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Validation and Calibration of Nuclear Thermal Hydraulics Multiscale Multiphysics Models - Subcooled Flow Boiling Study

In addition to validation data plan, development of advanced techniques for calibration and validation of complex multiscale, multiphysics nuclear reactor simulation codes are a main objective of the CASL VUQ plan. Advanced modeling of LWR systems normally involves a range of physico-chemical models describing multiple interacting phenomena, such as thermal hydraulics, reactor physics, coolant chemistry, etc., which occur over a wide range of spatial and temporal scales. To a large extent, the accuracy of (and uncertainty in) overall model predictions is determined by the correctness of various sub-models, which are not conservation-laws based, but empirically derived from measurement data. Such sub-models normally require extensive calibration before the models can be applied to analysis of real reactor problems. This work demonstrates a case study of calibration of a common model of subcooled flow boiling, which is an important multiscale, multiphysics phenomenon in LWR thermal hydraulics. The calibration process is based on a new strategy of model-data integration, in which, all sub-models are simultaneously analyzed and calibrated using multiple sets of data of different types. Specifically, both data on large-scale distributions of void fraction and fluid temperature and data on small-scale physics of wall evaporation were simultaneously used in this work’s calibration. In a departure from traditional (or common-sense) practice of tuning/calibrating complex models, a modern calibration technique based on statistical modeling and Bayesian inference was employed, which allowed simultaneous calibration of multiple sub-models (and related parameters) using different datasets. Quality of data (relevancy, scalability, and uncertainty) could be taken into consideration in the calibration process. This work presents a step forward in the development and realization of the “CIPS Validation Data Plan” at the Consortium for Advanced Simulation of LWRs to enable quantitative assessment of the CASL modeling of Crud-Induced Power Shift (CIPS) phenomenon, in particular, and the CASL advanced predictive capabilities, in general. This report is prepared for the Department of Energy’s Consortium for Advanced Simulation of LWRs program’s VUQ Focus Area.

97 MATHEMATICS AND COMPUTING↗

Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows

We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.

Luo, Li-Shi↗

High Fidelity Simulations of Plume Impingement to the International Space Station

With the retirement of the Space Shuttle, the United States now depends on recently developed commercial spacecraft to supply the International Space Station (ISS) with cargo. These new vehicles supplement ones from international partners including the Russian Progress, the European Autonomous Transfer Vehicle (ATV), and the Japanese H-II Transfer Vehicle (HTV). Furthermore, to carry crew to the ISS and supplement the capability currently provided exclusively by the Russian Soyuz, new designs and a refinement to a cargo vehicle design are in work. Many of these designs include features such as nozzle scarfing or simultaneous firing of multiple thrusters resulting in complex plumes. This results in a wide variety of complex plumes impinging upon the ISS. Therefore, to ensure safe "proximity operations" near the ISS, the need for accurate and efficient high fidelity simulation of plume impingement to the ISS is as high as ever. A capability combining computational fluid dynamics (CFD) and the Direct Simulation Monte Carlo (DSMC) techniques has been developed to properly model the large density variations encountered as the plume expands from the high pressure in the combustion chamber to the near vacuum conditions at the orbiting altitude of the ISS. Details of the computational tools employed by this method, including recent software enhancements and the best practices needed to achieve accurate simulations, are discussed. Several recent examples of the application of this high fidelity capability are presented. These examples highlight many of the real world, complex features of plume impingement that occur when "visiting vehicles" operate in the vicinity of the ISS.

