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NASA NTRSDate not supplied

NASA Earth Science Division’s Commitment to Increasing Safety in the Field

NASA's Earth Science Division (ESD) has led and supported field campaign research over many decades focused on advancing fundamental research, testing new instrument technologies, and promoting career development. ESD field campaign research is conducted over a wide range of projects that vary in size, science focus area, location, platform type, and people. ESD leadership has created a task team to address campaign physical and mental safety, with the goal of providing all participants in NASA field campaign research with an environment that promotes research, safety, inclusivity, and a positive experience. Building on resources that have been developed both within and outside NASA, we report on the task team’s accomplishments and near-term plans, including the recent establishment of a best practices document and guidelines for the development of “agreement of behaviors” document for field teams. We also describe progress in the development of an online training module for field campaign participation, the incorporation of campaign safety language in forthcoming NASA ROSES solicitations, and outreach activities. Finally, we report on recent joint interactions with the NASA Planetary Science Division’s Ethics in Fieldwork team.

Ocean-based measurements↗

NASA NTRS2013

Adoption of Test Driven Development and Continuous Integration for the Development of the Trick Simulation Toolkit

This paper describes the adoption of a Test Driven Development approach and a Continuous Integration System in the development of the Trick Simulation Toolkit, a generic simulation development environment for creating high fidelity training and engineering simulations at the NASA/Johnson Space Center and many other NASA facilities. It describes what was learned and the significant benefits seen, such as fast, thorough, and clear test feedback every time code is checked-in to the code repository. It also describes a system that encourages development of code that is much more flexible, maintainable, and reliable. The Trick Simulation Toolkit development environment provides a common architecture for user-defined simulations. Trick builds executable simulations using user-supplied simulation-definition files (S_define) and user supplied "model code". For each Trick-based simulation, Trick automatically provides job scheduling, checkpoint / restore, data-recording, interactive variable manipulation (variable server), and an input-processor. Also included are tools for plotting recorded data and various other supporting tools and libraries. Trick is written in C/C++ and Java and supports both Linux and MacOSX. Prior to adopting this new development approach, Trick testing consisted primarily of running a few large simulations, with the hope that their complexity and scale would exercise most of Trick's code and expose any recently introduced bugs. Unsurprising, this approach yielded inconsistent results. It was obvious that a more systematic, thorough approach was required. After seeing examples of some Java-based projects that used the JUnit test framework, similar test frameworks for C and C++ were sought. Several were found, all clearly inspired by JUnit. Googletest, a freely available Open source testing framework, was selected as the most appropriate and capable. The new approach was implemented while rewriting the Trick memory management component, to eliminate a fundamental design flaw. The benefits became obvious almost immediately, not just in the correctness of the individual functions and classes but also in the correctness and flexibility being added to the overall design. Creating code to be testable, and testing as it was created resulted not only in better working code, but also in better-organized, flexible, and readable (i.e., articulate) code. This was, in essence the Test-driven development (TDD) methodology created by Kent Beck. Seeing the benefits of Test Driven Development, other Trick components were refactored to make them more testable and tests were designed and implemented for them.

Penn, John M.↗

NASA NTRS1986

Exobiology experiment concepts for space station

The exobiology discipline uses ground based and space flight resources to conduct a multidiscipline research effort dedicated to understanding fundamental questions about the origin, evolution, and distribution of life and life related molecules throughout the universe. Achievement of this understanding requires a methodical research strategy which traces the history of the biogenic elements from their origins in stellar formation processes through the chemical evolution of molecules essential for life to the origin and evolution of primitive and, ultimately, complex living species. Implementation of this strategy requires the collection and integration of data from solar system exploration spacecraft and ground based and orbiting observatories and laboratories. The Science Lab Module (SLM) of the Space Station orbiting complex may provide an ideal setting in which to perform certain classes of experiments which form the cornerstone of exobiology research. These experiments could demonstrate the pathways and processes by which biomolecules are synthesized under conditions that simulate the primitive Earth, planetary atmospheres, cometary ices, and interstellar dust grains. Exobiology experiments proposed for the Space Station generally fall into four classes: interactions among gases and grains (nucleation, accretion, gas-grain reactions), high energy chemistry for the production of biomolecules, physical and chemical processes occurring on an artificial comet, and tests of the theory of panspermia.

