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NASA NTRSDate not supplied

Fluid-Structure Interaction Simulations of the ASPIRE SR01 Supersonic Parachute

High-fidelity computational fluid dynamics (CFD) simulations have so far only played exploratory and supporting roles in the study and qualification of parachutes for planetary entry. The last few years have seen the maturation of coupled computational methods that are capable of modeling the complex fluid-structure interactions between a parachute canopy and the supersonic flow in the wake of an entry vehicle in flight conditions. One of the primary goals of these methods is to predict the peak opening load experienced by the parachute during inflation. The Launch, Ascent, and Vehicle Aerodynamics (LAVA)team is developing efficient, high-fidelity numerical methods to perform such challenging fluid-structure interaction simulations. A loose coupling approach is used to advance the solutions of a Cartesian ghost cell immersed boundary method CFD solver and a finite element computational structural dynamics (CSD) solver in space and time. The coupled solver is employed to simulate the ASPIRE SR01 flight test, where a build-to-print version of the Mars Science Laboratory parachute was inflated in supersonic conditions in the upper terrestrial atmosphere. The simulations conducted in the current paper predict a peak opening load that is within 10% of that from the flight test. Grid convergence with respect to the volume and structural domains is demonstrated, and less than 1% variation in the peak opening load is predicted between all grid resolutions.

ARMD↗

NASA NTRS1991

Electric propulsion system technology

The work performed on the Ion Propulsion System Technology Task in FY90 is described. The objectives of this work fall under two broad categories. The first of these deals with issues associated with the application of xenon ion thrusters for primary propulsion of planetary spacecraft, and the second with the investigation of technologies which will facilitate the development of larger, higher power ion thrusters to support more advanced mission applications. Most of the effort was devoted to investigation of the critical issues associated with the use of ion thrusters for planetary spacecraft. These issues may be succinctly referred to as life time, system integration, and throttling. Chief among these is the engine life time. If the engines do not have sufficient life to perform the missions of interest, then the other issues become unimportant. Ion engine life time was investigated through two experimental programs: an investigation into the reduction of ion engine internal sputter erosion through the addition of small quantities of nitrogen, and a long duration cathode life test. In addition, a literature review and analysis of accelerator grid erosion were performed. The nitrogen addition tests indicated that the addition of between 0.5 and 1.0 percent of nitrogen by mass to the xenon propellant results in a reduction in the sputter erosion of discharge chamber components by a factor of between 20 and 50, with negligible reduction in thruster performance. The long duration test of a 6.35-mm dia. xenon hollow cathode is still in progress, and has accumulated more than 4,000 hours of operation at an emission current of 25 A at the time of this writing. One of the major system integration issues concerns possible interactions of the ion thruster produced charge exchange plasma with the spacecraft. A computer model originally developed to describe the behavior of mercury ion thruster charge exchange plasmas was resurrected and modified for xenon propellant. This model enables one to calculate the flow direction and local density of the charge exchange plasma, and indicates the degree to which this plasma can flow upstream of the thruster exhaust plane. A continuing effort to investigate the most desirable throttling technique for noble gas ion thrusters concentrated this year on experimentally determining the fixed flow rate throttling range of a 30-cm dia. thruster with a two-grid accelerator system. These experiments demonstrated a throttling capability which covers a 2.8 to 1 variation in input power. This throttling range is 55 percent greater than expected, and is due to better accelerator system performance at low net-to-total voltage ratios than indicated in the literature. To facilitate the development of large, higher power ion thrusters several brief studies were performed. These include the development of a technique which simulates ion thruster operation without beam extraction, the development of an optical technique to measure ion thruster grid distortion due to thermal expansion, tests of a capacitance measurement technique to quantify the accelerator system grid separation, and the development of a segmented thruster geometry which enables near term development of ion thrusters at power levels greater than 100 kW. Finally, a paper detailing the benefits of electric propulsion for the Space Exploration Initiative was written.

