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NASA NTRS1984

Volumetric representation for object model acquisition

This paper describes a volumetric representation that has been specified for use in a system that derives object models from a sequence of images with viewpoint specifications. This volumetric representation is an enumerative structure referred to here as a volume segment representation. The model acquisition system was designed to form an initial object approximation, then refine that approximation as subsequent information is obtained. The refinement process requires a readily modifiable object representation, while the overall goal of the system demands a representation descriptive of surface detail. The volume segment structure provides both of those capabilities.

Martin, W. N.↗

NASA NTRS2007

Integrating Human Factors into Crew Exploration Vehicle Design

With NASA's new Vision for Exploration to send humans beyond Earth orbit, it is critical to consider the human as a system that demands early and continuous user involvement, and an iterative prototype/test/redesign process. Addressing human-system interface issues early on can be very cost effective even cost reducing when performed early in the design and development cycle. To achieve this goal within Crew Exploration Vehicle (CEV) Project Office, human engineering (HE) team is formed. Key tasks are to apply HE requirements and guidelines to hardware/software, and provide HE design, analysis and evaluation of crew interfaces. Initial activities included many practice-orientated evaluations using low-fidelity CEV mock-ups. What follows is a description of such evaluations that focused on a HE requirement regarding Net Habitable Volume (NHV). NHV is defined as the total remaining pressurized volume available to on-orbit crew after accounting for the loss of volume due to deployed hardware and structural inefficiencies which decrease functional volume. The goal of the NHV evaluations was to develop requirements providing sufficient CEV NHV for crewmembers to live and perform tasks in support of mission goals. Efforts included development of a standard NHV calculation method using computer models and physical mockups, and crew/ stakeholder evaluations. Nine stakeholders and ten crewmembers participated in the unsuited evaluations. Six crewmembers also participated in a suited evaluation. The mock-up was outfitted with volumetric representation of sub-systems such as seats, and stowage bags. Thirteen scenarios were developed to represent mission/crew tasks and considered to be primary volume drivers (e.g., suit donning) for the CEV. Unsuited evaluations included a structured walkthrough of these tasks. Suited evaluations included timed donning of the existing launch and entry suit to simulate a contingency scenario followed by doffing/ stowing of the suits. All mockup evaluations were videotaped. Structured questionnaires were used to document user interface issues and volume impacts of layout configuration. Computer model and physical measures of the NHV agreed within 1 percent. This included measurement of the gross habitable volume, subtraction of intrusive volumes, and other non-habitable spaces. Calculation method developed was validated as a standard means of measuring NHV, and was recommended as a verification method for the NHV requirements. Evaluations confirmed that there was adequate volume for unsuited scenarios and suit donning/ doffing activity. Seats, suit design stowage and waste hygiene system noted to be critical volume drivers. The low-fidelity mock-up evaluations along with human modeling analysis generated discussions that will lead to high-level systems requirements and human-centered design decisions. This approach allowed HE requirements and operational concepts to evolve in parallel with engineering system concepts and design requirements. As the CEV design matures, these evaluations will continue and help with design decisions, and assessment, verification and validation of HE requirements.

Whitmore, Mihriban↗

NASA NTRSDate not supplied

Multiscale Modeling of Reconstructed Tricalcium Silicate using NASA Multiscale Analysis Tool

