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NASA NTRSDate not supplied

Uncrewed Lunar Surface Operations and Support Activities

Sustained human presence on the surface of the Moon and future missions to Mars require increased independence from surface crews and Earth-based mission control to operate efficiently, safely, and reliably. The time for surface crews to perform tasks will be limited. Extravehicular activities by surface personnel are burdensome and time-consuming, even when a continuous human presence on the surface occurs. Identifying and balancing human/automation roles and tasks and infusing automation and autonomy practices early in a system’s lifecycle will be essential to achieve mission objectives. Among these objectives are attaining a sustained human presence, improving performance and mission effectiveness, reducing operations and maintenance (O&M) costs, and ensuring operations that are robust to communication delays. To achieve these objectives, an operational shift toward increased automation and autonomy with less reliance on humans is needed. Uncrewed lunar surface operations and support activities occur when surface crews are not present or are independent of surface crew timeline activities requiring no surface crew oversight or intervention. These uncrewed surface opportunities can also be planned to minimize crew workload that avoids routine maintenance and support tasks, thus maximizing crew exploration time. Uncrewed preparations such as staging and prepositioning equipment and materials before the crew arrives could improve crew task efficiency. Additional opportunities exist to conduct uncrewed science, exploration, and utilization. Uncrewed surface architecture functions can include science and exploration; habitation; launch and landing support; surface communication and navigation; surface power generation and distribution; human surface mobility; lifting, handling, manipulating; excavation, construction, and site preparation; logistics management; maintenance and repair; surface resource utilization; integrated site operations and shared support services (e.g., site scheduling/prioritization, dust mitigation/contamination control, and surface safety). Early robotic lunar surface campaigns will provide information on the availability of resources, such as oxygen and water, and demonstrate surface-based technologies. After the Artemis III human lunar return mission, a series of landers will deliver surface systems, cargo, supplies, science packages, spare parts, and commodities. A balance of crewed and uncrewed surface operations will enable a sustained lunar surface presence at the South Pole of the Moon at a site that will be known as the Artemis Base Camp (ABC). It is envisioned that base camp operations on and around the Moon will then help prepare for the mission durations and activities needed to support the first human mission to Mars. Before long-duration crew missions to the base camp can occur, the necessary surface infrastructure will be pre-deployed and verified operational. Surface assets will be teleoperated and remotely managed from Earth. Additionally, robotic and short-duration crewed missions to the ABC will ensure the site’s merit to achieve long-term science objectives, availability of usable resources, and that terrain, seasonal variations, and illumination conditions are acceptable. ABC will consist of different areas where specific functions and services are rendered, including: • Launch and Landing Area • Habitation Area • Power Production Area • Resource Areas Launch and Landing Area—The launch and landing area will support associated functions for the arrival and departure of vehicles, such as crewed landing and ascent and uncrewed cargo deliveries and offloading. It will evolve from an unimproved site at the beginning of the exploration campaign to a more sustainable landing and launch area that can support repeated arrivals and departures. Initial uncrewed Lunar Terrain Vehicle (LTV) surface operations may include emplacement of navigation beacons and communication equipment, real-time video and photography of landing/liftoff events, and element repositioning, such as portable utility power (PUP) (applicable for other landed assets at other areas). Site preparations, such as surface leveling, soil compaction, and berm/path construction, may be needed for a more sustainable launch and landing area capable of accommodating vehicles that are increasingly more reusable and reduce the effects of plume surface interactions and ejecta impacts on nearby surface assets. During the ABC missions, cargo and logistics will be delivered to the lunar surface via robotic cargo landers before the crew arrives. These shipments, which can arrive in pressurized logistics carriers, will deliver the logistics necessary to support a crewed mission and include items such as food, water, equipment spares, etc. Providing the capability to retrieve, offload, and transport the logistics closer to the ABC site before the arrival of the crew will increase the overall efficiency of crew operations once they arrive. In the sustained phase of exploration, other supporting services may be needed, such as lander propellant servicing, surface power services, commodity refreshes, and additional inspection, maintenance, and repair capabilities, to sustain a cadence of extended personnel stays and cargo arrivals and departures. Habitation Area—Uncrewed support to surface habitation could involve supporting activation and pre-entry operations of the habitat while the crew is in orbit at the Gateway outpost preparing for a surface landing. Surface Habitat (SH) uncrewed operations may include bringing the cabin environment to a habitable temperature and air mix and activating other critical crew support systems. Potential crop production uncrewed tasks in the SH could also include autonomous watering and tending. Additionally, when the crew departs, the SH enters dormancy for the long period of uncrewed operation. A logistical staging area could also be collocated near the SH. If so, staging operations for crew supplies, waste re-location, and recycling operations may be opportunities for uncrewed operations. Power Production Area—The Fission Surface Power (FSP) element and its supporting distribution equipment provide power to surface elements as needed across the ABC to supplement day-to-day operations and survive lunar nights. Uncrewed support of this power system includes any initial LTV-assisted deployments of cables and other distributed equipment, associated electrical connections, and system testing and activation operations. Robotically performing some inspections, maintenance, or repair tasks on the power distribution equipment could reduce the surface crew workload. Resource Area— Uncrewed resource prospecting, mapping, and characterizing possible resource sites is likely to be time-consuming and represents an opportunity for uncrewed operations between crewed missions. Uncrewed mobile equipment operations will be needed in the extreme environments of permanently shadowed locations where resource extractions occur. As In-Situ Resource Utilization (ISRU) pilot plant operations begin, uncrewed surface support activities with available mobile and portable assets (LTV, PUP, etc.) will better support these operations. Any produced commodities can be stored at a centralized storage location for future use. Also associated with these operations is the use of mobile robotic excavators for resource acquisition and robotic/autonomous regolith processing. The waste tailings generated during excavation and regolith processing would also need to be transported and deposited at a dedicated location. Surface assets will continue operating between crew visits to maintain surface capabilities, conduct lunar surface science, technology demonstrations, and public outreach opportunities. Additionally, certain sustaining tasks that would consume valuable crew time could be performed before crew arrival, or after their departure. This capability may offer more affordable options to construct, activate, test, and maintain a broad set of surface assets. Telerobotically operated human surface mobility systems, such as the LTV and Pressurized Rover (PR), can be utilized for various tasks. Surface environmental conditions pose a distinct challenge for all these activities. Surface illumination and localized shadows are one such factor. Night-survival operations could consist of thermal management, battery pre-charging, and load shedding. Some surface systems may hibernate through the night and then awake and continue nominal operations. Uncrewed mobile assets may use a more adaptive approach to optimize their power and operations; one method is to follow the sunlight. Night-survival operations may be initiated remotely by teleoperation, automated, or accomplished by supervised autonomous operation. The ability to pre-deploy and control remote assets in orbit or on Mars before the arrival of the mission crew is a key capability that can be simulated on the moon. The base camp provides a venue where these advanced operational concepts, technologies, and autonomous methods and techniques, including the incorporation of time delays to simulate Earth-Mars latency can be replicated to help buy down future Mars mission risks. This paper will examine the evolution of uncrewed lunar surface operations and support activities. It will also discuss the lunar surface environmental conditions (thermal, lighting, terrain, topography, communications) along with the challenges they pose on uncrewed surface operations, and the performance of these activities with limited to minimal human interaction and/or teleoperation. Since lunar missions include Mars mission analogs, such investigation provides the framework for future uncrewed Mars mission support.