Brophy, John R.↗

DOE OSTI2026

The Energy Exascale Earth System Model Version 3: 2. Overview of the Coupled System

The Energy Exascale Earth System Model version 3 (E3SMv3) represents the latest advancement in Earth system modeling developed by the U.S. Department of Energy (DOE). Building upon previous versions, E3SMv3 introduces significant updates across its coupled components to enhance capability and improve fidelity. The atmosphere component incorporates advancements in chemistry, aerosol-cloud interactions, convection, and microphysics. The ocean features a new time-stepping scheme and a higher-resolution unstructured mesh with sub-ice-shelf cavities, while the sea ice model integrates advanced snow and ice physics for more realistic cryospheric simulations. The land model introduces prognostic vegetation dynamics and a new sub-grid topographic treatment of solar radiation. A new tri-grid configuration harmonizes the horizontal grids of the land and river components for improved process coupling. It is enabled by a new non-linear remapping between the atmosphere and land. E3SMv3 underwent extensive testing through a comprehensive simulation campaign, including pre-industrial control, idealized CO 2 experiments, and historical simulations spanning 1850–2024. The model demonstrates significant improvements in simulating the evolution of the historical surface temperature, particularly addressing the “pothole cooling” bias in earlier versions. Reduced aerosol-related forcing contributes to more realistic radiative forcing and better alignment with the observational record. Ocean heat content (OHC) and sea ice trends are also improved as a result.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Overcoming the Technical Challenges of Coordinating Distributed Load Resources at Scale (Final Report)

Significant recent research has investigated the potential for loads to provide balancing services to the grid. However, this research has not addressed key issues that may arise when such schemes are applied at scale including: 1. Distribution Network Issues. Coordination of large numbers of loads could result in power flows that violate distribution network constraints; 2. Stability Issues. Certain strategies to control loads can exhibit nonlinearity in the form of period-adding bifurcations and chaos. Other control strategies can potentially synchronize the behavior of large numbers of loads. In both cases, the outcome can be power oscillations and instability; 3. Communication Network Issues. Bidirectional low-latency communication channels between a central controller (or several distributed controllers) and each resource are expensive and likely not necessary for effective coordination. Our research questions were: What network, stability, and communication issues might arise in practice when we coordinate large aggregations of loads? How can we coordinate loads to achieve performance objectives in a cost effective manner while avoiding these issues? The ultimate technical goal of the project was the development of network-aware, communication-constrained, non-disruptive load control strategies with stability guarantees that achieve the performance requirements of typical balancing services at a sufficiently low cost to enable the load aggregator and customer to profit. The overall goal was to establish credibility for load control at scale and contribute to U.S. energy security and environmental goals. The team succeeded in answering these research questions and developing these control strategies. The overall approach was based on the development of three testing environments: a simulation testbed, an experimental testbed (20 physical model houses with window-box air conditioners) coupled with the simulation testbed, and a field testbed (100 actual homes in Austin, TX) coupled with the simulation testbed, which enabled controller testing, identification of issues, controller development, and controller validation. The resulting controller was used to demonstrate fast timescale grid balancing (frequency regulation) by aggregations of physical and virtual air conditioners, with sufficient quality to participate in the electricity market. Cost benefit analysis showed overall benefits to the participating households, load aggregators, and the grid, especially if the control technology was integrated directly into existing programmable communicating thermostats. The project provides a variety of wider benefits. Our technology transfer and outreach activities lead us to choose an open-source licensing commercialization pathway, enabling the project results to be available to researchers, industry, and the public. Furthermore, new grid balancing technologies will increase grid flexibility and will enable higher penetrations of intermittent renewable energy resources, such as wind and solar, to be connected to the grid, reducing its environmental impact, and mitigating climate change to the benefit of society.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRSDate not supplied