Griffiths, L. D.↗

NASA NTRS1987

Exobiology experiment concepts for Space Station

The exobiology discipline uses ground based and space flight resources to conduct a multidiscipline research effort dedicated to understanding fundamental questions about the origin, evolution, and distribution of life and life related molecules throughout the universe. Achievement of this understanding requires a methodical research strategy which traces the history of the biogenic elements from their origins in stellar formation processes through the chemical evolution of molecules essential for life to the origin and evolution of primitive and, ultimately, complex living species. Implementation of this strategy requires the collection and integration of data from solar system exploration spacecraft and ground based and orbiting observatories and laboratories. The Science Lab Module (SLM) of the Space Station orbiting complex may provide an ideal setting in which to perform certain classes of experiments which form the cornerstone of exobiology research. These experiments could demonstrate the pathways and processes by which biomolecules are synthesized under conditions that stimulate the primitive earth, planetary atmospheres, cometary ices, and interstellar dust grains. Exobiology experiments proposed for the Space Station generally fall into four classes: interactions among gases and grains (nucleation, accretion, gas-grain reactions), high energy chemistry for the production of biomolecules, physical and chemical processes occurring on an artificial comet, and tests of the theory of panspermia.

Griffiths, Lynn D.↗

NASA NTRS2010

Black-Hole Binaries, Gravitational Waves, and Numerical Relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events ' releasing tremendous amounts of energy in the form of gravitational radiation ' and are key sources for both ground- and spacebased gravitational wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only he calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit cnuld be simulated. Recently ' however, a series of dramatic advances in numerical relativity has ' for the first time, allowed stable / robust black hole merger simulations. We chronicle this remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging. We also discuss important applications of these fundamental physics results to astrophysics, to gravitationalwave astronomy, and in other areas.

Kelly, Bernard J.↗

NASA NTRS1994

Interactions between solidification and compositional convection in mushy layers

Mushy layers are ubiquitous during the solidification of alloys. They are regions of mixed phase wherein solid crystals are bathed in the melt from which they grew. The matrix of crystals forms a porous medium through which the melt can flow, driven either by external forces or by its own buoyancy in a gravitational field. Buoyancy-driven convection of the melt depends both on temperature gradients, which are necessary for solidification, and on compositional gradients, which are generated as certain components of the alloy are preferentially incorporated in the solid phase and the remaining components are expelled into the melt. In fully liquid regions, the combined action of temperature and concentration on the density of the liquid can cause various forms of double-diffusive convection. However, in the interior of mushy regions the temperature and concentration are thermodynamically coupled so only single-diffusive convection can occur. Typically, the effect of composition on the buoyancy of the melt is much greater than the effect of temperature, and thus convection in mushy layers in driven primarily by the computational gradients within them. The rising interstitial liquid is relatively dilute, having come from colder regions of the mushy layer, where the liquidus concentration is lower, and can dissolve the crystal matrix through which it flows. This is the fundamental process by which chimneys are formed. It is a nonlinear process that requires the convective velocities to be sufficiently large, so fully fledged chimneys (narrow channels) might be avoided by means that weaken the flow. Better still would be to prevent convection altogether, since even weak convection will cause lateral, compositional inhomogeneities in castings. This report outlines three studies that examine the onset of convection within mushy layers.

