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At least 379 records · Page 21

A study of sound generation in subsonic rotors, volume 2

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.

Chalupnik, J. D.↗

Differential rotation and turbulent convection: A new Reynolds stress model and comparison with solar data

In most hydrodynamic cases, the existence of a turbulent flow superimposed on a mean flow is caused by a shear instability in the latter. Boussinesq suggested the first model for the turbulent Reynolds stresses bar-(u(sub i)u(sub j)) in which the mean shear S(sub ij) is the cause (or source) of turbulence represented by the stress bar-(u(sub i)u(sub j)). In the case of solar differential rotation, exactly the reverse physical process occurs: turbulence (which must pre-exist) generates a mean flow which manifests itself in the form of differential rotation. Thus, the Boussinesq model is wholly inadequate because in the solar case, cause and effect are reversed. Since the Boussinesq model is inadequate, one needs an alternative model for the Reynolds stresses. We present a new dynamical model for the Reynolds stresses, convective fluxes, turbulent kinetic energy, and temperature fluctuations. The complete model requires the solution of 11 differential equations. We then introduce a set of simplifying assumptions which reduce the full dynamical model to a set of algebraic Reynolds stress models. We explicitly solve one of these models that entails only one differential equation. The overall agreement with the data is obtained with a model that is neither phenomenological nor one that requires a full numerical simulation, since it is algebraic in nature. The new model can play an important role in understanding the complex physics underlying the interplay between solar differential rotation and convection, as many physical processes can naturally be incorporated into the model.

Canuto, V. M.↗

Turbulence Model Validation Through Joint Experimental /Computational Studies of Separated Flow Over A Three-Dimensional Tapered Bump: Part I - Experimental Investigation

The results of a three-year experimental campaign aimed at comprehensively documenting the separated flow over a three-dimensional bump are presented with the purpose of generating a benchmark experimental database useful in validating computational fluid dynamics (CFD) flow simulations. The bump model geometry was designed to provide well-defined and repeatable smooth-body flow separation conditions that were suitable for both experiments and simulations. The bump had a Gaussian streamwise profile with a constant height equal to 8.5% of its width over the central 60% of the test section width. The remaining 40% were outboard spanwise portions that gradually taper to zero using an error function profile to minimize side-wall boundary layer effects. The model was immersed in a turbulent boundary layer that was developed on a suspended flat plate in the Notre Dame Mach 0.6 Wind Tunnel. In order to document the effect of the incoming boundary layer thickness on the flow separation, the bump model could be located at two streamwise positions. The mean velocity and turbulence intensity of the wind tunnel freestream flow field and approaching turbulent boundary layer were fully documented. The measurements of the flow separation region included surface visualization, wall shear stress using oil-film interferometry, mean and dynamic surface pressure, and planar and stereoscopic particle image velocimetry. The experiments were conducted over a range of Mach numbers from 0.05 to 0.2 corresponding to a range of Reynolds numbers based on the test section spanwise dimension (0.914m) of 1.0 × 10 6 ≤ Re L = U ∞ L/ν ≤ 4.0 × 10 6 . The bulk of the results are presented for the higher Mach number conditions of 0.1 and 0.2 with Re L = 2.0 × 10 6 and 4.0 × 10 6 , respectively. Extensive uncertainty analysis of the data was performed. The data is archived in the NASA Langley Turbulence Modeling Resource website at https://turbmodels.larc.nasa.gov/Other_exp_Data/speedbump_sep_exp.html. In addition to the experiments, a computational effort was made in parallel by the CFD group at Boeing Research & Technology highlighting the usefulness of the data set, which is outlined in the accompanying CFD report.

Flow separation↗

Validation of new and existing methods for time-domain simulations of turbulence and loads

We seek to obtain a second-by-second match between the simulated and measured structural loads of a utility-scale wind turbine. To obtain the one-to-one load simulations, we start with the furthest upstream component of the modeling chain: the turbulent inflow. We consider new and existing methods to generate constrained-turbulence flow fields. The new method is based on large-eddy simulations (LES) and machine learning (ML). The existing methods include Kaimal-based TurbSim and the superstatistical wind field model. The inflow measurements used to constrain these simulations are obtained with a nacelle-mounted scanning lidar. We compare the flow fields for the different inflow simulation approaches and validate their associated load predictions against measurements collected in the Rotor Aero-dynamics, Aeroelastics, and Wake (RAAW) field campaign. We find that the rotor-position control developed for this study is key in enabling the time match between measurements and simulations. When this control approach is used, the load simulation performance tracks with the inflow simulation fidelity, with LES+ML yielding errors ≤ 4% for the damage-equivalent loads of flapwise bending moment, and tower fore-aft bending moments.