WMLES for the Fifth High-Lift PredictionWorkshop Cases Using FUN3D

This paper presents solution assessments and grid convergence studies for the test cases outlined in the Fifth High-Lift Prediction Workshop (HLPW-5), focusing on the high-lift Common Research Models (CRM-HL). The study utilizes a wall-modeled large-eddy simulation (WMLES) methodology developed in the unstructured-grid, node-centered flow solver FUN3D. The second-order accurate simulations conducted in this study utilize a finite-volume spatial discretization and an implicit temporal scheme. Large-scale turbulent features are resolved away from the wall, with small-scale effects captured by the Vreman subgrid-scale model. An equilibrium wall function uses the first grid point off the wall serving as the critical interface between the wall model and the large-eddy simulation region, thus requiring careful placement in grid design. WMLES solutions are assessed for HLPW-5 cases, including a clean wing-body configuration and geometry-buildup configurations corresponding to the 5.1\% ONERA CRM-HL model. Grid-convergence studies are systematically conducted using uniformly refined grids. Moreover, simulation results and grid sensitivity are presented for the NASA 5.2\% CRM-HL configuration at both moderate and flight-scale Reynolds numbers. Overall, WMLES results are satisfactory and agree well with available experimental data, especially on sufficiently fine grids.

high-lift aerodynamics↗

DOE OSTI2021

Extreme metrics from large ensembles: investigating the effects of ensemble size on their estimates

Abstract. We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and – importantly – about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

A Modular AC to DC Interface Converter to Enable Lunar Surface Power Transmission

NASA is developing technology to enable sustained operations on extraterrestrial planetary bodies such as the Moon and Mars. One fundamentally enabling technology is long-distance electrical power transmission. This paper describes the Universal Modular Interface Converter (UMIC), which connects 120 VDC space power equipment to a 3 kVAC grid, and is intended to enable kilometer-distance transmission of 1s to 10s of kW of electrical power to support Artemis and future lunar missions. Specifically, this paper describes the technology within the UMIC product, its electrical power interfaces, and the state of its development. It also describes initial hardware and simulation test results of the UMIC.

Planetary surface power↗

DOE OSTI2024

Implementing a Hardware Testbed Using 3-Level ANPC Software Defined Inverters for Fault Analysis of a Transmission Network

In this paper, we propose the implementation of a hardware testbed using 3-level active neutral point clamped (ANPC) software-defined inverters for fault analysis. A test case transmission network equipped with two grid forming (GFM) inverters and four resistive loads is considered in this research. Firstly, grid forming control laws including PI feedback control and droop control are implemented to operate the inverters in parallel. Then, we implement a fault ride-through (FRT) logic and perform a simulation of the test system by applying a three-phase fault. Simulation results show the effectiveness of the fault recovery algorithm upon clearance of the fault. Finally, a 3-level ANPC software-defined inverter is programmed with required control laws and characterized through various lab experiments.

3-level ANPC inverter↗

DOE OSTI2017

A novel islanding detection technique for grid connected photovoltaic system

Islanding detection is the major issue in Grid Connected Photovoltaic (PV) System and still it remains a challenge for researchers to interconnect the PV system with the Grid. The algorithms which are listed in the literature are failed to identify the Islanding phenomena for the several source configuration. In this paper a novel islanding detection technique is presented to reduce the non-detection zone (NDZ) at the point of common coupling (PCC) and it can be widely used for various renewable energy system configurations. The simulations have been carried out in Matlab/Simulink for several test conditions. The simulations results are presented to confirm the effectiveness of the proposed method.

14 SOLAR ENERGY↗

DOE OSTI2025

Operation and Control of Electric Vehicle Charger with Enhanced Dynamic Performance Under Non-Ideal Grid Voltage Condition

This paper presents a three-phase electric vehicle charger connected to the grid, featuring multiple boost converters on the DC side, specifically designed to ensure smooth, oscillation-free power transfer during unsymmetrical voltage sags. Precise control mechanisms are implemented on the boost converter side to regulate both voltage and current on the electric vehicle side, thereby maintaining optimal charging conditions. The control architecture for both the grid-connected and boost converter components is based on the Lyapunov energy function, which is employed to achieve superior dynamic performance and stability. The system's robustness and reliability are demonstrated through its ability to maintain stable operation and efficient power transfer despite fluctuations in grid conditions. Furthermore, the implementation of Lyapunov-based control ensures rapid response and minimal energy loss, enhancing the overall efficiency of the system. To validate the effectiveness of this approach, a comprehensive model of the system was developed and tested using MATLAB/Simulink, with detailed computer simulations conducted across various significant case studies.

