produce commodities for propulsion, life support systems, and off-planet construction rather than transporting consumables from Earth. Molten Regolith Electrolysis (MRE) is a novel ISRU method of extracting oxygen gas and metal alloy from lunar regolith. The MRE process involves placing lunar regolith between two electrodes, through which current is passed, to melt the regolith and reduce the metal oxide constituents by direct electrolysis (e.g. FeO, SiO 2 , MgO, Al 2 O 3 ) into oxygen gas and metal alloys. The oxygen is liquefied and used as propellant for landers, while the metals (e.g. Ferro-alloys) are further processed and used in structural building materials and parts manufacturing. A system model was developed that accounted for the major processes of an MRE plant (from excavation of raw materials to storage of products) to assess the feasibility of a lunar MRE plant. The S ystem Engineering and Integration ( S E&I) I SRU M odeling and A nalysis (SIMA) team utilized its previously documented system sizing model, the Mission Analysis and Integration Tool (MAIT) as framework of the system model. MAIT uses MATLAB/Simulink to integrate subsystem models into a complete system model of the MRE plant. Total mass, volume, and power requirements were computed for numerous iterations of a MRE plant.

In-Situ Resource Utilization↗

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Gupta, V. K.↗

Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology

The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in an iteration loop. The interface utilizes a file share system to transfer geometry dimensions, temperatures, and material identifiers to OpenMC, which is used to perform a neutron transport simulation of a design like the government Testing Reference Design reactor. The interface is then able to post-process the results from OpenMC and use the same file share system to share a power shape and other important neutron transport parameters to the system performance code. Initial results show that neglecting the changes to power shape when comparing reactor configurations can yield inaccurate results. Furthermore, utilizing propellants other than hydrogen gas can cause significant changes to the power shape, and thus, the thermal performance of a specific reactor design. This methodology is being expanded to allow for multiple families of NTP reactors to be analyzed, including block moderator, particle bed, and NERVA-derived reactors.

multiphysics coupling↗

Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology

The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in an iteration loop. The interface utilizes a file share system to transfer geometry dimensions, temperatures, and material identifiers to OpenMC, which is used to perform a neutron transport simulation of a design like the government Testing Reference Design reactor. The interface is then able to post-process the results from OpenMC and use the same file share system to share a power shape and other important neutron transport parameters to the system performance code. Initial results show that neglecting the changes to power shape when comparing reactor configurations can yield inaccurate results. Furthermore, utilizing propellants other than hydrogen gas can cause significant changes to the power shape, and thus, the thermal performance of a specific reactor design. This methodology is being expanded to allow for multiple families of NTP reactors to be analyzed, including block moderator, particle bed, and NERVA-derived reactors.

multiphysics coupling↗

Computational Investigation of a Boundary-Layer Ingestion Propulsion System for the Common Research Model

This thesis will examine potential propulsive and aerodynamic benefits of integrating a boundary-layer ingestion (BLI) propulsion system with a typical commercial aircraft using the Common Research Model geometry and the NASA Tetrahedral Unstructured Software System (TetrUSS). The Numerical Propulsion System Simulation (NPSS) environment will be used to generate engine conditions for CFD analysis. Improvements to the BLI geometry will be made using the Constrained Direct Iterative Surface Curvature (CDISC) design method. Previous studies have shown reductions of up to 25% in terms of propulsive power required for cruise for other axisymmetric geometries using the BLI concept. An analysis of engine power requirements, drag, and lift coefficients using the baseline and BLI geometries coupled with the NPSS model are shown. Potential benefits of the BLI system relating to cruise propulsive power are quantified using a power balance method and a comparison to the baseline case is made. Iterations of the BLI geometric design are shown and any improvements between subsequent BLI designs presented. Simulations are conducted for a cruise flight condition of Mach 0.85 at an altitude of 38,500 feet and an angle of attack of 2deg for all geometries. A comparison between available wind tunnel data, previous computational results, and the original CRM model is presented for model verification purposes along with full results for BLI power savings. Results indicate a 14.3% reduction in engine power requirements at cruise for the BLI configuration over the baseline geometry. Minor shaping of the aft portion of the fuselage using CDISC has been shown to increase the benefit from boundary-layer ingestion further, resulting in a 15.6% reduction in power requirements for cruise as well as a drag reduction of eighteen counts over the baseline geometry.