17 WIND ENERGY↗

Shifts in hydropower operation to balance wind and solar will modify effects on aquatic biota

To avoid negative consequences to freshwater biota from climate change, society must complete the transition from fossil to renewable electricity sources. However, temporal patterns in hydropower generation (and flow releases that affect aquatic biota) may change with increased wind and solar penetration. We used power cost modeling to characterize current and future within-day and seasonal patterns in hydropower generation across the Eastern Interconnection in a wet and a dry year. Compared to the baseline, future hydropower generation across the grid decreased during the day and increased before dawn and after dusk. At a project level, such a pattern would suggest 'double peaking' operation (up- and down-ramping before dawn and after dusk, with lower releases midday). Variation in generation was higher in wet years than dry years, foreshadowing possible flow constraints on hydropower flexibility. At the grid scale, projected ramping rates were higher in all seasons. A review of the ecological literature suggests that these changes would shift the timing of invertebrate drift and elevate the risk of nest scouring during up-ramping and the risk of stranding or dewatering during down ramping. Thermal conditions may be moderated by increased ramping. Strategies for adapting to future shifts in the renewable portfolio range from re-regulation in reservoir cascades to providing flow refuge (structures and vegetation) below individual projects. Coordinated basin-scale operation can distribute peaking operation to maintain grid support while restricting local ramping at critical ecological times. In addition, research to design hybrid renewable systems that add battery storage is needed to understand how we can mitigate future risks to aquatic communities while promoting the use of renewable energy. This study, which is among the first to examine ecological side-effects of the shift to renewable energy in freshwater ecosystems, lays out a path toward understanding and navigating changes to flow regimes under the energy transition.

54 ENVIRONMENTAL SCIENCES↗

Measurement of flow properties coupled to experimental and numerical analyses of dense, granular flows for solar thermal energy storage

Granular flows of sintered bauxite proppants were researched along an inclined plane for solar thermal energy storage applications. Granular flow properties needed to drive numeric granular models were measured for improved numerical model predictions for Carbobead CP 50/140, 40/100, and 30/60 particles. Particle shape and size distributions were determined by coupling optical microscopy to an in-house image processing algorithm. The impulse excitation technique was used to measure elastic and shear moduli, and compute Poisson’s ratio. The coefficient of static sliding friction was measured using the slip-stick method, and the static rolling friction was determined from measured shear on particles positioned between two hot-pressed plates. The coefficient of restitution was measured by dropping particles on a surface and determining the kinetic energy before and after impact with the surface using high resolution particle tracking velocimetry. Particle size did not significantly impact the coefficients of restitution and static rolling friction, however, particle shape distribution resulted in a large variation in measurements. An inclined flow experiment was performed to characterize granular flows of Carbobead CP 30/60 particles using particle image velocimetry. Numerical models of the experiment using discrete element method were generated with the measured mechanical properties as inputs for comparison with experimental results. A constant directional torque rolling friction model best predicted bulk granular flow behavior. Furthermore, good agreement between the model and experiment was achieved at ambient, steady state conditions, with average velocity differences <10%.

14 SOLAR ENERGY↗

Crossflow effects on steady and fluctuating pressures on an ogive-cylinder cone-frustum model in supersonic separated flow

Wind-tunnel tests were conducted on an ogive-cylinder model with two axisymmetric protuberances having cone frustum angles of cone = 23 deg and 45 deg that were used to generate detached shock waves and the resulting separated flow areas downstream of the shock. The tests were conducted in a 9 by 7 foot supersonic wind tunnel at a free-stream Mach number of 2.0 and at Reynolds numbers of 1.5 x 1 million and 3.9 x 1 million, based on body diameter. The model had an afterbody fineness ratio of 8.3, and the ogive nose had a fineness ratio of 3.0. Two characteristics of the fluctuating pressures in surface vortex flows that result from the crossflow component, (velocity along the tunnel longitudinal axis free stream angle of attack), in combination with changes in the longitudinal pressure gradient were measured: (1) the broadband, rms-pressure coefficients and (2) the power spectral densities. Measurements are presented for various flow regions on the model such as the attached turbulent boundary layer, the detached frustum shock wave, and separated flow areas. The results indicate that the pressure fluctuations around or in the neighborhood of the foci of the vortex flows had broadband intensities and power spectral densities nearly identical to the levels previously measured in separated-flow regions at angles of attack of 0 deg.