DC-DC boost converter↗

DOE OSTI2018

Network Reduction Algorithm for Developing Distribution Feeders for Real-Time Simulators

As advanced grid-support functions (AGF) become more widely used in grid-connected photovoltaic (PV) inverters, utilities are increasingly interested in their impacts when implemented in the field. These effects can be understood by modeling feeders in real-time simulators and test PV inverters using power hardware-in-the-loop (PHIL) techniques. This paper presents a novel feeder model reduction algorithm using a ruin & reconstruct methodology that enables large feeders to be solved and operated on real-time computing platforms. Two Hawaiian Electric feeder models in Synergi Electric's load flow software were converted to reduced order models in OpenDSS, and subsequently implemented in the OPAL-RT real-time digital testing platform. Smart PV inverters were added to the realtime model with AGF responses modeled after characterizing commercially available hardware inverters. Finally, hardware inverters were tested in conjunction with the real-time model using PHIL techniques so that the effects of AGFs on the feeders could be analyzed.

14 SOLAR ENERGY↗

NASA NTRS2004

Preparing and Analyzing Iced Airfoils

SmaggIce version 1.2 is a computer program for preparing and analyzing iced airfoils. It includes interactive tools for (1) measuring ice-shape characteristics, (2) controlled smoothing of ice shapes, (3) curve discretization, (4) generation of artificial ice shapes, and (5) detection and correction of input errors. Measurements of ice shapes are essential for establishing relationships between characteristics of ice and effects of ice on airfoil performance. The shape-smoothing tool helps prepare ice shapes for use with already available grid-generation and computational-fluid-dynamics software for studying the aerodynamic effects of smoothed ice on airfoils. The artificial ice-shape generation tool supports parametric studies since ice-shape parameters can easily be controlled with the artificial ice. In such studies, artificial shapes generated by this program can supplement simulated ice obtained from icing research tunnels and real ice obtained from flight test under icing weather condition. SmaggIce also automatically detects geometry errors such as tangles or duplicate points in the boundary which may be introduced by digitization and provides tools to correct these. By use of interactive tools included in SmaggIce version 1.2, one can easily characterize ice shapes and prepare iced airfoils for grid generation and flow simulations.

Vickerman, Mary B.↗

DOE OSTI2021

Electric Water Heaters for Transactive Systems: Model Evaluations and Performance Quantification

Electric water heaters (EWHs) are opportune appliances for implementing demand-side control. EWH models serve as a fundamental step toward accurately estimating EWH flexibility potential and designing proper control strategies. Existing studies have adapted numerous modeling approaches in evaluating the potential of EWHs for a variety of grid applications. This paper presents an analytical study that evaluates the performance of state-of-art EWH models in terms of accuracy and computational complexity for adaptation in evaluation studies for the transactive system. The work proposes a transactive control strategy that optimally utilizes the thermal inertia of EWHs for providing grid services. Here, the performance of the control strategy and the impact of modeling accuracy is evaluated for device-level and feeder-level use cases using the IEEE 123 node test distribution system appropriately populated with EWHs. The simulation results illustrate the effectiveness of the control strategy in reducing the feeder demand during peak period by 13% and also quantities the impact of using simplified modeling approaches for determining the potential of EWHs for providing grid services.

42 ENGINEERING↗

DOE OSTI2026

Control and Real-Time Simulation of Microgrids with EV Fast-Charging and Grid-Forming Resources

Fast charging stations (FCSs) for electric vehicles (EVs) can behave as constant power loads, which is problematic for the operation of grid-forming (GFM) inverter-based resources (IBRs). To tackle this problem, this paper proposes a control suite that makes FCSs responsive to ac voltage and frequency disturbances. To test the performance of the FCS controls, the paper also sets forth theory to compensate for time-delays appearing in the real-time simulation of microgrid models divided into several central processing units (CPUs). Furthermore, these contributions are showcased via multi-CPU real-time simulations of a faulted microgrid having EV FCSs and GFM IBRs powered by photovoltaic solar arrays as well as power hardware-in-the-loop experiments. These contributions are significant to address NERC recommendations and IEEE standards.

