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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 217 records · Page 12

NASA Tech Briefs, March 2010

Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment.

Source record↗

Computational Aeroelastic Analysis of Ares Crew Launch Vehicle Bi-Modal Loading

A Reynolds averaged Navier-Stokes analysis, with and without dynamic aeroelastic effects, is presented for the Ares I-X launch vehicle at transonic Mach numbers and flight Reynolds numbers for two grid resolutions and two angles of attack. The purpose of the study is to quantify the force and moment increment imparted by the sudden transition from fully separated flow around the crew module - service module junction to that of the bi-modal flow state in which only part of the flow reattaches. The bi-modal flow phenomenon is of interest to the guidance, navigation and control community because it causes a discontinuous jump in forces and moments. Computations with a rigid structure at zero zero angle of attack indicate significant increases in normal force and pitching moment. Dynamic aeroelastic computations indicate the bi-modal flow state is insensitive to vehicle flexibility due to the resulting deflections imparting only very small changes in local angle of attack. At an angle of attack of 2.5deg, the magnitude of the pitching moment increment resulting from the bi-modal state nearly triples, while occurring at a slightly lower Mach number. Significant grid induced variations between the solutions indicate that further grid refinement is warranted.

Massey, Steven J.↗

Inflatable Aeroponic System

Aeroponics Internationals (AI) innovation is a self-contained, self-supporting, flexible low mass aeroponic crop production unit with integral environmental systems for the control and delivery of a nutrient mist to the roots. This FLEX Aeroponic System model was developed for commercialization as a result of the NASA SBIR Phase I contract for the research and development of a low-mass, Inflatable Aeroponic System (IAS) for producing pesticide-free lettuces, grains, peppers, tomatoes and other vegetables. The innovation addresses the needs of water and nutrient delivery systems technologies for food production in space. The inflatable nature of the innovation makes it lightweight, allowing it to be deflated so it takes up less volume during transportation and storage. It improves upon AI's current aeroponic system design that uses more rigid structures and takes advantage of vertical inclines to increase bio-mass production by over 600%.

Pelt, Jennifer Van↗

Lessons Learned in the Selection and Development of Test Cases for the Aeroelastic Prediction Workshop: Rectangular Supercritical Wing

The Aeroelastic Prediction Workshop brought together an international community of computational fluid dynamicists as a step in defining the state of the art in computational aeroelasticity. The Rectangular Supercritical Wing (RSW) was chosen as the first configuration to study due to its geometric simplicity, perceived simple flow field at transonic conditions and availability of an experimental data set containing forced oscillation response data. Six teams performed analyses of the RSW; they used Reynolds-Averaged Navier-Stokes flow solvers exercised assuming that the wing had a rigid structure. Both steady-state and forced oscillation computations were performed by each team. The results of these calculations were compared with each other and with the experimental data. The steady-state results from the computations capture many of the flow features of a classical supercritical airfoil pressure distribution. The most dominant feature of the oscillatory results is the upper surface shock dynamics. Substantial variations were observed among the computational solutions as well as differences relative to the experimental data. Contributing issues to these differences include substantial wind tunnel wall effects and diverse choices in the analysis parameters.