Mark E Lewis↗
NASA NTRS2012

Automation and Process Improvement Enables a Small Team to Operate a Low Thrust Mission in Orbit Around the Asteroid Vesta

NASA's Dawn mission to the asteroid Vesta and dwarf planet Ceres launched September 27, 2007 and arrived at Vesta in July of 2011. This mission uses ion propulsion to achieve the necessary delta-V to reach and maneuver at Vesta and Ceres. This paper will show how the evolution of ground system automation and process improvement allowed a relatively small engineering team to transition from cruise operations to asteroid operations while maintaining robust processes. The cruise to Vesta phase lasted almost 4 years and consisted of activities that were built with software tools, but each tool was open loop and required engineers to review the output to ensure consistency. Additionally, this same time period was characterized by the evolution from manually retrieved and reviewed data products to automatically generated data products and data value checking. Furthermore, the team originally took about three to four weeks to design and build about four weeks of spacecraft activities, with spacecraft contacts only once a week. Operations around the asteroid Vesta increased the tempo dramatically by transitioning from one contact a week to three or four contacts a week, to fourteen contacts a week (every 12 hours). This was accompanied by a similar increase in activity complexity as well as very fast turn around activity design and build cycles. The design process became more automated and the tools became closed loop, allowing the team to build more activities without sacrificing rigor. Additionally, these activities were dependent on the results of flight system performance, so more automation was added to analyze the flight data and provide results in a timely fashion to feed the design cycle. All of this automation and process improvement enabled up the engineers to focus on other aspects of spacecraft operations, including spacecraft health monitoring and anomaly resolution.