Blumenthal, Brennan↗

Computational Investigation of a Boundary-Layer Ingesting Propulsion System for the Common Research Model

The present paper examines potential propulsive and aerodynamic benefits of integrating a Boundary-Layer Ingestion (BLI) propulsion system into a typical commercial aircraft using the Common Research Model (CRM) geometry and the NASA Tetrahedral Unstructured Software System (TetrUSS). The Numerical Propulsion System Simulation (NPSS) environment is used to generate engine conditions for CFD analysis. Improvements to the BLI geometry are made using the Constrained Direct Iterative Surface Curvature (CDISC) design method. Previous studies have shown reductions of up to 25% in terms of propulsive power required for cruise for other axisymmetric geometries using the BLI concept. An analysis of engine power requirements, drag, and lift coefficients using the baseline and BLI geometries coupled with the NPSS model are shown. Potential benefits of the BLI system relating to cruise propulsive power are quantified using a power balance method, and a comparison to the baseline case is made. Iterations of the BLI geometric design are shown and any improvements between subsequent BLI designs presented. Simulations are conducted for a cruise flight condition of Mach 0.85 at an altitude of 38,500 feet and an angle of attack of 2 deg for all geometries. A comparison between available wind tunnel data, previous computational results, and the original CRM model is presented for model verification purposes along with full results for BLI power savings. Results indicate a 14.4% reduction in engine power requirements at cruise for the BLI configuration over the baseline geometry. Minor shaping of the aft portion of the fuselage using CDISC has been shown to increase the benefit from Boundary-Layer Ingestion further, resulting in a 15.6% reduction in power requirements for cruise as well as a drag reduction of eighteen counts over the baseline geometry.

Blumenthal, Brennan T.↗

Radioisotope Stirling Engine Powered Airship for Low Altitude Operation on Venus

The feasibility of a Stirling engine powered airship for the near surface exploration of Venus was evaluated. The heat source for the Stirling engine was limited to 10 general purpose heat source (GPHS) blocks. The baseline airship utilized hydrogen as the lifting gas and the electronics and payload were enclosed in a cooled insulated pressure vessel to maintain the internal temperature at 320 K and 1 Bar pressure. The propulsion system consisted of an electric motor driving a propeller. An analysis was set up to size the airship that could operate near the Venus surface based on the available thermal power. The atmospheric conditions on Venus were modeled and used in the analysis. The analysis was an iterative process between sizing the airship to carry a specified payload and the power required to operate the electronics, payload and cooling system as well as provide power to the propulsion system to overcome the drag on the airship. A baseline configuration was determined that could meet the power requirements and operate near the Venus surface. From this baseline design additional trades were made to see how other factors affected the design such as the internal temperature of the payload chamber and the flight altitude. In addition other lifting methods were evaluated such as an evacuated chamber, heated atmospheric gas and augmented heated lifting gas. However none of these methods proved viable.

Colozza, Anthony J.↗

Double Power-law Formation by Sequential Particle Acceleration

Spectral double power laws are common in solar high-energy phenomena such as flares and interplanetary energetic-electron events. However, the physical mechanism that produces the changes in power-law index within a single spectrum is unclear. We developed a fully analytical method of forming single power-law spectra from sequential acceleration of particles orbiting inside and hopping between simulated large-scale magnetic islands formed by flare reconnection. Here, we extend the analytical method to the formation of double power-law spectra by assuming sequential acceleration in two successive regions with different acceleration and particle-transport rates. The resulting spectral distribution is continuous and smooth, with a flattening at low energies, two power-law regions at mid-energies, and a steep rollover at high energies. The model provides analytical expressions for the spectral indices, all energy breaks, and normalization constants as functions of just three physical parameters of each acceleration region: (1) the energy gain in each accelerator, (2) the percentage of particles transferred between accelerators, and (3) the number of accelerators visited. One of the most salient predictions of our work is that the spectral index at high (low) energies is determined by the parameters of the first "seed" (second) acceleration region. By constructing the spectral distribution through an iterative analytical process, the evolution toward a double power law is easily characterized and explained. Our analytical model provides tools to interpret space- and ground-based observations from RHESSI, FOXSI, NuSTAR, Solar Orbiter/STIX, EOVSA, and future high-energy missions.

Solar flares↗

Evaluating Lunar Water Processing System Model Configurations for Small Scale Oxygen and Hydrogen Production Within JAXA'S ISRU Technology