Worster, M. Grae↗

NASA NTRS1990

Speculation on a Solar Chronometer for Climate

Solar activity has been correlated to climatic fluctuations and has been postulated as a major factor in quasi-periodic global climatic change. However, correlations are not explanations of physical mechanisms and do not couple cause with effect. A mechanism for a chronometer for solar output variability is proposed based on relations between properties of thermonuclear fusion, nuclear magnetic moment, and nuclear magnetic resonance. A fundamental oscillation of a nucleus with a net nuclear magnetic moment (NMM) is the precession of its axis of rotation when subjected to a magnetic field. Nuclear magnetic resonance (NMR) is the preferred frequency of precession for a nucleus of a particular isotope when placed in a magnetic field of specific intensity. The NMM for those isotopes involved in the proton-proton (p-p) chain pathway for solar fusion varies from strong positive to strong negative. Individual fusion events, for hydrogen and helium isotopes which release varying amounts of energy, may be controlled by NMR frequencies. The pulses of energy from fusion events occurring at NMR frequencies in the solar interior may be transformed into pressure or gravity waves that emerge as gravity or acoustic waves at the surface. Dictated by spherical harmonics, certain wavelengths may be reinforced and reenter the solar interior to modulate the fusion process. Qualitative analysis of solar and climatic data support the interaction of the three basic components of the chronometer, magnetic activity, oscillation frequency, and solar energy output.

Perry, Charles A.↗

NASA NTRS1994

Ignition and Wind Effects on the Transition to Flame Spread in a Microgravity Environment

The fundamental processes involved in ignition and flame spread have been extensively studied, they are generally studied separately without combining ignition and flame spread through the transition process. Moreover, the majority of the flame spread studies assume steady state flame spread. To study the transient aspects of ignition and the transition to flame spread, a time-dependent numerical model has been developed in which a thin strip is ignited along its width with either a pilot wire, radiative source, or both. For this configuration, the model is two-dimensional. Ignition is initiated away from either end of the sample, and two different flame fronts spread in opposite directions; one flows with and the other against a prescribed external flow. Usually, the flame spread is initiated by ignition at one end of the sample with or against a slow external flow, yielding one flame front. The present configuration is more realistic than the one flame front case because there is interaction between the two flames during the ignition and transition stages.

McGrattan, Kevin B.↗

NASA NTRS1997

Rocket Engine Numerical Simulator (RENS)

Work is being done at three universities to help today's NASA engineers use the knowledge and experience of their Apolloera predecessors in designing liquid rocket engines. Ground-breaking work is being done in important subject areas to create a prototype of the most important functions for the Rocket Engine Numerical Simulator (RENS). The goal of RENS is to develop an interactive, realtime application that engineers can utilize for comprehensive preliminary propulsion system design functions. RENS will employ computer science and artificial intelligence research in knowledge acquisition, computer code parallelization and objectification, expert system architecture design, and object-oriented programming. In 1995, a 3year grant from the NASA Lewis Research Center was awarded to Dr. Douglas Moreman and Dr. John Dyer of Southern University at Baton Rouge, Louisiana, to begin acquiring knowledge in liquid rocket propulsion systems. Resources of the University of West Florida in Pensacola were enlisted to begin the process of enlisting knowledge from senior NASA engineers who are recognized experts in liquid rocket engine propulsion systems. Dr. John Coffey of the University of West Florida is utilizing his expertise in interviewing and concept mapping techniques to encode, classify, and integrate information obtained through personal interviews. The expertise extracted from the NASA engineers has been put into concept maps with supporting textual, audio, graphic, and video material. A fundamental concept map was delivered by the end of the first year of work and the development of maps containing increasing amounts of information is continuing. Find out more information about this work at the Southern University/University of West Florida. In 1996, the Southern University/University of West Florida team conducted a 4day group interview with a panel of five experts to discuss failures of the RL10 rocket engine in conjunction with the Centaur launch vehicle. The discussion was recorded on video and audio tape. Transcriptions of the entire proceedings and an abbreviated video presentation of the discussion highlights are under development. Also in 1996, two additional 3year grants were awarded to conduct parallel efforts that would complement the work being done by Southern University and the University of West Florida. Dr. Prem Bhalla of Jackson State University in Jackson, Mississippi, is developing the architectural framework for RENS. By employing the Rose Rational language and Booch Object Oriented Programming (OOP) technology, Dr. Bhalla is developing the basic structure of RENS by identifying and encoding propulsion system components, their individual characteristics, and cross-functionality and dependencies. Dr. Ruknet Cezzar of Hampton University, located in Hampton, Virginia, began working on the parallelization and objectification of rocket engine analysis and design codes. Dr. Cezzar will use the Turbo C++ OOP language to translate important liquid rocket engine computer codes from FORTRAN and permit their inclusion into the RENS framework being developed at Jackson State University. The Southern University/University of West Florida grant was extended by 1 year to coordinate the conclusion of all three efforts in 1999.