To study microstructure characteristics of cementitious materials hydrated in space; previously, cement binder formations were processed under microgravity conditions and was further compared against ground-based experiments. For accurate estimation of process-structure-property linkage, particularly on samples hydrated in the microgravity environment, it is desired to have a high-fidelity volumetric representation of the microstructure. However, owing to small sample size and high porosity of the space-returned samples, conventional experimental characterization techniques are not viable. Hence, a deep learning-based reconstruction algorithm was employed to obtain high fidelity 3D volumes from sparse high resolution 2D Scanning Electron Microscopy (SEM) images, as inputs to micromechanics-based modeling. This machine learning-based reconstruction methodology validated against low-order statistical descriptors, captured the microstructural topology of both sample types (ground, 1g and microgravity, μg). Due to the lack of gravity, hydration products of the samples processed in space differed from those processed-on ground. Such AI-generated virtual samples were analyzed in a multiscale recursive micromechanics approach using the NASA Multiscale Analysis Tool (NASMAT). Here, we present a methodology to rapidly integrate and evaluate these AI-generated volumes in NASMAT. The synthesized microstructural volumes are directly employed as Representative Volume Elements (RVEs) to preserve the fidelity (1 pixel = 0.54 m). Invariably, analysis of such largescale problems (5123 voxels) requires huge amount of computational resources. By taking advantage of the NASMAT architecture, we also focused on systematic multiscale integration of these AI-reconstructed virtual volumes to reduce the computational demands. In this work, this methodology is demonstrated on the ground-based, 1g samples. The estimated stiffness value of 15.90 GPa is comparable to experimentally obtained modulus of hydrated tricalcium silicate sample. The workflow presented here paves the way for utilizing the NASMAT tool to perform multiscale analyses of other multi-phase material systems using either 3D virtual datasets synthesized using AI or obtained via micro-CT.

Machine Learning↗

NASA NTRS2016

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.

Scruggs, T.↗

NASA NTRS2004

Model of Mixing Layer With Multicomponent Evaporating Drops

A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The study is motivated by the fact that typical real petroleum fuels contain hundreds of chemical species. Previously, for the sake of computational efficiency, spray studies were performed using either models based on a single representative species or models based on surrogate fuels of at most 15 species. The present multicomponent model makes it possible to perform more realistic simulations by accounting for hundreds of chemical species in a computationally efficient manner. The model is used to perform Direct Numerical Simulations in continuing studies directed toward understanding the behavior of liquid petroleum fuel sprays. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and the drops, respectively. This representation is consistent with the expected volumetrically small loading of the drops in gas (of the order of 10 3), although the mass loading can be substantial because of the high ratio (of the order of 103) between the densities of liquid and gas. The drops are treated as point sources of mass, momentum, and energy; this representation is consistent with the drop size being smaller than the Kolmogorov scale. Unsteady drag, added-mass effects, Basset history forces, and collisions between the drops are neglected, and the gas is assumed calorically perfect. The model incorporates the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a distribution function. Distribution functions generally depend on many parameters. However, for mixtures of homologous species, the distribution can be approximated with acceptable accuracy as a sole function of the molecular weight. The mixing layer is initially laden with drops in its lower stream, and the drops are colder than the gas. Drop evaporation leads to a change in the gas-phase composition, which, like the composition of the drops, is described in a probabilistic manner

Bellan, Josette↗

NASA NTRS2017

A Comparative Study of Simulated and Measured Main Landing Gear Noise for Large Civil Transports

Computational results for the NASA 26%-scale model of a six-wheel main landing gear with and without a toboggan-shaped noise reduction fairing are presented. The model is a high-fidelity representation of a Boeing 777-200 aircraft main landing gear. A lattice Boltzmann method was used to simulate the unsteady flow around the model in isolation. The computations were conducted in free-air at a Mach number of 0.17, matching a recent acoustic test of the same gear model in the Virginia Tech Stability Wind Tunnel in its anechoic configuration. Results obtained on a set of grids with successively finer spatial resolution demonstrate the challenge in resolving/capturing the flow field for the smaller components of the gear and their associated interactions, and the resulting effects on the high-frequency segment of the farfield noise spectrum. Farfield noise spectra were computed based on an FWH integral approach, with simulated pressures on the model solid surfaces or flow-field data extracted on a set of permeable surfaces enclosing the model as input. Comparison of these spectra with microphone array measurements obtained in the tunnel indicated that, for the present complex gear model, the permeable surfaces provide a more accurate representation of farfield noise, suggesting that volumetric effects are not negligible. The present study also demonstrates that good agreement between simulated and measured farfield noise can be achieved if consistent post-processing is applied to both physical and synthetic pressure records at array microphone locations.