Heeg, Jennifer↗

The Characterization of the Selected Materials for Space Shuttle

The harsh conditions to which the Space Shuttles are exposed during flight required the development and use of many unique materials. These materials were specially designed to withstand extreme temperatures, in some cases over 1600 C, while other material must withstand the cryogenic conditions of -253 C, and others must operate while under extreme loads. All of these materials must not only operate in the harsh condition but they must be light weight as well. The Space Shuttle is composed of three major components when configured for launch, Figure 1; the Shuttle, solid rocket boosters, and external tank (ET). The different heat shields of the Shuttle make up the thermal protection system (TPS); this system consists of many different types of components designed to operate on various parts of the vehicle. The body of the Shuttle and ET are composed mainly of aluminum alloy and graphite epoxy. The TPS consists of reinforced carbon-carbon (RCC) used on the wing leading edges and nose cap areas while the upper forward fuselage areas, the entire underside of the Shuttle, the Orbiter maneuvering system, and reaction control system utilize blacc high temperature reusable surface insulation (HRSI) tiles, Figure 2. Other areas of the Orbiter are protected by fibrous refractory composite insulation (FRCI) tiles. Areas where the temperature stays below 649 C, such as the forward fuselage, mid-fuselage, aft fuselage, vertical tail, and upper wing, are protected by other material such as, white low temperature reusable surface insulation (LRSI) tiles, advanced flexible reusable surface insulation (AFRSI) blankets, and felt reusable surface insulation (FRSI) white blankets. The RCC is a pyrolized laminated carbon with the outer surface converted to silicon carbide to prevent oxidation. The FiRST tiles are made of a low-density, high purity silica 99.8-percent amorphous fiber insulation that is made rigid by ceramic bonding resulting in 90-percent void and 10-percent materials. The RCC and HRSI are used in areas where the temperature rises above 1260 T. The FRCI tiles are high strength tiles derived by adding alumina-bososilicate fiber to the pure silica tile slurry that welds the micron-sizes fibers of pure silica into a rigid structure during sintering. The FRCI is composed of 20-percent alumina-borosilicate fibers and 80-percent silica fibers, and provided improved strength, durability and resistance to coating cracking and weight reduction than HRSI.

Kim, Hae-Soo↗

Extravehicular Activity Asteroid Exploration and Sample Collection Capability

NASA's Asteroid Redirect Crewed Mission (ARCM) is challenged with primary mission objectives of demonstrating deep space Extravehicular Activity (EVA) and tools, and obtaining asteroid samples to return to Earth for further study. Although the Modified Advanced Crew Escape Suit (MACES) is used for the EVAs, it has limited mobility which increases fatigue and decreases the crews' capability to perform EVA tasks. Furthermore, previous Shuttle and International Space Station (ISS) spacewalks have benefited from EVA interfaces which have been designed and manufactured on Earth. Rigid structurally mounted handrails, and tools with customized interfaces and restraints optimize EVA performance. For ARCM, some vehicle interfaces and tools can leverage heritage designs and experience. However, when the crew ventures onto an asteroid capture bag to explore the asteroid and collect rock samples, EVA complexity increases due to the uncertainty of the asteroid properties. The variability of rock size, shape and composition, as well as bunching of the fabric bag will complicate EVA translation, tool restraint and body stabilization. The unknown asteroid hardness and brittleness will complicate tool use. The rock surface will introduce added safety concerns for cut gloves and debris control. Feasible solutions to meet ARCM EVA objectives were identified using experience gained during Apollo, Shuttle, and ISS EVAs, terrestrial mountaineering practices, NASA Extreme Environment Mission Operations (NEEMO) 16 mission, and during Neutral Buoyancy Laboratory testing in the MACES suit. The proposed concept utilizes expandable booms and integrated features of the asteroid capture bag to position and restrain the crew at the asteroid worksite. These methods enable the capability to perform both finesse, and high load tasks necessary to collect samples for scientific characterization of the asteroid. This paper will explore the design trade space and options that were examined for EVA, the overall concept for the EVAs including translation paths and body restraint methods, potential tools used to extract the samples, design implications for the Asteroid Redirect Vehicle (ARV) for EVA, the results of early development testing of potential EVA tasks, and extensibility of the EVA architecture to NASA's exploration missions.

