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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3

Autonomous attitude estimation via star sensing and pattern recognition

Results are reported on the development of an autonomous, onboard, near real time spacecraft attitude estimation technique. The approach uses CCD based star sensors to digitize relative star positions. Three microcomputers are envisioned, configured in parallel, to: (1) determine star image centroids and delete spurious images; (2) identify measured stars with stars in an onboard catalog and determine discrete attitude estimates; (3) integrate gyro rate measurements and determine optimal real time attitude estimates for use in the control system and for feedback to the star identification algorithm. Algorithms for the star identification are presented. The discrete attitude estimation algorithm recovers thermally varying interlock angles between two star sensors. The optimal state estimation process recovers rate gyro biases in addition to real time attitude estimates.

Junkins, J. L.↗

Advances in the Development of a WCl6 CVD System for Coating UO2 Powders with Tungsten

W-UO2 CERMET fuels are under development to enable Nuclear Thermal Propulsion (NTP) for deep space exploration. Research efforts with an emphasis on fuel fabrication, testing, and identification of potential risks is underway. One primary risk is fuel loss due to CTE mismatch between W and UO2 and the grain boundary structure of W particles resulting in higher thermal stresses. Mechanical failure can result in significant reduction of the UO2 by hot hydrogen. Fuel loss can be mitigated if the UO2 particles are coated with a layer of high density tungsten before the consolidation process. This paper discusses the work to date, results, and advances of a fluidized bed chemical vapor deposition (CVD) system that utilizes the H2-WCl6 reduction process. Keywords: Space, Nuclear, Thermal, Propulsion, Fuel, CERMET, CVD, Tungsten, Uranium

Mireles, Omar R.↗

The Iodine Satellite (iSat) Propellant Feed System - Design and Demonstration

CUBESATS are relatively new spacecraft platforms that are typically deployed from a launch vehicle as a secondary payload, providing low-cost access to space for a wide range of end-users. These satellites are comprised of building blocks having dimensions of 10x10x10 cm3 and a mass of 1.33 kg (a 1-U size). While providing low-cost access to space, a major operational limitation is the lack of a propulsion system that can fit within a CubeSat and is capable of executing high Delta V maneuvers. This makes it difficult to use CubeSats on missions requiring certain types of maneuvers (i.e. formation flying, spacecraft rendezvous). Work has been performed investigating the use of iodine as a propellant for Hall-effect thrusters (HETs) that could subsequently be used to provide a high specific impulse path to CubeSat propulsion. One of the systems under development to support such a technology is the propellant feed system, which must be capable of storing solid iodine propellant, applying heat to sublime the stored solid into the vapor phase, and then control the flow of low-pressure gaseous iodine to both the thruster and cathode. In a test conducted in 2016, a first-generation iodine propellant feed system was integrated with a cathode and Hall thruster. While this test had to be terminated, the feed system in this first test was able to support both cathode and integrated cathode and thruster operation prior to the termination of the test. In the present paper, we describe work performed since that initial integrated test. The effort uses lessons learned from the previous integrated test, retiring risk associated with the iodine propellant feed system, answering open design-space questions, and demonstrating iodine flow control in an integrated system. The work is undertaken at both the component level and then at the integrated subsystem level to systematically improve the feed system design, improving the hardware fidelity so the appearance and operation of the system are as flight-like as possible. At the component level, the work focuses on the propellant tank, the feed system tubing, the valves used to control the flow to the cathode and thruster, and the heaters that maintain the temperature of the flowpaths and keep iodine from redepositing and clogging the system. Work on the propellant reservoir focuses on fabricating a tank that matches the geometry of the flight design, which allows for the identification of flight tank fabrication issues that may arise and permits thermal testing of a tank possessing the same size and thermal mass as the flight design, which can be used to anchor thermal modeling of the component. This is critical for finalizing the tank heater power requirements that feed into the heater design. All metallic materials in the feed system are hastelloy or Inconel, as these materials are resistant to chemical attack by the highly-reactive iodine vapor. The tubing in the iodine feed system must possess ports to permit a neutral gas purge of the system that clear impurities after iodine is loaded into the propellant tank. A procedure is discussed whereby these ports are crimped and sealed after the purge process is completed so as to not re-expose the iodine system to air. The valves are a critical component for control of the flow to the thruster and the cathode. Significant effort has gone into upgrading the materials of the valves to make them more resistant to chemical attack and into developing an understanding of the use of these valves during the startup and operation of the cathode and thruster. The heaters that line the entire feed system are designed to draw minimal power from the power processing unit (PPU) while still having the capacity to maintain all the feed system components at the temperatures required to discourage iodine deposition inside components downstream of the propellant tank exit. The heaters possess two separate resistive traces, giving the design redundancy should a failure occur in the primary heater circuit of one of the heater zones. The task of operating a feed system in conjunction with a thruster and cathode is undertaken in a series of sub-steps. The system is first assembled and operated on xenon gas, using the valves for cathode startup and thruster control based on measurement of the discharge current. After startup and control on xenon are demonstrated, the thruster will be transitioned to iodine operation, demonstrating thruster startup and feed system control while using a xenon-fed cathode. Finally, the last step is to integrate an iodine-compatible cathode with the system, demonstrate autonomous cathode start-up with open-loop control and thruster start-up with closed-loop control for multiple cycles.