Konig, Benedikt↗

NASA NTRS2002

Image Dis-Integration for Improved Plasmasphere Visualization

Traditionally, study of the plasmasphere has involved terrestrial observation of local characteristics. Global modeling of the plasmasphere in such an observation regime made use of an ensemble of (sparse) local measurements. Recently, sensors aboard the IMAGE (Imager for Magnetopause-to-Aurora Global Exploration) satellite (in particular, the EUV (Extreme Ultra Violet) Imager) have created the potential for truly global study of the plasmasphere. IMAGE was launched in spring of 2000 in an orbit with apogee altitude 7.2 R E (Earth radii) and perigee altitude 1000 km. IMAGE's EUV sensor allows an external view of the distribution of cold plasma in the plasmasphere to be acquired. EUV is designed to image light emission at 30.4 nanometers, which is the emission wavelength of the He + ion in the presence of solar radiation. He + makes up approximately 15-20% of the plasma in the plasmasphere, thus imaging of He + enables determination of plasma distribution. The EUV instrument provides a 90° by 84° field of view which is imaged as an equally spaced 150x140 pixel array on a spherical imaging surface. The EUV produces an image approximately every 10 minutes when the sensor is operating. Since EUV images contain line-of-sight integrations of plasma distributions, they do not directly express equatorial plane density (which would enable comparison of observed plasma distributions with predictions from models). Furthermore, the plasma density at any point in three-space is not known. The goal of our work was development of a technique that can enable plasma density to be determined throughout three-space. Our approach to creation of a three-space representation of the plasma distribution involves disintegrating the EUV lines of sight to form a volumetric map of plasma densities.

Timothy S. Newman↗

NASA NTRS1995

A predictor-corrector technique for visualizing unsteady flow

We present a method for visualizing unsteady flow by displaying its vortices. The vortices are identified by using a vorticity-predictor pressure-corrector scheme that follows vortex cores. The cross-sections of a vortex at each point along the core can be represented by a Fourier series. A vortex can be faithfully reconstructed from the series as a simple quadrilateral mesh, or its reconstruction can be enhanced to indicate helical motion. The mesh can reduce the representation of the flow features by a factor of one thousand or more compared with the volumetric dataset. With this amount of reduction it is possible to implement an interactive system on a graphics workstation to permit a viewer to examine, in three dimensions, the evolution of the vortical structures in a complex, unsteady flow.

Banks, David C.↗

NASA NTRS2014

Ice Roughness in Short Duration SLD Icing Events

Ice accretion codes depend on models of roughness parameters to account for the enhanced heat transfer during the ice accretion process. While mitigating supercooled large droplet (SLD or Appendix O) icing is a significant concern for manufacturers seeking future vehicle certification due to the pending regulation, historical ice roughness studies have been performed using Appendix C icing clouds which exhibit mean volumetric diameters (MVD) much smaller than SLD clouds. Further, the historical studies of roughness focused on extracting parametric representations of ice roughness using multiple images of roughness elements. In this study, the ice roughness developed on a 21-in. NACA 0012 at 0deg angle of attack exposed to short duration SLD icing events was measured in the Icing Research Tunnel at the NASA Glenn Research Center. The MVD's used in the study ranged from 100 micrometer to 200 micrometers, in a 67 m/s flow, with liquid water contents of either 0.6 gm/cubic meters or 0.75 gm/cubic meters. The ice surfaces were measured using a Romer Absolute Arm laser scanning system. The roughness associated with each surface point cloud was measured using the two-dimensional self-organizing map approach developed by McClain and Kreeger (2013) resulting in statistical descriptions of the ice roughness.