ground system automation↗
NASA NTRS1999

Automated Flight Dynamics Product Generation for the EOS AM-1 Spacecraft

As part of NASA's Earth Science Enterprise, the Earth Observing System (EOS) AM-1 spacecraft is designed to monitor long-term, global, environmental changes. Because of the complexity of the AM-1 spacecraft, the mission operations center requires more than 80 distinct flight dynamics products (reports). To create these products, the AM-1 Flight Dynamics Team (FDT) will use a combination of modified commercial software packages (e.g., Analytical Graphic's Satellite ToolKit) and NASA-developed software applications. While providing the most cost-effective solution to meeting the mission requirements, the integration of these software applications raises several operational concerns: (1) Routine product generation requires knowledge of multiple applications executing on variety of hardware platforms. (2) Generating products is a highly interactive process requiring a user to interact with each application multiple times to generate each product. (3) Routine product generation requires several hours to complete. (4) User interaction with each application introduces the potential for errors, since users are required to manually enter filenames and input parameters as well as run applications in the correct sequence. Generating products requires some level of flight dynamics expertise to determine the appropriate inputs and sequencing. To address these issues, the FDT developed an automation software tool called AutoProducts, which runs on a single hardware platform and provides all necessary coordination and communication among the various flight dynamics software applications. AutoProducts, autonomously retrieves necessary files, sequences and executes applications with correct input parameters, and deliver the final flight dynamics products to the appropriate customers. Although AutoProducts will normally generate pre-programmed sets of routine products, its graphical interface allows for easy configuration of customized and one-of-a-kind products. Additionally, AutoProducts has been designed as a mission-independent tool, and can be easily reconfigured to support other missions or incorporate new flight dynamics software packages. After the AM-1 launch, AutoProducts will run automatically at pre-determined time intervals . The AutoProducts tool reduces many of the concerns associated with the flight dynamics product generation. Although AutoProducts required a significant effort to develop because of the complexity of the interfaces involved, its use will provide significant cost savings through reduced operator time and maximum product reliability. In addition, user satisfaction is significantly improved and flight dynamics experts have more time to perform valuable analysis work. This paper will describe the evolution of the AutoProducts tool, highlighting the cost savings and customer satisfaction resulting from its development. It will also provide details about the tool including its graphical interface and operational capabilities.

Matusow, Carla↗
NASA NTRS2018

Payload Operations Center - Lessons from Commercial Engagement

The International Space Station (ISS) Payload Operations and Integration Center (POIC) at NASA's Marshall Space Flight Center (MSFC) in Huntsville, Alabama, United States, has gone through an evolution from supporting exclusively government ISS users to providing 50% (or more) of their support to commercial users. At the same time, they have expanded ground and facility operations to support a United States Orbital Segment crew expansion from three to four astronauts allowing an additional of 34 hours crew time per week. These additional hours are dedicated to utilization and have already surpassed the 100 hour peak weekly milestone in July 2018. This paper discusses the Center's changes in planning, staffing, coordination, and operations while addressing topics from the addition of secondary flight control positions to dynamic operations product reviews. MSFC's Human Exploration and Development Operations Office, which manages payload operations, seeks through this paper to highlight the higher priority commercial users now receive in replanning and in additional crew time.