Polzin, Kurt A.↗

Evaluation of a strain-gage load calibration on a low-aspect-ratio wing structure at elevated temperature

The environmental aspect of elevated temperature and its relationship to the science of strain gage calibrations of aircraft structures are addressed. A section of a wing designed for a high-speed aircraft structure was used to study this problem. This structure was instrumented with strain gages calibrated at both elevated and room temperatures. Load equations derived from a high-temperature load calibration were compared with equations derived from an identical load calibration at room temperature. The implications of the high temperature load calibration were studied from the viewpoint of applicability and necessity. Load equations derived from the room temperature load calibration resulted in generally lower equation standard errors than equations derived from the elevated temperature load calibration. A distributed load was applied to the structure at elevated temperature and strain gage outputs were measured. This applied load was then calculated using equations derived from both the room temperature and elevated temperature calibration data. It was found that no significant differences between the two equation systems existed in terms of computing this applied distributed load, as long as the thermal shifts resulting from thermal stresses could be identified. This identification requires a heating of the structure. Therefore, it is concluded that for this structure, a high temperature load calibration is not required. However, a heating of the structure is required to determine thermal shifts.

Reardon, Lawrence F.↗

Hydrofluoroether (HFE) Cleaning Fluid Replacement and Qualification

This NASA Engineering and Safety Center (NESC) Technical Assessment Report addresses the urgent need to identify, test, and qualify replacement cleaning solvents and technologies following 3M’s decision to discontinue production of hydrofluoroether (HFE) products, including Novec HFE-7100, by the end of 2025. HFE-7100 is widely used across NASA for precision cleaning of ground and flight hardware, especially in oxygen system components, and as a heat transfer fluid in high-power-density thermal control systems. The assessment evaluates commercially available replacement solvents, alternative cleaning technologies, and their compatibility with NASA’s operational requirements. Key findings include the identification of viable solvent replacements, their performance in contaminant removal, materials compatibility, and oxygen system safety. The report also explores novel cleaning approaches, including aqueous, supercritical CO₂, cryogenic aerosol, plasma, UV-ozone, magnetically optimized fluids, and induced charge active filtration, highlighting their merits, limitations, and readiness for NASA adoption. The NESC provides recommendations for solvent selection, facility adaptation, and continued technology maturation to ensure mission continuity and regulatory compliance.