Icing↗

NASA NTRS2013

Development of Two-Moment Cloud Microphysics for Liquid and Ice Within the NASA Goddard Earth Observing System Model (GEOS-5)

This work presents the development of a two-moment cloud microphysics scheme within the version 5 of the NASA Goddard Earth Observing System (GEOS-5). The scheme includes the implementation of a comprehensive stratiform microphysics module, a new cloud coverage scheme that allows ice supersaturation and a new microphysics module embedded within the moist convection parameterization of GEOS-5. Comprehensive physically-based descriptions of ice nucleation, including homogeneous and heterogeneous freezing, and liquid droplet activation are implemented to describe the formation of cloud particles in stratiform clouds and convective cumulus. The effect of preexisting ice crystals on the formation of cirrus clouds is also accounted for. A new parameterization of the subgrid scale vertical velocity distribution accounting for turbulence and gravity wave motion is developed. The implementation of the new microphysics significantly improves the representation of liquid water and ice in GEOS-5. Evaluation of the model shows agreement of the simulated droplet and ice crystal effective and volumetric radius with satellite retrievals and in situ observations. The simulated global distribution of supersaturation is also in agreement with observations. It was found that when using the new microphysics the fraction of condensate that remains as liquid follows a sigmoidal increase with temperature which differs from the linear increase assumed in most models and is in better agreement with available observations. The performance of the new microphysics in reproducing the observed total cloud fraction, longwave and shortwave cloud forcing, and total precipitation is similar to the operational version of GEOS-5 and in agreement with satellite retrievals. However the new microphysics tends to underestimate the coverage of persistent low level stratocumulus. Sensitivity studies showed that the simulated cloud properties are robust to moderate variation in cloud microphysical parameters. However significant sensitivity in ice cloud properties was found to variation in the dispersion of the ice crystal size distribution and the critical size for ice autoconversion. The implementation of the new microphysics leads to a more realistic representation of cloud processes in GEOS-5 and allows the linkage of cloud properties to aerosol emissions.

Aerosol-Cloud Interactions↗

NASA NTRS1989

Correlative visualization techniques for multidimensional data

Critical to the understanding of data is the ability to provide pictorial or visual representation of those data, particularly in support of correlative data analysis. Despite the advancement of visualization techniques for scientific data over the last several years, there are still significant problems in bringing today's hardware and software technology into the hands of the typical scientist. For example, there are other computer science domains outside of computer graphics that are required to make visualization effective such as data management. Well-defined, flexible mechanisms for data access and management must be combined with rendering algorithms, data transformation, etc. to form a generic visualization pipeline. A generalized approach to data visualization is critical for the correlative analysis of distinct, complex, multidimensional data sets in the space and Earth sciences. Different classes of data representation techniques must be used within such a framework, which can range from simple, static two- and three-dimensional line plots to animation, surface rendering, and volumetric imaging. Static examples of actual data analyses will illustrate the importance of an effective pipeline in data visualization system.

Treinish, Lloyd A.↗

NASA NTRS2013

Virtual Construction of Space Habitats: Connecting Building Information Models (BIM) and SysML

Current trends in design, construction and management of complex projects make use of Building Information Models (BIM) connecting different types of data to geometrical models. This information model allow different types of analysis beyond pure graphical representations. Space habitats, regardless their size, are also complex systems that require the synchronization of many types of information and disciplines beyond mass, volume, power or other basic volumetric parameters. For this, the state-of-the-art model based systems engineering languages and processes - for instance SysML - represent a solid way to tackle this problem from a programmatic point of view. Nevertheless integrating this with a powerful geometrical architectural design tool with BIM capabilities could represent a change in the workflow and paradigm of space habitats design applicable to other aerospace complex systems. This paper shows some general findings and overall conclusions based on the ongoing research to create a design protocol and method that practically connects a systems engineering approach with a BIM architectural and engineering design as a complete Model Based Engineering approach. Therefore, one hypothetical example is created and followed during the design process. In order to make it possible this research also tackles the application of IFC categories and parameters in the aerospace field starting with the application upon the space habitats design as way to understand the information flow between disciplines and tools. By building virtual space habitats we can potentially improve in the near future the way more complex designs are developed from very little detail from concept to manufacturing.