Davidian, Kenneth O.↗

NASA NTRS1987

Self-consistent inclusion of space-charge in the traveling wave tube

It is shown how the complete field of the electron beam may be incorporated into the transmission line model theory of the traveling wave tube (TWT). The fact that the longitudinal component of the field due to the bunched beam is not used when formulating the beam-to-circuit coupling equation is not well-known. The fundamental partial differential equation for the traveling wave field is developed and compared with the older (now standard) one. The equation can be solved numerically using the same algorithms, but now the coefficients can be updated continuously as the calculation proceeds down the tube. The coefficients in the older equations are primarily derived from preliminary measurements and some trial and error. The newer coefficients can be found by a recursive method, since each has a well defined physical interpretation and can be calculated once a reasonable first trial solution is postulated. The results of the new expression were compared with those of the older forms, as well as to a field theory model to show the ease in which a reasonable fit to the field prediction is obtained. A complete summary of the existing transmission line modeling of the TWT is given to explain the somewhat vague ideas and techniques in the general area of drifting carrier-traveling circuit wave interactions. The basic assumptions and inconsistencies of the existing theory and areas of confusion in the general literature are examined and hopefully cleared up.

Freeman, Jon C.↗

NASA NTRS2008

Project Integration Architecture

The Project Integration Architecture (PIA) is a distributed, object-oriented, conceptual, software framework for the generation, organization, publication, integration, and consumption of all information involved in any complex technological process in a manner that is intelligible to both computers and humans. In the development of PIA, it was recognized that in order to provide a single computational environment in which all information associated with any given complex technological process could be viewed, reviewed, manipulated, and shared, it is necessary to formulate all the elements of such a process on the most fundamental level. In this formulation, any such element is regarded as being composed of any or all of three parts: input information, some transformation of that input information, and some useful output information. Another fundamental principle of PIA is the assumption that no consumer of information, whether human or computer, can be assumed to have any useful foreknowledge of an element presented to it. Consequently, a PIA-compliant computing system is required to be ready to respond to any questions, posed by the consumer, concerning the nature of the proffered element. In colloquial terms, a PIA-compliant system must be prepared to provide all the information needed to place the element in context. To satisfy this requirement, PIA extends the previously established object-oriented- programming concept of self-revelation and applies it on a grand scale. To enable pervasive use of self-revelation, PIA exploits another previously established object-oriented-programming concept - that of semantic infusion through class derivation. By means of self-revelation and semantic infusion through class derivation, a consumer of information can inquire about the contents of all information entities (e.g., databases and software) and can interact appropriately with those entities. Other key features of PIA are listed.

Jones, William Henry↗

NASA NTRSDate not supplied

Human Systems Integration Relationships Between Deep Space and Deepwater Exploration Challenges

NASA pursuit of human missions Beyond Earth Orbit (BEO) to the moon and eventually Mars will pose many new challenges. These missions are characterized by increased risks to human performance due to stress, fatigue, radiation exposure, and isolation. Fundamental changes in spaceflight operations will be required as well. A very critical part of future missions will be assisting the crew with problem-solving and contingency resolution using next-generation smart spacecraft systems. Human Systems Integration (HSI) must be included as part of the systems engineering process. Gateway1 will serve as part of the proving ground for maturing technology such as autonomous systems and space operations procedures to help meet moon mission goals and prepare humans for missions to Mars. For deep space missions, risk factors affecting humans such as mission duration, distance, and physiological/psychological effects, must be considered. A human is not a simple component but rather a system in a systems-of-systems application-a system influenced by cognitive and biological factors that are difficult to model/analyze. System complexity will demand an integrated approach that requires multiple viewpoints, including the understanding of the astronauts' capabilities and limitations to enhance safety, performance, and satisfaction on the interaction between all system users in a variety of environments to achieve acceptable mission goals and performance. HSI will play a vital role in the development of these future missions. This paper provides a discussion of HSI used at NASA and the critical role human factors engineering will play in the HSI process for future missions along with the challenges. Industries such as oil and gas (O&G) could benefit from the content of this paper to help improve the safety and operations of deepwater/oil and gas exploration activities. NASA engineering and human systems subject-matter expert personnel reviewed challenges reported in space-related environments for long space duration missions and identified similarities with the challenges encountered in deepwater exploration. The researchers noted the space industry's current solutions and proposed a system development view to solve future deepwater exploration challenges using HSI principles. This paper discusses the results of the review.