Alternative Cleaning Technologies↗

REIMR - A Process for Utilizing Liquid Rocket Propulsion-Oriented 'Lessons Learned' to Mitigate Development Risk in Nuclear Thermal Propulsion

This paper is a summary overview of a study conducted at the NASA Marshall Space Flight Center (NASA MSFC) during the initial phases of the Space Launch Initiative (SLI) program to evaluate a large number of technical problems associated with the design, development, test, evaluation and operation of several major liquid propellant rocket engine systems (i.e., SSME, Fastrac, J-2, F-1). One of the primary results of this study was the identification of the Fundamental Root Causes that enabled the technical problems to manifest, and practices that can be implemented to prevent them from recurring in future propulsion system development efforts, such as that which is currently envisioned in the field of nuclear thermal propulsion (NTF). This paper will discuss the Fundamental Root Causes, cite some examples of how the technical problems arose from them, and provide a discussion of how they can be mitigated or avoided in the development of an NTP system

Ballard, RIchard O.↗

Rapid data comparison technique development for N-ray/X-ray analysis

An operational N-ray/X-ray computer analysis system for nondestructive testing problems was realized by developing: (1) more efficient data transfer routines for use in existing image processing systems; (2) the capability to store and analyze multiple N-ray/X-ray images; (3) an efficient 2-D Fast Fourier Transform; and (4) transfer functions compensation capability to correct for distortions and nonlinearities of N-rays/X-rays. Applications of the technique are summarized for the following: thermal protection system tile with hydraulic fluid; thermal protection system tile with corrosion; thermal protection system tile debonding; stainless steel tubing corrosion; defective electrical devices; fast film restoration and deblur; corrosion tracking over time; reduction of source vignetting, and identification of materials (0 rings, Teflon parts, soft goods) via table look up.

Butterfield, R. L.↗

An Analysis of Exploration Capability Gaps for Future Habitation Systems to Inform Risk Assessment and Development Priorities

Within NASA, exploration capability gaps are defined as the difference between the current state-of-the-art in capabilities and the anticipated needs of future human spaceflight architectures. As NASA and its partners’ capabilities for human exploration of deep space continue to mature, it is necessary to understand the capability gaps that require closure to support future habitation systems, such as the Lunar Surface Habitat (SH) and Mars Transit Habitat (TH) currently in concept development. This paper will identify high-priority capability gaps for exploration habitation and show potential options for gap closure through investment in technology, development, and testing. High-priority capability gaps are divided into the following general taxonomy areas: human health/life support/habitation systems, flight computing and avionics, power and energy storage, communications and navigation, thermal management systems, human exploration destination systems, autonomous systems, sensors and instruments, GNC (guidance, navigation, and control), robotic systems, ground and uncrewed surface systems, and materials/structures/mechanical systems/manufacturing. In the gap identification process, teams of discipline experts from across NASA reviewed the latest habitation architecture needs against current capabilities to understand where gaps may exist. The results of the assessment established a basis for the current state-of-the-art within each gap and identified the capability needs of the proposed exploration missions the gap links to. An assessment of how each test platform (e.g., Ground, International Space Station (ISS), Commercial Low Earth Orbit (LEO) Destinations, Gateway) may be leveraged to mature capabilities and potentially provide a route to gap closure will be discussed. The notional timeline for gap closure to support reference missions and impacts to overall schedule are also assessed where appropriate. Based on the capability gap analysis described above, the paper summarizes important technology maturation considerations for human exploration architectures, with a focus on the Mars TH. The previously published NASA habitation ground rules and assumptions document is used as the basis to classify gaps as enabling, enhancing, or “push” opportunities for a particular architecture. Stepwise technology maturation plans/considerations are presented for some selected critical gaps. Overall, the analysis in this paper is intended to help influence development priorities for habitation systems, where high-priority, critical gaps are those currently assessed as having a low probability of closure by the anticipated need date. Capability gap analysis also informs the risk register for exploration habitation systems and mitigation strategies to ensure readiness of key technologies to support future mission timelines. Linkage between capability gaps for Moon and Mars is noted, as closure of a gap at a Lunar destination may subsequently enable or enhance Mars TH architectures.

technology development↗

An Analysis of Exploration Capability Gaps for Future Habitation Systems to Inform Risk Assessment and Development Priorities