space architecture↗

NASA NTRS2010

Relating Linear and Volumetric Variables Through Body Scanning to Improve Human Interfaces in Space

Designing space suits and vehicles for the diverse human population present unique challenges for the methods of traditional anthropometry. Space suits are bulky and allow the operator to shift position within the suit and inhibit the ability to identify body landmarks. Limited suit sizing options also cause variability in fit and performance between similarly sized individuals. Space vehicles are restrictive in volume in both the fit and the ability to collect data. NASA's Anthropometric and Biomechanics Facility (ABF) has utilized 3D scanning to shift from traditional linear anthropometry to explore and examine volumetric capabilities to provide anthropometric solutions for design. Overall, the key goals are to improve the human-system performance and develop new processes to aid in the design and evaluation of space systems. Four case studies are presented that illustrate the shift from purely linear analyses to an augmented volumetric toolset to predict and analyze the human within the space suit and vehicle. The first case study involves the calculation of maximal head volume to estimate total free volume in the helmet for proper air exchange. Traditional linear measurements resulted in an inaccurate representation of the head shape, yet limited data exists for the determination of a large head volume. Steps were first taken to identify and classify a maximum head volume and the resulting comparisons to the estimate are presented in this paper. This study illustrates the gap between linear components of anthropometry and the need for overall volume metrics in order to provide solutions. A second case study examines the overlay of the space suit scans and components onto scanned individuals to quantify fit and clearance to aid in sizing the suit to the individual. Restrictions in space suit size availability present unique challenges to optimally fit the individual within a limited sizing range while maintaining performance. Quantification of the clearance and fit between similarly sized individuals is critical in providing a greater understanding of the human body's function within the suit. The third case study presented in this paper explores the development of a conformal seat pan using scanning techniques, and details the challenges of volumetric analyses that were overcome in order to develop a universal seat pan that can be utilized across the entire user population. The final case study explores expanding volumetric capabilities through generation of boundary manikins. Boundary manikins are representative individuals from the population of interest that represent the extremes of the population spectrum. The ABF developed a technique to take three-dimensional scans of individuals and manipulate the scans to reflect the boundary manikins' anthropometry. In essence, this process generates a representative three-dimensional scan of an individual from anthropometry, using another individual's scanned image. The results from this process can be used in design process modeling and initial suit sizing work as a three dimensional, realistic example of individuals from the population, maintaining the variability between and correlation to the relevant dimensions of interest.

Margerum, Sarah E.↗

NASA NTRS2010

Simplified Model for iLIDS IDD

The NASA Docking System (NDS) Project has provided simplified volumetric models for use by potential hosts vehicles to assess vehicle integration. It should be noted that the JSC-65795 NDS Interface Definition Document (IDD) takes precedence over this simplified model. The simplified model serves as a graphical representation only. It is therefore important to state that dimensions and tolerances are to be taken from the IDD document and supersede any measurements derived from the provided simplified model geometry.

Lewis, James L.↗

NASA NTRS2001

[Real time 3D echocardiography]

Three-dimensional representation of the heart is an old concern. Usually, 3D reconstruction of the cardiac mass is made by successive acquisition of 2D sections, the spatial localisation and orientation of which require complex guiding systems. More recently, the concept of volumetric acquisition has been introduced. A matricial emitter-receiver probe complex with parallel data processing provides instantaneous of a pyramidal 64 degrees x 64 degrees volume. The image is restituted in real time and is composed of 3 planes (planes B and C) which can be displaced in all spatial directions at any time during acquisition. The flexibility of this system of acquisition allows volume and mass measurement with greater accuracy and reproducibility, limiting inter-observer variability. Free navigation of the planes of investigation allows reconstruction for qualitative and quantitative analysis of valvular heart disease and other pathologies. Although real time 3D echocardiography is ready for clinical usage, some improvements are still necessary to improve its conviviality. Then real time 3D echocardiography could be the essential tool for understanding, diagnosis and management of patients.