14 SOLAR ENERGY↗

DOE OSTI2025

A Review of Quantum Computing Technologies in Power System Optimization

As modern power grids increasingly integrate variable renewable generation, distributed energy resources, and energy storage systems, classical optimization techniques are facing unprecedented challenges. This review examines the emerging application of quantum computing to overcome these challenges in power system optimization, including optimal power flow (OPF), unit commitment (UC), economic dispatch (ED), and intelligent switching and topology optimization (IS-TO). Recent research has introduced various quantum methodologies—such as gate-based, annealing-based, variational algorithms, and quantum-inspired algorithms—to address the combinatorial complexity inherent in grid reconfiguration and energy management. The review summaries the quantum algorithms, quantum devices and the power system test cases, highlighting hybrid quantum–classical strategies that leverage the complementary strengths of both paradigms. Some quantum advantages have been observed, including theoretical speedup, accurate simulation results, scalable qubit usage, efficient QUBO mapping. In particular, the review emphasizes the importance of integrating quantum optimization techniques with classical control frameworks, these hybrid approaches demonstrate the potential to improve real-time grid management and operational reliability. A significant portion of the analysis is devoted to the practical limitations of current quantum devices. Present-day quantum hardware, operating in the noisy intermediate-scale quantum (NISQ) era, remains highly sensitive to noise and limited in qubit connectivity, which constrains the scale and accuracy of implemented algorithms. The review delves into specific challenges such as the need for qubit-efficient encoding techniques and error mitigation strategies that are critical for handling real-world grid optimization problems. In addition, the work draws attention to the performance discrepancies between theoretical quantum speedups and experimental validations, underscoring the importance of rigorous benchmark studies using representative power grid test cases. In summary, this review highlights both the promise and limitations of quantum computing for power system optimization. It provides a comprehensive overview of the state-of-the-art technologies, categorizes recent advancements in algorithm design, and discusses practical considerations for implementation, and serves as an informative resource on current research. Future research directions include developing robust hybrid frameworks, advancing qubit-efficient formulations, and scaling up experimental demonstrations to confirm the theoretical advantages of quantum methods in large-scale power system operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2009

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes - Part 1

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

Diskin, Boris↗

DOE OSTI2019

Test-Based Modeling of Photovoltaic Inverter Impact on Distribution Systems

Distributed PV has important effects on overcurrent, overvoltage and islanding protection. These effects are more difficult to analyze because the faulted behavior of PV inverters is less well understood than for rotating machines. Full transient models of the inverter can be accurate, but that approach requires inverter design details and simulation software that doesn’t easily interoperate with utility protection system software. Further, anomalous model behaviors often emerge at different grid conditions, and these are difficult to fix in a proprietary model. Testing provides another approach to characterize inverters, validate models or answer questions of application. This earlier work found major impacts from the inverter design, firmware, operating point and balance-of-system components. Our objective is to characterize PV inverters from black-box testing, leading to standard test reports that could provide parameter sets for widely-implemented models in software tools. The tool vendors can then develop standard inverter models, as they did for rotating machines and exciters. Besides fully detailed transient models, inverters can be represented with steady-state current sources, dynamically controlled current sources or non-linear frequency-dependent black boxes. Type-test data could support the last three kinds of model. Short circuit and sag tests would encompass the basic fault types, reporting the maximum transient and rms currents over all power levels and points-on-wave within four time ranges : 1) 0 to 1 cycles, for close and latch consideration 2) 1 to 4 cycles, for equipment withstand 3) 4 to 30 cycles, for interrupt ratings 4) 30 cycles and beyond, for backup protection analysis Open circuit tests would vary output power and power factor, and report the maximum rms voltage from 1 to 10 cycles after the event. Without models, the type-test data could also provide upper limits on the expected overvoltages and overcurrents.

Wieserman, Laura M.↗

DOE OSTI2017

An Investigation into Solution Verification for CFD-DEM

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.

97 MATHEMATICS AND COMPUTING↗