Within NASA, exploration capability gaps are defined as the difference between the current state-of-the-art in capabilities and the anticipated needs of future human spaceflight architectures. As NASA and its partners’ capabilities for human exploration of deep space continue to mature, it is necessary to understand the capability gaps that require closure to support future habitation systems, such as the Lunar Surface Habitat (SH) and Mars Transit Habitat (TH) currently in concept development. This paper will identify high-priority capability gaps for exploration habitation and show potential options for gap closure through investment in technology, development, and testing. High-priority capability gaps are divided into the following general taxonomy areas: human health/life support/habitation systems, flight computing and avionics, power and energy storage, communications and navigation, thermal management systems, human exploration destination systems, autonomous systems, sensors and instruments, GNC (guidance, navigation, and control), robotic systems, ground and uncrewed surface systems, and materials/structures/mechanical systems/manufacturing. In the gap identification process, teams of discipline experts from across NASA reviewed the latest habitation architecture needs against current capabilities to understand where gaps may exist. The results of the assessment established a basis for the current state-of-the-art within each gap and identified the capability needs of the proposed exploration missions the gap links to. An assessment of how each test platform (e.g., Ground, International Space Station (ISS), Commercial Low Earth Orbit (LEO) Destinations, Gateway) may be leveraged to mature capabilities and potentially provide a route to gap closure will be discussed. The notional timeline for gap closure to support reference missions and impacts to overall schedule are also assessed where appropriate. Based on the capability gap analysis described above, the paper summarizes important technology maturation considerations for human exploration architectures, with a focus on the Mars TH. The previously published NASA habitation ground rules and assumptions document is used as the basis to classify gaps as enabling, enhancing, or “push” opportunities for a particular architecture. Stepwise technology maturation plans/considerations are presented for some selected critical gaps. Overall, the analysis in this paper is intended to help influence development priorities for habitation systems, where high-priority, critical gaps are those currently assessed as having a low probability of closure by the anticipated need date. Capability gap analysis also informs the risk register for exploration habitation systems and mitigation strategies to ensure readiness of key technologies to support future mission timelines. Linkage between capability gaps for Moon and Mars is noted, as closure of a gap at a Lunar destination may subsequently enable or enhance Mars TH architectures.

technology development↗

Prognostics of Power Electronics, Methods and Validation Experiments

Abstract Failure of electronic devices is a concern for future electric aircrafts that will see an increase of electronics to drive and control safety-critical equipment throughout the aircraft. As a result, investigation of precursors to failure in electronics and prediction of remaining life of electronic components is of key importance. DC-DC power converters are power electronics systems employed typically as sourcing elements for avionics equipment. Current research efforts in prognostics for these power systems focuses on the identification of failure mechanisms and the development of accelerated aging methodologies and systems to accelerate the aging process of test devices, while continuously measuring key electrical and thermal parameters. Preliminary model-based prognostics algorithms have been developed making use of empirical degradation models and physics-inspired degradation model with focus on key components like electrolytic capacitors and power MOSFETs (metal-oxide-semiconductor-field-effect-transistor). This paper presents current results on the development of validation methods for prognostics algorithms of power electrolytic capacitors. Particularly, in the use of accelerated aging systems for algorithm validation. Validation of prognostics algorithms present difficulties in practice due to the lack of run-to-failure experiments in deployed systems. By using accelerated experiments, we circumvent this problem in order to define initial validation activities.

Kulkarni, Chetan S.↗

On the nature of the companion to Van Biesbroeck 8

Results of the first numerical evolutionary calculations for very low-mass stars with ages up to the age of the Galaxy are presented. The calculations shed new light on the nature of the recently discovered object VB 8B, the companion to Van Biesbroeck's star no. 8, and support the identification of this object as a low-mass star in which hydrogen burning was never able to establish thermal equilibrium. For plausible ages of this binary stellar system, the mass of VB 8B is estimated to be in the range 0.04-0.08 solar mass. The object is supported primarily by degenerate electron pressure; its present values of central density and temperature are found to be 500-2000 g/cu cm and 1.0-1.5 million K. An orbital period of more than about 40 yr is predicted for the binary system. The presented evolutionary tracks are also applicable to the interpretation of observations of other very low-luminosity dwarfs.