Review↗

NASA NTRS2013

Bulk Moisture and Salinity Sensor

Measurement and feedback control of nutrient solutions in plant root zones is critical to the development of healthy plants in both terrestrial and reduced-gravity environments. In addition to the water content, the amount of fertilizer in the nutrient solution is important to plant health. This typically requires a separate set of sensors to accomplish. A combination bulk moisture and salinity sensor has been designed, built, and tested with different nutrient solutions in several substrates. The substrates include glass beads, a clay-like substrate, and a nutrient-enriched substrate with the presence of plant roots. By measuring two key parameters, the sensor is able to monitor both the volumetric water content and salinity of the nutrient solution in bulk media. Many commercially available moisture sensors are point sensors, making localized measurements over a small volume at the point of insertion. Consequently, they are more prone to suffer from interferences with air bubbles, contact area of media, and root growth. This makes it difficult to get an accurate representation of true moisture content and distribution in the bulk media. Additionally, a network of point sensors is required, increasing the cabling, data acquisition, and calibration requirements. measure the dielectric properties of a material in the annular space of the vessel. Because the pore water in the media often has high salinity, a method to measure the media moisture content and salinity simultaneously was devised. Characterization of the frequency response for capacitance and conductance across the electrodes was completed for 2-mm glass bead media, 1- to 2-mm Turface (a clay like media), and 1- to 2-mm fertilized Turface with the presence of root mass. These measurements were then used to find empirical relationships among capacitance (C), the dissipation factor (D), the volumetric water content, and the pore water salinity.

Nurge, Mark↗

NASA NTRS1992

Comparison of radiated noise from shrouded and unshrouded propellers

The ducted propeller in a free field is modeled using the finite element method. The generation, propagation, and radiation of sound from a ducted fan is described by the convened wave equation with volumetric body forces. Body forces are used to introduce the blade loading for rotating blades and stationary exit guide vanes. For an axisymmetric nacelle or shroud, the problem is formulated in cylindrical coordinates. For a specified angular harmonic, the angular coordinate is eliminated, resulting in a two-dimensional representation. A finite element discretization based on nine-node quadratic isoparametric elements is used.

Eversman, Walter↗

NASA NTRS2013

Influence of Computational Drop Representation in LES of a Droplet-Laden Mixing Layer

Multiphase turbulent flows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent flows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of pollutant dispersion, etc. Two-phase flows contain millions and sometimes billions of particles. For flows with volumetrically dilute particle loading, the most accurate method of numerically simulating the flow is based on direct numerical simulation (DNS) of the governing equations in which all scales of the flow including the small scales that are responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary. Because of high computational cost, numerical simulations of such flows cannot track all these drops. The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics, and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provide minimal error in flow prediction. For this purpose, several Large Eddy Simulation (LES) of a mixing layer with evaporating drops have been performed by using coarse, medium, and fine grid spacings and computational drops, rather than physical drops. To define computational drops, an integer NR is introduced that represents the ratio of the number of existing physical drops to the desired number of computational drops; for example, if NR=8, this means that a computational drop represents 8 physical drops in the flow field. The desired number of computational drops is determined by the available computational resources; the larger NR is, the less computationally intensive is the simulation. A set of first order and second order flow statistics, and of drop statistics are extracted from LES predictions and are compared to results obtained by filtering a DNS database. First order statistics such as Favre averaged stream-wise velocity, Favre averaged vapor mass fraction, and the drop stream-wise velocity, are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when NR is less than 32, and by the coarse mesh LES reasonably accurately for all NR values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.

Bellan, Josette↗