George Salazar↗

NASA NTRS2005

A Fundamental Mathematical Model of a Microbial Predenitrification System

Space flight beyond Low Earth Orbit requires sophisticated systems to support all aspects of the mission (life support, real-time communications, etc.). A common concern that cuts across all these systems is the selection of information technology (IT) methodology, software and hardware architectures to provide robust monitoring, diagnosis, and control support. Another dimension of the problem space is that different systems must be integrated seamlessly so that communication speed and data handling appear as a continuum (un-interrupted). One such team investigating this problem is the Advanced Integration Matrix (AIM) team whose role is to define the critical requirements expected of software and hardware to support an integrated approach to the command and control of Advanced Life Support (ALS) for future long-duration human space missions, including permanent human presence on the Moon and Mars. A goal of the AIM team is to set the foundation for testing criteria that will assist in specifying tasks, control schemes and test scenarios to validate and verify systems capabilities. This project is to contribute to the goals of the AIM team by assisting with controls planning for ALS. Control for ALS is an enormous problem it involves air revitalization, water recovery, food production, solids processing and crew. In more general terms, these systems can be characterized as involving both continuous and discrete processes, dynamic interactions among the sub-systems, nonlinear behavior due to the complex operations, and a large number of multivariable interactions due to the dimension of the state space. It is imperative that a baseline approach from which to measure performance is established especially when the expectation for the control system is complete autonomous control.

Hoo, Karlene A.↗

NASA NTRS1974

An investigation of the open-loop amplification of a Reynolds number dependent process by wave distortion

The response of a constant-temperature hot-wire anemometer to sinusoidal and distorted sinusoidal acoustic oscillations is examined. The output of the anemometer is dependent upon the Reynolds number of the flow over the wire. The response is a measure of the interaction between the anemometer output and the acoustic pressure in the neighborhood of the wire. It is an open-loop prediction of the characteristics of actual closed-loop operation of a system. If the open-loop response is large enough, unstable closed-loop operation is predicted. The study was motivated by a need to investigate the stability limits of liquid-propellant rockets when perturbed by pressure oscillations. The sinusoidal and distorted sinusoidal acoustic oscillations used for this study are the same as those characteristic of unstable rocket combustion. Qualitatively, the results are similar--the response of the system to pure sinusoidal acoustic vibration of the fluid surrounding the wire is small, even when the magnitude of the acoustic pressure is quite large; but the response can be increased by as much as an order of magnitude with respect to the sinusoidal case by the addition of distortion. The amplitude and phase of the distortion component, relative to the fundamental component, are the dominant factors in the increase in the response.

Ventrice, M. B.↗

NASA NTRSDate not supplied

Biological Research and Space Health Enabled by Machine Learning to Support Deep Space Missions