Scoville, Zebulon↗

Extravehicular Activity Asteroid Exploration and Sample Collection Capability

One of the challenging primary objectives associated with NASA's Asteroid Redirect Crewed Mission (ARCM) is to demonstrate deep space Extravehicular Activity (EVA) and tools and to obtain asteroid samples to return to Earth for further study. Prior Shuttle and International Space Station (ISS) spacewalks have benefited from engineered EVA interfaces which have been designed and manufactured on Earth. Rigid structurally mounted handrails, and tools with customized interfaces and restraints optimize EVA performance. For ARCM, EVA complexity increases due to the uncertainty of the asteroid properties. The variability of rock size, shape and composition, as well as behavior of the asteroid capture mechanism will complicate EVA translation, tool restraint, and body stabilization. The unknown asteroid hardness and brittleness will complicate tool use. The rock surface will introduce added safety concerns for cut gloves and debris control. Feasible solutions to meet ARCM EVA objectives were identified using experience gained during Apollo, Shuttle, and ISS EVAs, terrestrial mountaineering practices, NASA Extreme Environment Mission Operations (NEEMO) 16 mission, and during Neutral Buoyancy Laboratory testing in the Modified Advanced Crew Escape Suit (MACES) suit. This paper will summarize the overall operational concepts for conducting EVAs for the ARCM mission including translation paths and body restraint methods, potential tools used to extract the samples, design implications for the Asteroid Redirect Vehicle (ARV) for EVA, and the results of early development testing of potential EVA tasks.

Sipila, Stephanie A.↗

Extravehicular Activity Asteroid Exploration and Sample Collection Capability

One of the challenging primary objectives associated with NASA's Asteroid Redirect Crewed Mission (ARCM) is to demonstrate deep space Extravehicular Activity (EVA) and tools and to obtain asteroid samples to return to Earth for further study. Prior Shuttle and International Space Station (ISS) spacewalks have benefited from engineered EVA interfaces which have been designed and manufactured on Earth. Rigid structurally mounted handrails, and tools with customized interfaces and restraints optimize EVA performance. For ARCM, EVA complexity increases due to the uncertainty of the asteroid properties. The variability of rock size, shape and composition, as well as behavior of the asteroid capture mechanism will complicate EVA translation, tool restraint, and body stabilization. The unknown asteroid hardness and brittleness will complicate tool use. The rock surface will introduce added safety concerns for cut gloves and debris control. Feasible solutions to meet ARCM EVA objectives were identified using experience gained during Apollo, Shuttle, and ISS EVAs, terrestrial mountaineering practices, NASA Extreme Environment Mission Operations (NEEMO) 16 mission, and during Neutral Buoyancy Laboratory testing in the Modified Advanced Crew Escape Suit (MACES) suit. This paper will summarize the overall operational concepts for conducting EVAs for the ARCM mission including translation paths and body restraint methods, potential tools used to extract the samples, design implications for the Asteroid Redirect Vehicle (ARV) for EVA, and the results of early development testing of potential EVA tasks.

Sipila, Stephanie A.↗

AHED: The Astrobiology Habitable Environments Database

About the AHED (Astrobiology Habitable Environments Database): Mineral spectroscopy database; Rigid structure; Any change in structure requires extensive re‐programming; Diverse datatypes; Flexible structure; Ability to change design and include new data at any time.

The Astrobiology Habitable Environments Database↗

LEAVES: Lofted Environmental and Atmospheric Venus Sensors

LEAVES (Lofted Environmental Atmospheric Venus Sensors) is a design exercise with the goal of dramatically decreasing the cost of obtaining prioritized chemical and physical data in planetary atmospheres. Through the application of a swarm approach this concept parallelizes atmospheric exploration, with geographic coverage far exceeding what is possible with conventional monolithic platforms or sondes. Each unit in the swarm is exceptionally compact, with a powered payload mass of only a few tens of grams and a high-drag, semi-rigid structure that acts to slow each probe as it descends through the atmosphere. This structural design can collapse into a planar form to allow for efficient stowage prior to arrival at the target body. With a total per-unit mass of only 120 g, a fleet of 100 (or more) units can be very reasonably accommodated on a carrier spacecraft.Science operations, which begin when the LEAVES probes reach an altitude of 100 km, are targeted for the cloud-bearing region of Venus' atmosphere. During the roughly 9 hour, terminal velocity descent through the atmosphere, LEAVES collects data of the state and composition of the atmosphere in parallel across multiple units. These data would represent an unprecedented constraint on the distribution and concentration of targeted chemical species, and the detection of local and regional variations in both chemistry and physical properties.A novel and compelling result of this exercise was that the same optimization that produced a structure with an exceptionally low areal mass density (0.126 kg/m2) also resulted in a probe that can be deployed directly from an aerobraking orbit (~140 km at 5 km/s) without the need for aeroshell protection. This translates to a tremendous mass savings and gives LEAVES the flexibility to be carried as a secondary payload aboard either a descending surface probe or an orbital radar mapper. Because such missions are under active development or have already been proposed (but not flown), we infer that LEAVES is well positioned as a technology