Lumpkin, Forrest E., III↗

Elucidating the effects of adsorbent flexibility on fluid adsorption using simple models and flat-histogram sampling methods

Using flat-histogram Monte Carlo methods, we investigate the adsorptive behavior of the square-well fluid in two simple slit-pore-like models intended to capture fundamental characteristics of flexible adsorbent materials. Both models require as input thermodynamic information about the flexible adsorbent material itself. An important component of this work involves formulating the flexible pore models in the appropriate thermodynamic (statistical mechanical) ensembles, namely, the osmotic ensemble and a variant of the grand-canonical ensemble. Two-dimensional probability distributions, which are calculated using flat-histogram methods, provide the information necessary to determine adsorption thermodynamics. For example, we are able to determine precisely adsorption isotherms, (equilibrium) phase transition conditions, limits of stability, and free energies for a number of different flexible adsorbent materials, distinguishable as different inputs into the models. While the models used in this work are relatively simple from a geometric perspective, they yield non-trivial adsorptive behavior, including adsorption-desorption hysteresis solely due to material flexibility and so-called “breathing” of the adsorbent. The observed effects can in turn be tied to the inherent properties of the bare adsorbent. Some of the effects are expected on physical grounds while others arise from a subtle balance of thermodynamic and mechanical driving forces. In addition, the computational strategy presented here can be easily applied to more complex models for flexible adsorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Instrumentation, performance visualization, and debugging tools for multiprocessors

The need for computing power has forced a migration from serial computation on a single processor to parallel processing on multiprocessor architectures. However, without effective means to monitor (and visualize) program execution, debugging, and tuning parallel programs becomes intractably difficult as program complexity increases with the number of processors. Research on performance evaluation tools for multiprocessors is being carried out at ARC. Besides investigating new techniques for instrumenting, monitoring, and presenting the state of parallel program execution in a coherent and user-friendly manner, prototypes of software tools are being incorporated into the run-time environments of various hardware testbeds to evaluate their impact on user productivity. Our current tool set, the Ames Instrumentation Systems (AIMS), incorporates features from various software systems developed in academia and industry. The execution of FORTRAN programs on the Intel iPSC/860 can be automatically instrumented and monitored. Performance data collected in this manner can be displayed graphically on workstations supporting X-Windows. We have successfully compared various parallel algorithms for computational fluid dynamics (CFD) applications in collaboration with scientists from the Numerical Aerodynamic Simulation Systems Division. By performing these comparisons, we show that performance monitors and debuggers such as AIMS are practical and can illuminate the complex dynamics that occur within parallel programs.

Yan, Jerry C.↗

Restraint of Liquid Jets by Surface Tension in Microgravity Modeled

Tension in Microgravity Modeled Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, jets must be contained by surface tension forces. Recent NASA experiments in microgravity (Tank Pressure Control Experiment, TPCE, and Vented Tank Pressure Experiment, VTRE) resulted in a wealth of data about jet behavior in microgravity. VTRE was surprising in that, although it contained a complex geometry of baffles and vanes, the limit on liquid inflow was the emergence of a liquid jet from the top of the vane structure. Clearly understanding the restraint of liquid jets by surface tension is key to managing fluids in low gravity. To model this phenomenon, we need a numerical method that can track the fluid motion and the surface tension forces. The fluid motion is modeled with the Navier-Stokes equation formulated for low-speed incompressible flows. The quantities of velocity and pressure are placed on a staggered grid, with velocity being tracked at cell faces and pressure at cell centers. The free surface is tracked via the introduction of a color function that tracks liquid as 1/2 and gas as -1/2. A phase model developed by Jacqmin is used. This model converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly. Previous attempts at this formulation have been criticized for smearing the interface. However, by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function, interface smearing is avoided. These equations can be rewritten as two coupled Poisson equations that also include the velocity. The method of solution is as follows: first, the phase equations are solved from this solution, a velocity field is generated, then a successive overrelaxation scheme is used to solve for a pressure field consistent with the velocity solution. After the code was implemented in axisymmetric form and verified by several test cases, the drop tower runs of Aydelott were modeled. The model handed the free-surface deformation quite nicely, even to the point of modeling geyser growth in the regime where the free surface was no longer restrained. A representative run is shown.