Nelson, L. A.↗

Application of statistical process control and process capability analysis procedures in orbiter processing activities at the Kennedy Space Center

Successful ground processing at KSC requires that flight hardware and ground support equipment conform to specifications at tens of thousands of checkpoints. Knowledge of conformance is an essential requirement for launch. That knowledge of conformance at every requisite point does not, however, enable identification of past problems with equipment, or potential problem areas. This paper describes how the introduction of Statistical Process Control and Process Capability Analysis identification procedures into existing shuttle processing procedures can enable identification of potential problem areas and candidates for improvements to increase processing performance measures. Results of a case study describing application of the analysis procedures to Thermal Protection System processing are used to illustrate the benefits of the approaches described in the paper.

Safford, Robert R.↗

System technology analysis of aeroassisted orbital transfer vehicles. Moderate lift/drag (0.75-1.5): Volume 1A, part 2: Executive summary, phase 2

Significant achievements and activities of Phase 2 of a study to assess aeroassisted orbit transfer vehicle (AOTV) system technology are summarized. Phase 2 was directed towards identification and prioritization of technology payoffs of representative space based mid lift/drag ratio (L/D) AOTV's and the cryofueled propulsion subsystem - configuration interactions. Enhancing technology areas were identified which could provide substantial transport cost reduction. These include: (1) improved lifetime of storable propellant engines; (2) avionics weight reduction; (3) external thermal protection system weight reduction; (4) decrease of uncertainties in aerodynamic and aerothermodynamic performance; electrical power subsystem weight reduction due to incorporation of advanced materials; and (6) structural shell weight reduction. Results indicated that advanced aerothermodynamic methodology and aft end configuring may provide an enlarged allowable zone for engine nozzle protrusions into the separated flow region. Payload manifesting and non-hydrogen propellant manifesting at the space station is recommended.

Source record↗

Post-Flight Assessment of Avcoat Thermal Protection System for the Exploration Flight Test-1

On December 5, 2014 NASA conducted the first flight test of its next generation human-class Orion spacecraft. The flight was called the Exploration Flight Test -1 (EFT-1) which lasted for 4 hours and culminated into a re-entry trajectory at 9 km/s. This flight test of the 5-meter Orion Crew Module demonstrated various sub-systems including the Avcoat ablative thermal protection system (TPS) on the heat shield. The Avcoat TPS had been developed from the Apollo-era recipe with a few key modifications. The engineering for thermal sizing was supported by modeling, analysis, and ground tests in arc jet facilities. This paper will describe a postlfight analysis plan and present results from post-recovery inspections, data analysis from embedded sensors, TPS sample extraction and characterization in the laboratory. After the recovery of the vehicle, a full photographic survey and surface scans of the TPS were performed. The recovered vehicle showed physical evidence of flow disturbances, varying degrees of surface roughness, and excessive recession downstream of compression pads. The TPS recession was measured at more than 200 locations of interest on the Avcoat surface. The heat shield was then processed for sample extraction prior to TPS removal using the 7-Axis Milling machine at Marshall Space Flight Center. Around 182 rectangular TPS samples were extracted for subsequent analysis and investigation. The final paper will also present results of sample analysis. The planned investigation includes sidewall imaging, followed by image analysis to characterize TPS response by quantifying different layers in the char and pyrolysis zones. A full postmortem of the instrumentation and sensor ports will also be performed to confirm no adverse effects due to the sensors themselves. A subset of the samples will undergo structural testing and perform detailed characterization of any cracks and integrity of gore seams. Finally, the material will be characterized with layer-by-layer density measurements and SEM investigations to evaluate material morphology at microstructural level including identification of elements and compounds.