Introduction: In-Situ Resource Utilization (ISRU) refers to novel methods of extracting and processing local resources for use in life support and propulsion systems, reducing or eliminating the required consumables to be transferred from Earth. Current estimates of water-ice availability embedded in regolith within the Moon’s permanently shadowed regions (PSR’s) range between 1-5% by weight. However, the composition and characteristics of the “wet” regolith is unknown. Alternate ISRU excavation techniques and Concept of Operations (ConOps) must be explored to optimize surface system operations based on these factors. To assess the feasibility of different ISRU subsystem technologies and compare system architecture configurations, an interchangeable system model was generated to incorporate technologies spanning excavation of raw materials to storage of products and determine optimal arrangement of total system processing needs. Total Mass, Volume, and Power (M/V/P) requirements were computed for 168 design iterations of this water processing plant. System Model: In FY24, the System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team developed a lunar water processing system model using the Mission Analysis and Integration Tool (MAIT) to estimate the M/V/P for ISRU subsystems operating under a wide range of Hydrogen (H2) and Oxygen (O2) production targets for the Space Technology Mission Directorate (STMD) [1]. Based on Japan Aerospace Exploration Agency’s (JAXA) surface operational requirements, this system architecture was modified to include the ability to excavate consolidated icy regolith (versus granular ice excavation using Kennedy Space Center’s (KSC) ISRU Pilot Excavator, IPEx) and explore the feasibility of processing the lunar water both inside and outside of the PSR. For the consolidated icy regolith case study, excavation was performed via a mobility transport chassis outfitted with The Regolith Ice Drill for Exploring New Terrain (TRIDENT) for drilling [2] and the Cold Operable Lunar Deployable Arm (COLDArm) [3] for regolith transfer. The system model determines the required rover and payload. M/V/P to handle the required regolith processing rates. The regolith is then sorted and heated to sublimate the ice (via an auger dryer). The exiting high temperature, low pressure vapor is cleaned of volatiles (via cold trap) and electrolyzed to produce H2 and O2. These products are then dried, liquified with 20 K and 90 K cryocoolers (for H2 and O2, respectively), and stored in cylindrical tanks. Study Goals: Due to the different ConOps options of regolith transport to the ridge for processing versus processing it directly inside the PSR, as well as the unknown regolith/water-ice composition, new excavation techniques and their power configurations are being evaluated within a ISRU system architecture for production targets less than NASA’s pilot plant (1 mT). This analysis investigates the feasibility of numerous excavation techniques, power architectures, and logistical operations and determines an optimal system configuration with regards to M/V/P. It aims to investigate which parameters, both locally and globally, have the greatest effect on each subsystem within the plant. This can be used to identify the most critical components of the plant, and guide future decisions on allocating funding for research and development. The results from this study may provide subsystem developers with appropriate interfaces with excavation subsystems and downstream processes, and assessing the overall feasibility of each excavation technique, power architecture, and logistical timeframe. References: [1] Carlson, A. et. al. (2024) ICES. [2] Zacny, K., et. al. (2024) “ASCE Earth and Space”. [3] McCormick, R., et. Al. (2024) IEEE Xplore.

ISRU↗

Radioisotope Stirling Engine Powered Airship for Atmospheric and Surface Exploration of Titan

The feasibility of an advanced Stirling radioisotope generator (ASRG) powered airship for the near surface exploration of Titan was evaluated. The analysis did not consider the complete mission only the operation of the airship within the atmosphere of Titan. The baseline airship utilized two ASRG systems with a total of four general-purpose heat source (GPHS) blocks. Hydrogen gas was used to provide lift. The ASRG systems, airship electronics and controls and the science payload were contained in a payload enclosure. This enclosure was separated into two sections, one for the ASRG systems and the other for the electronics and payload. Each section operated at atmospheric pressure but at different temperatures. The propulsion system consisted of an electric motor driving a propeller. An analysis was set up to size the airship that could operate near the surface of Titan based on the available power from the ASRGs. The atmospheric conditions on Titan were modeled and used in the analysis. The analysis was an iterative process between sizing the airship to carry a specified payload and the power required to operate the electronics, payload and cooling system as well as provide power to the propulsion system to overcome the drag on the airship. A baseline configuration was determined that could meet the power requirements and operate near the Titan surface. From this baseline design additional trades were made to see how other factors affected the design such as the flight altitude and payload mass and volume.

Titan↗

Phase-Based Adaptive Estimation of Magnitude-Squared Coherence Between Turbofan Internal Sensors and Far-Field Microphone Signals

A cross-power spectrum phase based adaptive technique is discussed which iteratively determines the time delay between two digitized signals that are coherent. The adaptive delay algorithm belongs to a class of algorithms that identifies a minimum of a pattern matching function. The algorithm uses a gradient technique to find the value of the adaptive delay that minimizes a cost function based in part on the slope of a linear function that fits the measured cross power spectrum phase and in part on the standard error of the curve fit. This procedure is applied to data from a Honeywell TECH977 static-engine test. Data was obtained using a combustor probe, two turbine exit probes, and far-field microphones. Signals from this instrumentation are used estimate the post-combustion residence time in the combustor. Comparison with previous studies of the post-combustion residence time validates this approach. In addition, the procedure removes the bias due to misalignment of signals in the calculation of coherence which is a first step in applying array processing methods to the magnitude squared coherence data. The procedure also provides an estimate of the cross-spectrum phase-offset.

Combustion↗

Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology

The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in a Picard iteration.

Jacob Stonehill↗