Chato, David J.↗

Retrospective on Recent DOE-Funded Studies Concerning the Extraction of Rare Earth Elements & Lithium from Geothermal Brines (Final Report)

Rare earth elements (REE) and lithium are non-toxic metals that are considered critical materials due to their use in electronics, magnets, batteries, and a wide variety of industrial processes important for the economy and military preparedness. Demand for REE and lithium is increasing and these critical materials are imported, so identifying and exploiting domestic sources of REE and lithium is a national priority. The U.S. Department of Energy (DOE) Geothermal Technologies Office (GTO) has been in the forefront of sponsoring research investigating the potential recovery of REE, lithium, and other critical minerals from geothermal brines. It has been proposed that the future of geothermal energy should include “hybrid systems” that combine electricity generation with other revenue-generating activities, such as recovery of valuable and critical minerals, including REE and lithium. Two recent GTO funding opportunities have focused on the recovery of REE and other valuable minerals from geothermal brines. The research supported by the GTO’s mineral recovery program is focused on three areas: resource characterization, technology for the extraction of REE, and technology for the extraction of lithium (Tables 1 and 2). This report is a retrospective study examining the outcome of GTO’s two recent mineral recovery programs (DE-FOA-0001016 in FY 2014 and DE-FOA-0001376 in FY 2016). In this report, the knowledge, technology, and techniques that were developed by researchers funded by GTO are summarized and discussed. Four projects were funded to assess the concentrations and amounts of REE found in geothermal brines and oil field produced waters. The GTO-funded studies compiled publically available data on REE concentrations from brines and produced water from all over the USA. In addition, new samples were collected and characterized from major geothermal and hydrocarbon basins in the Western USA. The studies examined the relationship between lithology and REE concentrations and developed models examining the influence of geology on REE concentrations in produced brines. It was determined that REE are frequently found at higher concentrations in oil field produced water than geothermal brines, but that some geothermal areas had significant REE resources. Significant reservoirs of REE were identified in the Western USA. In some cases, concentrations of REE were more than 1000 times the concentrations found in seawater. Collectively, these studies represent a comprehensive picture of REE resources associated with geothermal and hydrocarbon systems in the USA. The studies did not examine lithium resources, but in some cases, lithium concentration data was collected. Data from these studies are housed in the Geothermal Data Repository (GDR) and represent a significant information resource and it is recommended that these data be further analyzed in a future study. Eight projects were funded to develop new technology for REE extraction from geothermal fluids. These projects investigated sorption as an approach for removal and recovery of REE from geothermal brines. The projects investigated cutting-edge technology for selective sorption of ions from complex solutions, including the application of metal-organic frameworks and biosorbent proteins. The REE sorption studies tested different combinations of metal-binding ligands and solid supports. The most promising metal-binding ligands for REE included phosphonic acid, thiol, and carboxylic acid functional groups. Ligands were attached or incorporated into a wide variety of solid supports. In most cases, attachment was via covalent bonding to organic resins, polymers, or silica-based supports. Most of the REE projects were conducted at a low technology readiness level (TRL) and showed promise, but direct comparison between technologies was not possible based on the available information. It is recommended that testing and reporting be standardized to the extent possible to facilitate comparisons between technologies. Two projects were directed at novel lithium extraction technology. Both projects investigated the use of inorganic sorbents, including manganese oxides. One study also examined the use of metal- ion imprinted polymers as selective ion-exchange resins for the separation of lithium and manganese from brines. Both approaches showed promise for the selective extraction of lithium from brines, including potentially geothermal brines. Results from these GTO studies indicated that selective REE and lithium extraction is possible, but interference from co-occurring solutes, such as calcium, magnesium, or heavy metals, will interfere with process efficiency and negatively impact process economics. Techno-economic analysis conducted as part of the resource and technology studies suggest extraction of REE from geothermal brines is unlikely to be economically viable, especially since non-geothermal produced waters frequently have higher REE concentrations. It is recommended that benchmarks for techno-economic analysis be established to the extent possible for future studies, to facilitate direct comparison of various technologies. Based on the collective results of this program, it appears that hybrid geothermal power would benefit more from recovery of lithium and other metals, rather than REE. It is recommended that future studies be conducted at a higher- TRL and that sorbents be tested against actual geothermal fluid samples. Prior higher-TRL efforts to extract metals from geothermal brines should be further evaluated for lessons learned.