Dods, J. B., Jr.↗

Granular Temperature Modeling with Large-Scale CFD-DEM Data

The granular temperature is a measure of solids-phase fluctuating kinetic energy in particle-laden gas-solid flows. This report focuses on reduced-order models of granular temperature in triply-periodic cluster induced turbulent flow. The granular temperature data was generated by post-processing large-scale CFD-DEM simulations that were carried out as part of an ALCC awarded study. The algebraic model of Tang et al, originally fit to DNS data, was found to be amenable to the present data. The results of several regression analyses are presented building on the original expression. This work was performed in part through the National Nuclear Security Administration (NNSA) Minority Serving Institutions Internship Program (MSIIP).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data and Scripts associated with “Lambda-PFLOTRAN: Workflow for Incorporating Organic Matter Chemistry Informed by Ultra High Resolution Mass Spectrometry into Biogeochemical Modeling.”

This data package is associated with the publication “Lambda-PFLOTRAN: Workflow for Incorporating Organic Matter Chemistry Informed by Ultra High Resolution Mass Spectrometry into Biogeochemical Modeling” submitted to Geoscientific Model Development (Muller et al., 2024). In this manuscript, organic matter chemistry and thermodynamics are directly connected to reactive transport simulators through the newly developed Lambda-PFLOTRAN (Parallel Reactive Flow and Transport model) workflow tool that succinctly incorporates organic matter chemistry data generated from Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) into reaction networks to simulate aerobic respiration of the organic matter and the resulting biogeochemistry. Lambda-PFLOTRAN is a python-based workflow, executed through a Jupyter Notebook interface, that digests raw FTICR-MS data, develops a representative reaction network based on substrate-explicit thermodynamic modeling (also termed lambda modeling due to its key thermodynamic parameter λ used therein), and completes a biogeochemical simulation with the open source, reactive flow, and transport code PFLOTRAN. This data package contains Jupyter Notebook based workflows for two test cases for running biogeochemical simulations of organic matter oxidation identified by FTICR-MS. It contains four primary folders (workflow, data, src, and analysis), a file-level metadata file (Muller_2024_Lambda_PFLOTRAN_Manuscript_Data_Package_flmd.csv) that lists all the files contained in this data package with a short description of each, and a data dictionary (Muller_2024_Lambda_PFLOTRAN_Manuscript_Data_Package_dd.csv) file that describes the tabular column headers. The ‘workflow’ folder contains the Jupyter Notebook based workflows for running the lambda analysis, PFLOTRAN simulation, sensitivity analysis and parameter estimation. The ‘data’ folder contains the FTICR-MS data, initial conditions, and incubation data for test cases 1 and 2 in folders titled ‘WHONDRS’ and ‘Colloids’, respectively. The data folder also has a ‘Database’ folder containing a reaction network for bulk organic matter (assumed to be CH2O) and a general database for PFLOTRAN (hanford_rxn_network). The CH2O reaction network defines bulk organic matter oxidation. Biogeochemical simulations are completed for both the lambda binned organic matter and bulk organic matter reaction networks. The ‘hanford_rxn_network’ database includes information required for PFLTORAN simulations including ion size, molar mass, and charge of the aqueous species, gases, and minerals phases. The ‘src’ folder contains python source codes for performing lambda analysis, PFLOTRAN simulation, sensitivity analysis and parameter estimation. The ‘analysis’ folder contains outputs from the test cases 1 and 2 including lambda analysis, PFLOTRAN runs and the calibration results.

54 ENVIRONMENTAL SCIENCES↗

Numerical Generation of Asymmetric Flows about Slender Bodies of Revolution at Extreme Incidence

It is well known that slender bodies of revolution will develop an asymmetric, unsteady flow pattern in experimental tests, if the angle of incidence to the oncoming stream is above a critical value. It has been suggested that the origin of these asymmetric flows may stem from geometric imperfections of the model being tested, or from disturbances in the oncoming stream. In numerical simulations, it is possible to generate bodies of revolution which are perfectly symmetric about their longitudinal axis, and to impose uniform flow conditions which are free from disturbances. The current work presents numerical simulations of the flow about an ogive-cylinder configuration at 40 and 60 degree angle of incidence. These simulations. were performed using numerical algorithms which are also symmetric about the lateral plane of the cylinder body. The flowfields at 40 degree angle of attack were seen to remain symmetric to the round-off accuracy of the computer. At 60 degree angle of attack, a lateral force coefficient developed of O(1) which progressed to an alternate vortex shedding in time. The nature of this lateral force generation and vortex shedding was dependent on the choice of numerical algorithm. The origin of the asymmetries observed in the 60 degree angle of attack computations were traced to round-off errors in the implicit block-matrix inverter. A means of inverting the implicit operator matrices, which maintains the symmetry of the overall numerical algorithm was implemented.