A key science goal of the NASA “Moon to Mars” campaign is to understand how biology responds to the Lunar, Martian, and deep space environments in order to advance fundamental knowledge and support human space missions. Through artificial intelligence (AI) and machine learning (ML), a paradigm shift has begun in space biosciences and engineered astronaut health systems, to enable Earth-independence and mission operations autonomy. We describe current AI/ML methods to support 1) fundamental biology, 2) in situ analytics, 3) high performance computing, 4) automated science, 5) self-driving labs, 6) remote data management, 7) integrated mission biomonitoring, and 8) a Precision Space Health system. AI/ML approaches that can be integrated to support these domains include active learning, explainable AI, adaptive learning, causal inference, knowledge graphs, federated learning, transfer learning, and large language models. Finally, we present results from several current ML projects that are underway in the space biology field to address key challenges of small sample n, high feature count, heterogeneity, and sparse data. These include 1) connecting omics to phenotypic data using an ensemble model to infer causality of rodent liver health disruption, 2) usage of explainable ML to interrogate muscular underpinnings of muscle atrophy, 3) ML models analyzing and determining directed acyclic graphs of human health risk leveraging rodent bone datasets, 4) usage of large pre-trained models connecting biomedical knowledgebases with small spaceflight datasets to understand gene-to-gene interactions, and 5) a suite of benchmarked open science datasets enabling programmers to identify best algorithms to answer space biology questions.

space biology↗

NASA NTRSDate not supplied

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG↗

NASA NTRS1987

Arcjet thruster research and technology. Phase 1: Executive summary

The principal objective of this two phase program is to conduct the development research required to make the low power arcjet a flight ready technology. Many important results were obtained during Phase 1 to move closer to this objective. Fundamental analyses were performed of the arcjet nozzle, the gas kinetic reaction effects, the thermal environment, and the arc stabilizing vortex. These aided the conceptual understanding of the arcjet and guided design work. A hydrazine (N2H4) arcjet was designed that combined a flight qualified catalyst bed with a modular arcjet. Extensive testing was performed which demonstrated the feasibility of using this propellant in an arcjet for the first time. Startup techniques were developed, stability maintained, material compatibility tests conducted, and performance mapping tests performed. Specific impulse values from 400 to 730 seconds were produced with a non-optimized design. These levels are higher than were originally thought possible and proved that extremely high enthalpy values can be obtained with constricted arc technology. Erosion rate data are promising for lifetime extensions to meet flight application requirements. Power control unit (PCU) development was started with the design and fabrication of a laboratory high switching frequency supply. Valuable data were obtained on PCU operation and on the interaction with the dynamic arc. Phase 2 efforts presently underway are resolving key issues for multi-hundred hour lifetimes, are continuing to investigate arcjet/PCU interactions, and will demonstrate duty cycle N2H4 arcjet/PCU operation in a simulated flight mode for lifetimes consistent with initial applications.

Source record↗

NASA NTRS2003

Noise Generation by Fans with Supersonic Tip Speeds

Fan noise continues to be a significant issue for commercial aircraft engines and there still exists a requirement for improved understanding of the fundamental issues associated with fan noise source mechanisms. At the present time, most of the prediction methods identify the dominant acoustic sources to be associated with the stator vanes or blade trailing edges which are downstream of the fan face. However recent studies have shown that acoustic waves are significantly attenuated as they propagate upstream through a rotor, and if the appropriate corrections are applied, sound radiation from the engine inlet is significantly underpredicted. The prediction models can only be applied to fans with subsonic tip speeds. In contrast, most aircraft engines have fan tip speeds which are transonic and this implies an even higher attenuation for upstream propagating acoustic waves. Consequently understanding how sound propagates upstream through the fan is an important, and not well understood phenomena. The objective of this study is to provide improved insight into the upstream propagation effects through a rotor which are relevant to full scale engines. The focus of this study is on broadband fan noise generated by boundary layer turbulence interacting with the trailing edges of the fan blades. If this source mechanism is important upstream of the fan, the sound must propagate upstream through a transonic non uniform flow which includes large gradients and non linearities. Developing acoustic propagation models in this type of flow is challenging and currently limited to low frequency applications, where the frequency is of the same order as the blade passing frequency of the fan. For trailing edge noise, much higher frequencies are relevant and so a suitable approach needs to be developed, which is not limited by an unacceptably large computational effort. In this study we are in the process of developing a computational method which applies for the high frequencies of interest, and allows for any type of flow field associated with the fan. In this progress report the approach to be used and the basic equations will be presented. Some initial results will be given, but these are preliminary and need further verification.

Glegg, Stewart↗