36 MATERIALS SCIENCE↗

Evanescent and inertial-like waves in rigidly rotating odd viscous liquids

Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves ( J. Fluid Mech ., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity 𝛺, give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection ( J. Fluid Mech ., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers 𝜅 which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies 𝜔 < 2⁢𝛺. We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.

Mechanics↗

Automated and Adaptive Mission Planning for Orbital Express

The Orbital Express space mission was a Defense Advanced Research Projects Agency (DARPA) lead demonstration of on-orbit satellite servicing scenarios, autonomous rendezvous, fluid transfers of hydrazine propellant, and robotic arm transfers of Orbital Replacement Unit (ORU) components. Boeing's Autonomous Space Transport Robotic Operations (ASTRO) vehicle provided the servicing to the Ball Aerospace's Next Generation Serviceable Satellite (NextSat) client. For communication opportunities, operations used the high-bandwidth ground-based Air Force Satellite Control Network (AFSCN) along with the relatively low-bandwidth GEO-Synchronous space-borne Tracking and Data Relay Satellite System (TDRSS) network. Mission operations were conducted out of the RDT&E Support Complex (RSC) at the Kirtland Air Force Base in New Mexico. All mission objectives were met successfully: The first of several autonomous rendezvous was demonstrated on May 5, 2007; autonomous free-flyer capture was demonstrated on June 22, 2007; the fluid and ORU transfers throughout the mission were successful. Planning operations for the mission were conducted by a team of personnel including Flight Directors, who were responsible for verifying the steps and contacts within the procedures, the Rendezvous Planners who would compute the locations and visibilities of the spacecraft, the Scenario Resource Planners (SRPs), who were concerned with assignment of communications windows, monitoring of resources, and sending commands to the ASTRO spacecraft, and the Mission planners who would interface with the real-time operations environment, process planning products and coordinate activities with the SRP. The SRP position was staffed by JPL personnel who used the Automated Scheduling and Planning ENvironment (ASPEN) to model and enforce mission and satellite constraints. The lifecycle of a plan began three weeks outside its execution on-board. During the planning timeframe, many aspects could change the plan, causing the need for re-planning. These variable factors, ranging from shifting contact times to ground-station closures and required maintenance times, are discussed along with the flexibility of the ASPEN tool to accommodate changes to procedures and the daily or long-range plan, which contributed to the success of the mission. This paper will present an introduction to ASPEN, a more in-depth discussion on its use on the Orbital Express mission, and other relative work. A description of ground operations after the SRP deliveries were made is included, and we briefly discuss lessons learned from the planning perspective and future work.

scheduling↗

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory

It is fundamental for the flourishing biological cells that membrane proteins mediate the process. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. Here, we present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.

59 BASIC BIOLOGICAL SCIENCES↗

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). Here, we demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.

42 ENGINEERING↗

Computer simulation of reaction and transport of core-scale serpentinization of Fe-bearing olivine and evolution of geological hydrogen

We present reactive flow and transport simulations of core-scale serpentinization of forsteritic, Fe-bearing olivine under hydrothermal conditions. The model captures fluid flow, evolving porosity–permeability, and redox-controlled H 2 production in a cylindrical core over 55 days at 245 °C and 37 bar. Key processes include olivine dissolution, precipitation of serpentine and magnetite, and oxidation of Fe2+ to Fe 3+ . Here, results show strong coupling among flow velocity, alteration front propagation, and spatially heterogeneous H 2 generation. Elevated H2 concentrations align with inlet-localized magnetite precipitation, consistent with experiments. Secondary mineral formation reduces porosity and permeability, altering transport pathways. Reactive flow at the fluid–solid interface governs H 2 generation rates and distribution. Dissolved SiO2 promotes serpentine and talc formation by suppressing brucite, while bicarbonate extends reaction duration and moderates surface complexation effects.