Murman, Scott M.↗

Gas-Liquid Flow Modeling for Renewable Fuels Production

Aerobic/anaerobic and gas fermentation pathways have emerged as promising new technologies for the generation of renewable fuels/chemicals from biomass derived sugars, and mixtures of greenhouse/energy rich gas streams (CO2/CH4/H2/CO) via microbial action. Example pathways include sugars-to-ethanol conversion, biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the scale-up, design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of at-scale (~500 m3) bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for gas uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM [1], to perform these simulations, which has been validated against small-scale reactors in our previous work [2]. There is currently a knowledge-gap regarding bubble-size distributions when using gas mixtures with vastly different properties, which can have a significant impact overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a population balance model (PBM) for bubble-size-distribution modeling that is validated against small-scale experiments in our solver with an uncertainty quantification study for bubble coalescence and break-up model parameters. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient are analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors. This work will also examine the performance of different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor mass-transfer coefficient, gas hold-up, and dissolved gas distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented. [1] Weller, H., Tabor, G., Jasak, H. and Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, 12, 6, 620--631, 1998. [2] Rahimi, M., Sitaraman, H., Humbird, D. and Stickel, J., Computational fluid dynamics study of full-scale aerobic bioreactors: Evaluation of gas-liquid mass transfer, oxygen uptake, and dynamic oxygen distribution, Chemical Engineering Research and Design, 139: 283-295.

BIOMASS FUELS↗

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗

Feasibility of Varying Geo-Fence Around an Unmanned Aircraft Operation Based on Vehicle Performance and Wind

Managing trajectory separation is critical to ensuring accessibility, efficiency, and safety in the unmanned airspace. The notion of geo-fences is an emerging concept, where distance buffers enclose individual trajectories and areas of operation in order to manage the airspace. Currently, the Air Traffic Management system for commercial travel defines static distance buffers around the aircraft; however, commercial UASs are envisioned to operate in significantly closer proximity to other UAS requiring a geo-fence for spacing operations. The geo-fence size can be determined based on vehicle performance characteristics, state of the airspace, weather, and other unforeseen events such as emergency or disaster response. Calculation of the geo-fence size could be determined as part of pre-flight planning and during real-time operations. A largely non-homogeneous fleet of UASs will be operating in low altitude and will likely be commercially developed. Due to intellectual property concerns, the operators may not provide detailed specifications of the control system to UTM. In addition, the huge variety of UAS makes modeling each control system prohibitive and flight data for these vehicles may not exist. Therefore, a generalized, simple geo-fence sizing algorithm must be developed such that it does not rely on detailed knowledge of the vehicle control system, accounts for the presence of urban winds, and is sufficiently accurate. In this work, two simple models are investigated to determine its feasibility as an adequate means for calculating the geo-fence size. The vehicle data used in this work are provided by UAS manufactures who have partnered with NASA's UTM project and some publicly available websites. The first model utilizes wind data processed from the NOAA HRRR (Hourly Rapid Refresh) product and Sonar Annemometer data provided by San Jose State. The second model utilizes OpenFOAM which is a CFD code used to generate a wind field for flow around a single building. The key vehicle performance parameters can include UAS response time to disturbances, command to actuation latency, control system rate limits, time to recovery to desired path, and aerodynamics. It was found that the first model provides an initial understanding of geo-fence sizing, but does not provide enough accuracy to provide UTM with an efficient means of scheduling vehicles. The results of the second model reveal that modeling UAS controls systems with a linearized plant and gain scheduled PID controller does not allow capture the UAS flight dynamics within a significant envelope of the wind disturbances.

uncertainty↗

Modeling Shock-Separated Flow with the Active Model Split

The predictive accuracy of typical hybrid RANS/LES models is limited by several shortcomings, such as modeled-stress depletion and a dependence on scalar grid measures. The "active model-split" (AMS) hybrid RANS/LES model was developed by Haering, Oliver, and Moser to address these shortcomings. In this model, the mean and fluctuating portions of the stress are modeled separately; this allows for a consistent treatment of the mean flow even in the presence of resolved fluctuations. Part of this hybrid model is an active forcing, which generates turbulent fluctuations in regions that support LES-type fluctuations. In this presentation, some recent results are shown using the active model-split for shock-separated flows. The effects of the active forcing are examined, including the effects on anisotropy and acoustics. Superior predictive accuracy over RANS is shown for some quantities of interest, such as the shock location.