Watkins, Bobby J.↗
NASA NTRS2018

Human-in-the-Loop Evaluation of Dynamic Multi-Flight Common Route Advisories

Flights often experience large delays when they are routed around weather. Multi-flight common route advisories provide delay recovery by suggesting time-saving re-routes for groups of flights whose current weather-avoidance routes have become outdated because the weather has dissipated and/or moved away. A laboratory evaluation of these advisories was conducted by four subject matter experts having extensive experience in traffic flow management operations. These experts provided a total of 120 data points in the airspace of Houston Center. The multi-flight common route tool provides time-saving route change advisories taking into account flight plans, wind fields, and the spatio-temporal evolution of predicted convective weather. It is not designed to account for complex operational factors such as non-standard sector traversal and interactions with local traffic management initiatives; hence a relatively low percentage (37%) of advisories generated by the tool were rated as acceptable. However, a high percentage (81%) of advisories were rated as acceptable after the subject matter experts used the tool's user interface to make route modifications that accounted for relevant operational factors not considered by the tool. The workload associated with using the tool, as measured by the NASA Task Load Index, was quite low (1.1 on a scale of 0 to 10). The results of this evaluation make a good case for human-automation teaming to design operationally valid weather re-routes for delay recovery.

Traffic Flow Management↗
NASA NTRS2018

Human-in-the-Loop Evaluation of Dynamic Multi-Flight Common Route Advisories

Flights often experience large delays when they are routed around weather. Multi-flight common route advisories provide delay recovery by suggesting time-saving re-routes for groups of flights whose current weather-avoidance routes have become outdated because the weather has dissipated and/or moved away. A laboratory evaluation of these advisories was conducted by four subject matter experts having extensive experience in traffic flow management operations. These experts provided a total of 120 data points in the airspace of Houston Center. The multi-flight common route tool provides time-saving route change advisories taking into account flight plans, wind fields, and the spatio-temporal evolution of predicted convective weather. It is not designed to account for complex operational factors such as non-standard sector traversal and interactions with local traffic management initiatives; hence a relatively low percentage (37%) of advisories generated by the tool were rated as acceptable. However, a high percentage (81%) of advisories were rated as acceptable after the subject matter experts used the tool's user interface to make route modifications that accounted for relevant operational factors not considered by the tool. The workload associated with using the tool, as measured by the NASA Task Load Index, was quite low (1.1 on a scale of 0 to 10). The results of this evaluation make a good case for human-automation teaming to design operationally valid weather re-routes for delay recovery.

Traffic Flow Management↗
NASA NTRS1987

Orbiter transfer vehicle concept definition and system analysis study. Volume 4: Space station accommodations. Revision 1

A brief summary is given of the key objectives of Task 5 of the Space Station Accommodations Concept Definition. Space station accommodations were assessed and defined for each potential candidate Space-Based OTV concept and for the composite OTV fleet. To accomplish this, the functional and physical interactions between each OTV concept and the space station were defined. Then, conceptual accommodation designs were prepared and optimized for approach and configuration. Initial space station requirements were identified, including the ability to accommodate and support evolution to maturity, and then a time-phasing of accommodations was prepared showing that evolution. In the process of developing physical and functional interactions, operational requirements were defined, together with associated timelines. In that the crew complement is subject to limitations, the operational requirements derivation is biased toward automation wherever possible. For each candidate Ground-Based OTV concept, operating in conjunction with the space station, the above process was repeated.

Randall, Roger M.↗
NASA NTRS2019

Temperature Stability in the Sub-milliHertz Band With Lisa Pathfinder

LISA Pathfinder (LPF) was a technology pioneering mission designed to test key technologies required for gravitational wave detection in space. In the low frequency regime (milliHertz and below), where space-based gravitational wave observatories will operate, temperature fluctuations play a crucial role since they can couple into the interferometric measurement and the test masses’ free-fall accuracy in many ways. A dedicated temperature measurement subsystem, with noise levels in 10 μKHz −1/2 down to 1 mHz was part of the diagnostics unit onboard LPF. In this paper we report on the temperature measurements throughout mission operations, characterize the thermal environment, estimate transfer functions between different locations, and report temperature stability (and its time evolution) at frequencies as low as 10 μHz, where typically values around 1KHz −1/2 were measured.

gravitational waves↗
NASA NTRS2004

Dusty Disks, Diffuse Clouds, and Dim Suns: Galactic Science with the Infrared Spectrograph on the Spitzer Space Telescope