Swarm↗

Boundary-Layer Flow Simulations Over Ablating Woven Thermal Protection System Material

Spallation is the mechanical removal of small chunks of material gets removed typically due to high shear conditions of the flow field. This reduces the ability of the thermal protection system (TPS) material to protect the spacecraft as well as cause turbulence in the flow causing higher heating rates. In this work, we focus on the material removal through ablation and high shear flow within the boundary layer region of woven TPS material. Woven TPS (WTPS) material is the latest class of material developed by NASA, to be used within the next generation of space flights. They are complex interlocked weaves designed to create a rigid structure that is highly resistant to heat and can be easily designed and tailored for a wide variety of entry environments. Due to material removal resulting from chemical degradation, the structural integrity of TPS material is affected. Spallation occurs when this structurally compromised material is exposed to the high shear flow conditions within the boundary layer. In order to understand the spallation mechanism within WTPS material, we first perform the material removal simulations which occur primarily through oxidation to obtain the microstructure at various stages of degradation. These simulations are performed using the Porous Microstructure Analysis (PuMA) software developed at NASA Ames. The micro-structure geometry used within these simulations were generated artificially to be similar to the 3D weave architecture of MSR-EEV (Mars Sample Return - Earth Entry Vehicle). The various eroded TPS micro-structures are then subjected to the boundary layer flow conditions to obtain critical surface quantities which contribute to the structural failure mechanism such as heat flux, pressure, and shear stress. The direct simulation Monte Carlo (DSMC) methodology is used to perform these simulations in order to accurately capture the strong gradients within the high-temperature boundary layer flow over the intricate geometry of WTPS material. The boundary layer profile is directly taken from the Computational Fluid Dynamics (CFD) simulation and provided as boundary conditions to the DSMC inlet and outlet. Further, the variation of these properties as the microstructure undergoes changes due to oxidation is also investigated. Finally, these quantities are used as input in PuMA to understand the material expansion/compression and strain within the woven TPS geometry and help in developing a comprehensive spallation and structure failure model.

microstructure↗

Boundary-Layer Flow Simulations Over Ablating Woven Thermal Protection System Material

Spallation is the mechanical removal of small chunks of material gets removed typically due to high shear conditions of the flow field. This reduces the ability of the thermal protection system (TPS) material to protect the spacecraft as well as cause turbulence in the flow causing higher heating rates. In this work, we focus on the material removal through ablation and high shear flow within the boundary layer region of woven TPS material. Woven TPS (WTPS) material is the latest class of material developed by NASA, to be used within the next generation of space flights. They are complex interlocked weaves designed to create a rigid structure that is highly resistant to heat and can be easily designed and tailored for a wide variety of entry environments. Due to material removal resulting from chemical degradation, the structural integrity of TPS material is affected. Spallation occurs when this structurally compromised material is exposed to the high shear flow conditions within the boundary layer. In order to understand the spallation mechanism within WTPS material, we first perform the material removal simulations which occur primarily through oxidation to obtain the microstructure at various stages of degradation. These simulations are performed using the Porous Microstructure Analysis (PuMA) software developed at NASA Ames. The micro-structure geometry used within these simulations were generated artificially to be similar to the 3D weave architecture of MSR-EEV (Mars Sample Return - Earth Entry Vehicle). The various eroded TPS micro-structures are then subjected to the boundary layer flow conditions to obtain critical surface quantities which contribute to the structural failure mechanism such as heat flux, pressure, and shear stress. The direct simulation Monte Carlo (DSMC) methodology is used to perform these simulations in order to accurately capture the strong gradients within the high-temperature boundary layer flow over the intricate geometry of WTPS material. The boundary layer profile is directly taken from the Computational Fluid Dynamics (CFD) simulation and provided as boundary conditions to the DSMC inlet and outlet. Further, the variation of these properties as the microstructure undergoes changes due to oxidation is also investigated. Finally, these quantities are used as input in PuMA to understand the material expansion/compression and strain within the woven TPS geometry and help in developing a comprehensive spallation and structure failure model.