RANS↗

Elliptic flow coalescence to identify the $f_0$(980) content

Here we use a simple coalescence model to generate $f_0$(980) particles for three configurations: a $s\bar{s}$ meson, a $u\bar{u}s\bar{s}$ tetraquark, and a $K^+K^–$ molecule. The phase-space information of the coalescing constituents is taken from a multiphase transport (AMPT) simulation of heavy-ion collisions. It is shown that the number of constituent quarks scaling of the elliptic flow anisotropy can be used to discern $s\bar{s}$ from $u\bar{u}s\bar{s}$ and $K^+K^–$ configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Further development of a method for computing three-dimensional subsonic viscous flows in turbofan lobe mixers

Procedure for computing subsonic, turbulent flow in turbofan lobe mixers was extended to allow consideration of flow fields in which a swirl component of velocity may be present. Additional, an optional k-lambda turbulence model was added to the procedure. The method of specifying the initial flow field was also modified, allowing parametric specification or radial secondary flow velocities, and making it possible to consider initial flow fields which have significant inlet secondary flow vorticity. A series of example calculations was performed which demonstrate the various capabilities of the modified code. These calculations demonstrate the effects of initial secondary flows of various magnitudes, the effects of swirl, and the effects of turbulence model on the mixing process. The results of these calculations indicate that the initial secondary flows, presumed to be generated within the lobes, play a dominant role in the mixing process, and that the predicted results are relatively insensitive to the turbulence model used.

Lin, S. J.↗

Understanding How Reservoir Operations Influence Methane Emissions: A Conceptual Model

Because methane is a potent greenhouse gas (GHG), understanding controls on methane emissions from reservoirs is an important goal. Yet, reservoirs are complex ecosystems, and mechanisms by which reservoir operations influence methane emissions are poorly understood. In part, this is because emissions occur in ‘hot spots’ and ‘hot moments’. In this study, we address three research questions, ‘What are the causal pathways through which reservoir operations and resulting water level fluctuations (WLF) influence methane emissions?’; ‘How do influences from WLF differ for seasonal drawdown and diurnal hydropeaking operations?’; and ‘How does understanding causal pathways inform practical options for mitigation?’. A graphical conceptual model is presented that links WLF in reservoirs to methane emissions via four causal pathways: (1) water-column mixing (2) drying–rewetting cycles, (3) sediment delivery and redistribution, and (4) littoral vegetation. We review what is known about linkages for WLF at seasonal and diurnal resolutions generate research questions, and hypothesize strategies for moderating methane emissions by interrupting each causal pathway. Those related to flow management involve basin-scale management of tributary flows, seasonal timing of hydropeaking (pathway #1), timing and rates of drawdown (pathway #2). In addition, we describe how sediment (pathway #3) and vegetation management (pathway #4) could interrupt linkages between WLF and emissions. We demonstrate the strength of conceptual modeling as a tool for generating plausible hypotheses and suggesting mitigation strategies. Future research is needed to develop simpler models at appropriate timescales that can be validated and used to manage flow releases from reservoirs.

13 HYDRO ENERGY↗

Aerodynamic stability and heating analyses for the aeroassist flight experiment vehicle

Since ground based flow simulations are presently unable to model flight conditions expected for AOTVs (Aeroassist Orbital Transfer Vehicle) and other hypersonic space vehicles, computer codes are being developed to provide design parameters necessary for structure, guidance, and control aspects. Over the past four years, VRFLO (Viscous Reactive Flow) has been written to model finite-rate chemistry and viscous effects for a variety of aerobrake bodies. VRFLO includes a number of unique features that are summarized as follows: (1) Grid generation is an integral part of the code for several aerobrake configurations which includes the wake flow region; (2) The formulation is valid for three air chemical models; (3) An ADI central difference technique is used to solve the Navier-Stokes and species continuity equations in split groups; and (4) Grid density and numerical damping are minimized by shock-fitting and conformal mapping of body points.

Mcgary, J.↗