The Infrared Spectrograph (IRS) on the Spitzer Space Telescope has now been in routine science operations since Dec. 14,2003. The IRS Science Team has used a portion of their guaranteed time to pursue three major science themes in galactic astronomy: the evolution of protostellar disks and debris disks; the composition and evolution of diffuse matter and clouds in the interstellar medium; and the composition and structure of brown dwarfs and low-mass main-sequence stars. We report here on the results from the first five months of IRS observations in these programs. Full IRS Spectra have already been obtained for large samples of YSO/protoplanetary disks in the Taurus and TW Hya associations, and or debris disks around main-sequence stars, in which many aspects of the evolution of planetary systems can be addressed for the first time. As anticipated, the mid-infrared IRS observations of brown dwarfs have yielded important new information about their atmospheres, including the identification of NH3 and measurements of new methane features. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under NASA contract 1407. Support for this work was provided by NASA's Office of Space Science.

Roellig, T. L.↗
NASA NTRS1993

Adjoint-Operator Learning For A Neural Network

Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

Barhen, Jacob↗
NASA NTRS1981

Science and Applications Space Platforms - A NASA overview

An overview of past, present, and future activities relating to space platforms is presented, with emphasis placed on implementation of the initial platform. It is noted that the challenge at present is to define an initial system that can accommodate high priority science, that possesses the capability of doing multi-discipline science, and that demonstrates on-orbit servicing and payload exchange through use of the Shuttle. The evolution of the Science and Applications Space Platform (SASP), which will provide significantly more time on-orbit for instrument operations without increasing Space Shuttle orbiter time on-orbit, is traced. The importance of completing all required activities to support a new start for the SASP in fiscal year 1983 is stressed. While the initial SASP will support only a limited set of investigations, the program will evolve by replication, upgrading, or the development of new systems to support a broader and generally more demanding set of system requirements.

De Sanctis, C. E.↗
NASA NTRSDate not supplied

Spaceflight KID Readout Electronics Development for PRIMA

We present the design and testing of spaceflight multiplexing kinetic inductance detector (KID) readout electronics for the PRobe far-Infrared Mission for Astrophysics (PRIMA). PRIMA is a mission proposed to the 2023 NASA Astrophysics Probe Explorer (APEX) Announcement of Opportunity that will answer fundamental questions about the formation of planetary systems, as well as the formation and evolution of stars, supermassive black holes, and dust over cosmic time. The readout electronics for PRIMA must be compatible with operation at Earth-Sun L2 and capable of multiplexing more than 1000 detectors over 2 GHz bandwidth while consuming around 30 W per readout chain. The electronics must also be capable of switching between the two instruments, which have different readout bands,: the hyperspectral imager (PRIMAger, 2.5-5.0 GHz) and the spectrometer (FIRESS, 0.4-2.4 GHz). We present the driving requirements, design, and measured performance of a laboratory brassboard system.

Sumit Dahal↗
NASA NTRS2004

Oh! I Slipped the Surly Bounds of Earth....and Ran into Space Weather!

Over the past decade the concept of space weather has been introduced and matured in both the scientific community and popular press. Likewise the concept of space climatology recently also is being advanced. Closely linked to these concepts are their impacts on ground- and space-based technological systems; one such system commonly mentioned is manned space flight exemplified by the Space Shuttle and International Space Station (ISS). From a manned space flight perspective, space weather and space climatology have significant effects on the amount of radiation exposure received by humans in space from the ambient high-energy charged particles present in interplanetary space and trapped in the geomagnetosphere. Whereas the impact of space weather for most technological systems is usually discrete and well correlated in time, the principle impact of space weather and space climatology is to increase the probability of latent cancer formation in thetraveler cohort. In this regard, while space weather may be the dominating factor for a given mission, over the life of a long-term program such as the Space Shuttle or ISS space climatology is the controlling factor of latent cancer risk. Human radiation exposure enhancements associated with space weather disturbances has been a concern among scientist and mission controllers since the inception of manned spaceflight nearly forty years ago. This led NASA to develop, in conjunction with the Environmental Science Services Administration s Space Disturbance Forecast Center and the USAF/AWS, the Solar Particle Alert Network (SPAN)-the foundation of an initial U.S. space weather monitoring and forecasting service. Since Apollo, routine space flight operations have evolved to include the use of space weather and climatology data provided through a world-wide network of operational space weather data services to predict and recommend actions to minimize astronaut radiation exposures. NASA Space Radiation Analysis Group (SRAG) flight controllers use real-time space weather data to detect and assess the impact of solar particle events, outer electron belt enhancements, the formation of pseudo-stable additional trapped radiation belts, and the solar cycle modulation of trapped radiation belts and galactic cosmic rays. Energetic particle data from GOES spacecraft are automatically ingested from NOAA Space Environment Center data servers and used to drive a model for the estimating the exposure to astronauts from solar particle events. While adequate for current manned space flight support, the existing operational space weather support system requires improvements to address the anticipated evolution in both the character of manned missions as well as space flight operations management. Necessary space weather data improvements include: reliably available (near) real-time space weather data on a fixed schedule via redundant access methods that support autonomous data acquisition by computer systems behind enterprise firewalls; and rapid transition of promising research sensors into operational systems.