Geologic hydrogen↗

Spatial and temporal modeling of sub- and supercritical thermal energy storage

This paper describes a thermodynamic model that simulates the discharge cycle of a single-tank thermal energy storage (TES) system that can operate from the two-phase (liquid-vapor) to supercritical regimes for storage fluid temperatures typical of concentrating solar power plants. State-of-the-art TES design utilizes a two-tank system with molten nitrate salts; one major problem is the high capital cost of the salts (International Renewable Energy Agency, 2012). The alternate approach explored here opens up the use of low-cost fluids by considering operation at higher pressures associated with the two-phase and supercritical regimes. The main challenge to such a system is its high pressures and temperatures which necessitate a relatively high-cost containment vessel that represents a large fraction of the system capital cost. To mitigate this cost, the proposed design utilizes a single-tank TES system, effectively halving the required wall material. A single-tank approach also significantly reduces the complexity of the system in comparison to the two-tank systems, which require expensive pumps and external heat exchangers. A thermodynamic model is used to evaluate system performance; in particular it predicts the volume of tank wall material needed to encapsulate the storage fluid. The transient temperature of the tank is observed to remain hottest at the storage tank exit, which is beneficial to system operation. It is also shown that there is an optimum storage fluid loading that generates a given turbine energy output while minimizing the required tank wall material. Overall, this study explores opportunities to further improve current solar thermal technologies. The proposed single-tank system shows promise for decreasing the cost of thermal energy storage. (C) 2014 Elsevier Ltd. All rights reserved.

Tse, LA↗

Surface grid generation for wing-fuselage bodies

In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.

Smith, R. E.↗

Three-dimensional turbopump flowfield analysis

A program was conducted to develop a flow prediction method applicable to rocket turbopumps. The complex nature of a flowfield in turbopumps is described and examples of flowfields are discussed to illustrate that physics based models and analytical calculation procedures based on computational fluid dynamics (CFD) are needed to develop reliable design procedures for turbopumps. A CFD code developed at NASA ARC was used as the base code. The turbulence model and boundary conditions in the base code were modified, respectively, to: (1) compute transitional flows and account for extra rates of strain, e.g., rotation; and (2) compute surface heat transfer coefficients and allow computation through multistage turbomachines. Benchmark quality data from two and three-dimensional cascades were used to verify the code. The predictive capabilities of the present CFD code were demonstrated by computing the flow through a radial impeller and a multistage axial flow turbine. Results of the program indicate that the present code operated in a two-dimensional mode is a cost effective alternative to full three-dimensional calculations, and that it permits realistic predictions of unsteady loadings and losses for multistage machines.

Sharma, O. P.↗

Code Validation Study for Base Flows

New and old rocket launch concepts recommend the clustering of motors for improved lift capability. The flowfield of the base region of the rocket is very complex and can contain high temperature plume gases. These hot gases can cause catastrophic problems if not adequately designed for. To assess the base region characteristics, advanced computational fluid dynamics (CFD) is being used. As a precursor to these calculations the CFD code requires validation on base flows. The primary objective of this code validation study was to establish a high level of confidence in predicting base flows with the USA CFD code. USA has been extensively validated for fundamental flows and other applications. However, base heating flows have a number of unique characteristics so it was necessary to extend the existing validation for this class of problems. In preparation for the planned NLS 1.5 Stage base heating analysis, six case sets were studied to extend the USA code validation data base. This presentation gives a cursive review of three of these cases. The cases presented include a 2D axi-symmetric study, a 3D real nozzle study, and a 3D multi-species study. The results of all the studies show good general agreement with data with no adjustments to the base numerical algorithms or physical models in the code. The study proved the capability of the USA code for modeling base flows within the accuracy of available data.

Ascoli, Edward P.↗