Aerothermodynamics↗

Integrated support structure for GASCAN 2

The focus of the Worcester Polytechnic Institute (WPI) Advanced Space Design Program was the preliminary design of the Integrated Support Structure for GASCAN II, a Get Away Special canister donated by the MITRE Corporation. Two teams of three students each worked on the support structure. There was a structural design team and a thermal design team. The structure will carry three experiments also undergoing preliminary design this year, the mu-gravity Ignition Experiment, the Rotational Flow in Low Gravity Experiment, and the Ionospheric Properties and Propagation Experiment. The structural design team was responsible for the layout of the GASCAN and the preliminary design of the structure itself. They produced the physical interface specifications defining the baseline weights and volumes for the equipment and produced layout drawings of the system. The team produced static and modal finite element analysis of the structure using ANSYS. The thermal design team was responsible for the power and timing requirements of the payload and for the identification and preliminary analysis of potential thermal problems. The team produced the power, timing, and energy interface specifications and assisted in the development of the specification of the battery pack. The thermal parameters of each experiment were cataloged and the experiments were subjected to worst case heat transfer scenarios.

Source record↗

Affordable Development and Demonstration of a Small Nuclear Thermal Rocket (NTR) Engine and Stage: How Small Is Big Enough?

The Nuclear Thermal Rocket (NTR) derives its energy from fission of uranium-235 atoms contained within fuel elements that comprise the engine's reactor core. It generates high thrust and has a specific impulse potential of approximately 900 specific impulse - a 100 percent increase over today's best chemical rockets. The Nuclear Thermal Propulsion (NTP) project, funded by NASA's Advanced Exploration Systems (AES) program, includes five key task activities: (1) Recapture, demonstration, and validation of heritage graphite composite (GC) fuel (selected as the Lead Fuel option); (2) Engine Conceptual Design; (3) Operating Requirements Definition; (4) Identification of Affordable Options for Ground Testing; and (5) Formulation of an Affordable Development Strategy. During fiscal year (FY) 2014, a preliminary Design Development Test and Evaluation (DDT&E) plan and schedule for NTP development was outlined by the NASA Glenn Research Center (GRC), Department of Energy (DOE) and industry that involved significant system-level demonstration projects that included Ground Technology Demonstration (GTD) tests at the Nevada National Security Site (NNSS), followed by a Flight Technology Demonstration (FTD) mission. To reduce cost for the GTD tests and FTD mission, small NTR engines, in either the 7.5 or 16.5 kilopound-force thrust class, were considered. Both engine options used GC fuel and a common fuel element (FE) design. The small approximately 7.5 kilopound-force criticality-limited engine produces approximately157 thermal megawatts and its core is configured with parallel rows of hexagonal-shaped FEs and tie tubes (TTs) with a FE to TT ratio of approximately 1:1. The larger approximately 16.5 kilopound-force Small Nuclear Rocket Engine (SNRE), developed by Los Alamos National Laboratory (LANL) at the end of the Rover program, produces approximately 367 thermal megawatts and has a FE to TT ratio of approximately 2:1. Although both engines use a common 35-inch (approximately 89-centimeters) -long FE, the SNRE's larger diameter core contains approximately 300 more FEs needed to produce an additional 210 thermal megawatts of power. To reduce the cost of the FTD mission, a simple one-burn lunar flyby mission was considered to reduce the liquid hydrogen (LH2) propellant loading, the stage size and complexity. Use of existing and flight proven liquid rocket and stage hardware (e.g., from the RL10B-2 engine and Delta Cryogenic Second Stage) was also maximized to further aid affordability. This paper examines the pros and cons of using these two small engine options, including their potential to support future human exploration missions to the Moon, near Earth asteroids (NEA), and Mars, and recommends a preferred size. It also provides a preliminary assessment of the key activities, development options, and schedule required to affordably build, ground test and fly a small NTR engine and stage within a 10-year timeframe.

Spacecraft design↗

Building application of solar energy. Study no. 2: Representative buildings for solar energy performance analysis and market penetration

The following topics are discussed: (1) Assignment of population to microclimatic zones; (2) specifications of the mix of buildings in the SCE territory; (3) specification of four typical buildings for thermal analysis and market penetration studies; (4) identification of the materials and energy conserving characteristics of these typical buildings; (5) specifications of the HVAC functions used in each typical building, and determination of the HVAC systems used in each building; and (6) identification of the type of fuel used in each building.

Hirshberg, A. S.↗

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