Golightly, Michael J.↗
NASA NTRS1978

Diagrammatic analysis of the density operator for nonlinear optical calculations Pulsed and CW responses

In the present paper a diagrammatic analysis of the density operator for the evaluation of nonlinear optical quantities is considered. The present approach extends earlier diagrammatic analysis by treating the time evolution of both the wave function and its complex conjugate. Time-ordered graphs result, each of which corresponds to a term in the density matrix. Examples involving the third-order susceptibility are discussed for both monochromatic and pulse excitation. In particular coherent rotational transient birefringence is discussed. The diagrams provide a convenient means by which nonlinear optical processes can be precisely defined and the susceptibility readily evaluated.

Yee, T. K.↗
NASA NTRS1995

Dynamics of Vapour Bubbles in Nucleate Boiling: Evolution of Thermally Controlled Bubbles - 2

The previously developed dynamic theory of growth and detachment of vapour bubbles under conditions of nucleate pool boiling is applied to study motion and deformation of a bubble evolving at a single nucleation site. The bubble growth is presumed to be thermally controlled, and two components of heat transfer to the bubble are accounted of: the one from the bulk of surrounding liquid and the one due to heat conduction across a liquid microlayer formed underneath the bubble. Bubble evolution is governed by the buoyancy and an effective surface tension force, both the forces making the bubble centre of mass move away from the wall and, thus, assisting its detachment. Buoyancy-controlled and surface-tension-controlled regimes are considered separately in a meticulous way. The duration of the whole process of bubble evolution till detachment, the rate of growth, and the bubble departure size are found as functions of time and physical and operating parameters. Some repeatedly observed phenomena, such as an influence of gravity on the growth rate, are explained. Inferences of the model agree qualitatively with available experimental evidence, and conclusions pertaining to the dependence on gravity of the bubble radius at detachment and the whole time of the bubble development when being attached to the wall are confirmed quantitatively.

Buyevich, Yu A.↗
NASA NTRS1989

Secular change in chert distribution: a reflection of evolving biological participation in the silica cycle

In the modern oceans, the removal of dissolved silica from sea water is principally a biological process carried out by diatoms, with lesser contributions from radiolaria, silicoflagellates, and sponges. Because such silica in sediments is often redistributed locally during diagenesis to from nodular or bedded chert, stratigraphic changes in the facies distribution of early diagenetic chert provide important insights into the development of biological participation in the silica cycle. The abundance of chert in upper Proterozoic peritidal carbonates suggests that at this time silica was removed from seawater principally by abiological processes operating in part of the margins of the oceans. With the evolution of demosponges near the beginning of the Cambrian Period, subtidal biogenetic cherts became increasingly common, and with the Ordovician rise of radiolaria to ecological and biogeochemical prominence, sedimented skeletons became a principal sink for oceanic silica. Cherts of Silurian to Cretaceous age share many features of facies distribution and petrography but they differ from Cenozoic siliceous deposits. These differences are interpreted to reflect the mid-Cretaceous radiation of diatoms and their subsequent rise to domination of the silica cycle. Biogeochemical cycles provide an important framework for the paleobiological interpretation of the organisms that participate in them.

Non-NASA Center↗
NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