microstructure↗

Transformable Linkage-Based Gripper for Multi-Mode Grasping and Manipulation

Gripper hardware design often involves a trade-off between distinct and sometimes opposing goals (e.g., high grasping force vs. gentleness). To address this trade-off within a single device, we present a multi-mode gripper with fingers that are scissor linkages, that can actively transform between three distinct modes by varying the number and locations of mechanical singularities. Each of these modes has properties that are suitable for specific needs. Mode 1 provides high grip strength, using a short lever arm and rigid structure. Mode 2 allows precise finger positioning and in-hand manipulation, using two independently controlled DOFs per finger. Mode 3 provides underactuated grasping that can passively adapt to delicate or irregularly shaped objects, with four DOFs per finger. The kinematic relationships, joint torques, and fingertip forces are derived analytically for each of the three modes. Gripper performance and the kinematic model are verified experimentally.

Junghan Kwon↗

Method of making a modular off-axis solar concentrator

A method of making a solar concentrator may include forming a receiving wall having an elongated wall, a first side wall and a second side wall; attaching the first side wall and the second side wall to a reflecting wall to form a housing having an internal volume with an opening; forming a lip on the receiving wall and the reflecting wall; attaching a cover to the receiving wall and the reflecting wall at the lip to seal the opening into the internal volume, thereby creating a rigid structure; and mounting at least one receiver having at least one photovoltaic cell on the elongated wall to receive solar radiation entering the housing and reflected by the receiving wall, the receiver having an axis parallel with a surface normal of the photovoltaic cell, such that the axis is disposed at a non-zero angle relative to the vertical axis of the opening.

14 SOLAR ENERGY↗

Internal spoke gimbal joint

A gimbal apparatus is disclosed, including a tubular envelope with a variable length between first and second rim structures. A rigid ring structure inside the tubular envelope is connected to diametrically opposite first and second portions of the first rim structure, and is connected to diametrically opposite first and second portions of the second rim structure. A spoke bisects the ring structure.

Sparks, Michael Stephen↗

Composite foam structures

A composite rigid foam structure that has a skin or coating on at least one of its surfaces. The skin is formed in situ by thermal spray techniques. The skin is bonded substantially throughout the surface of the porous substrate to the peripheries of the pores. The skin on the average does not penetrate the surface of the substrate by more than the depth of about 2 to 5 pores. Thus, thermal spraying the skin onto the rigid foam produces a composite that is tightly and uniformly bonded together without unduly increasing the weight of the composite structure. Both thermal conductivity and bonding are excellent.

Williams, Brian E.↗

Rigid collapsible dish structure

A collapsible dish structure composed of a plurality of rows of rigid radial petal assemblies concentric with the axis of the dish. The petal assemblies consist of a center petal and two side petals, the center petal hinged on an axis tangent to a circle concentric with the axis of the dish and the side petals hinged to the center petal at their mating edge. The center petal is foldable inwardly and the side petals rotate about their hinges such that the collapsed dish structure occupies a much smaller volume than the deployed dish. Means of controlling the shape of the dish to compensate for differential expansion of the deployed dish are also provided.

Palmer, William B.↗

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