Results for “Multiphysics systems” — Page 2

NASA NTRS2005

Verification of a Multiphysics Toolkit against the Magnetized Target Fusion Concept

In the spring of 2004 the Advanced Concepts team at MSFC embarked on an ambitious project to develop a suite of modeling routines that would interact with one another. The tools would each numerically model a portion of any advanced propulsion system. The tools were divided by physics categories, hence the name multiphysics toolset. Currently most of the anticipated modeling tools have been created and integrated. Results are given in this paper for both a quarter nozzle with chemically reacting flow and the interaction of two plasma jets representative of a Magnetized Target Fusion device. The results have not been calibrated against real data as of yet, but this paper demonstrates the current capability of the multiphysics tool and planned future enhancements

Thomas, Scott↗

NASA NTRS2023

Multiphysics Modeling of Electrode Dissolution under Hydrodynamic Conditions in Low Conductivity Water

Efficient plug-flow electrochemical reactors are characterized by their ability to effectively convert species with significant ionic strength and/or with the assistance of a well-behaved electrolyte. Because of the classic electroconductivity requirement, electrochemical reactors are not particularly attractive options for applications with low-conductivity conditions, especially for low-pressure feeds. However, these reactors can still find application in dedicated processes such as ultra-clean water conditioning and biological-coupled separation systems. Consequently, a multi-physics model was developed using COMSOL Multiphysics to characterize different reactor-design conditions based on the Tertiary Current Distribution which accounts for the effects of expected variations in electrolyte composition and ionic strength on the electrochemical process, as well as solution resistance and electrode kinetics. The modelling framework presented here employs single-phase laminar fluid flow, the Nernst-Planck equation, the water-based electroneutrality condition, and concentration-dependent overpotentials. This investigation particularly explores the electrolysis process of “anodic dissolution,” in which elemental species dissociate from the solid matrix of the electrode and enter the liquid phase of the electrolyte as soluble ions. The reactor configuration of interest has a rectangular parallel-electrode design and is operated galvanostatically. A series of parametric studies are carried out to inspect the response of the system when hydrodynamic, kinetic, and geometric conditions are changed. The parametric sweep resulted in variable effluent concentrations and system voltage, which reveal underlaying optimization patterns for electrode dissolution in low conductivity water.

Multiphysics↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗

NASA NTRS2023

Coupled Fluid Dynamics and Material Response Simulations for Nitrogen High Enthalpy Flows

The study focuses on the interaction of nitrogen flows with thermal protection systems during atmospheric re-entry for NASA flight missions. The Ares multiphysics coupling tool is employed to investigate the coupling between the fluid (US3D) and material response (Icarus) solvers using various modeling approaches. These approaches include the equilibrium thin-film coefficients approach, a weakly coupled approach with temperature coupling, and an approach considering the full chemical composition of the surface and the transfer of pyrolysis gases. The objective is to understand and accurately represent the mechanisms of nitrogen interaction with the surface, such as nitridation and catalytic recombination. The study aims to assess the accuracy of the different approaches by comparing them to experimental results obtained from NASA arc-jet facilities. By addressing these challenges and improving the understanding of nitrogen-surface interactions, it is expected to enhance the design and performance analysis of thermal protection systems for future missions.

Ablation↗

NASA NTRS2005

CFD Multiphysics Tool

The recent bold initiatives to expand the human presence in space require innovative approaches to the design of propulsion systems whose underlying technology is not yet mature. The space propulsion community has identified a number of candidate concepts. A short list includes solar sails, high-energy-density chemical propellants, electric and electromagnetic accelerators, solar-thermal and nuclear-thermal expanders. For each of these, the underlying physics are relatively well understood. One could easily cite authoritative texts, addressing both the governing equations, and practical solution methods for, e.g. electromagnetic fields, heat transfer, radiation, thermophysics, structural dynamics, particulate kinematics, nuclear energy, power conversion, and fluid dynamics. One could also easily cite scholarly works in which complete equation sets for any one of these physical processes have been accurately solved relative to complex engineered systems. The Advanced Concepts and Analysis Office (ACAO), Space Transportation Directorate, NASA Marshall Space Flight Center, has recently released the first alpha version of a set of computer utilities for performing the applicable physical analyses relative to candidate deep-space propulsion systems such as those listed above. PARSEC, Preliminary Analysis of Revolutionary in-Space Engineering Concepts, enables rapid iterative calculations using several physics tools developed in-house. A complete cycle of the entire tool set takes about twenty minutes. PARSEC is a level-zero/level-one design tool. For PARSEC s proof-of-concept, and preliminary design decision-making, assumptions that significantly simplify the governing equation sets are necessary. To proceed to level-two, one wishes to retain modeling of the underlying physics as close as practical to known applicable first principles. This report describes results of collaboration between ACAO, and Embry-Riddle Aeronautical University (ERAU), to begin building a set of level-two design tools for PARSEC. The "CFD Multiphysics Tool" will be the propulsive element of the tool set. The name acknowledges that space propulsion performance assessment is primarily a fluid mechanics problem. At the core of the CFD Multiphysics Tool is an open-source CFD code, HYP, under development at ERAU. ERAU is renowned for its undergraduate degree program in Aerospace Engineering the largest in the nation. The strength of the program is its applications-oriented curriculum, which culminates in one of three two-course Engineering Design sequences: Aerospace Propulsion, Spacecraft, or Aircraft. This same philosophy applies to the HYP Project, albeit with fluid physics modeling commensurate with graduate research. HYP s purpose, like the Multiphysics Tool s, is to enable calculations of real (three-dimensional; geometrically complex; intended for hardware development) applications of high speed and propulsive fluid flows.

Perrell, Eric R.↗

NASA NTRS2019

Towards Multiphysics Prediction Capability for the KSC Launch Environment

Launching powerful space vehicles like the next-generation Space Launch System (SLS) creates extreme pressure waves that could damage the vehicle and the launch environment at NASA’s Kennedy Space Center (KSC). To ensure mission safety, the Ignition Overpressure Protection and Sound Suppression (IOP/SS) water deluge system suppresses the strong acoustic waves by delivering almost a half-million gallons of water to the mobile launcher and flame deflector. To better understand the effectiveness of this system at different operating conditions, the Launch Ascent and Vehicle Analysis (LAVA) code, developed at NASA’s Ames Research Center, is currently being modified and extended to incorporate the complex physics needed to model the IOP/SS system.

Angel, Jordan B.↗

NASA NTRS2015

The Effect of Resistance on Rocket Injector Acoustics

Combustion instability, where unsteady heat release couples with acoustic modes, has long been an area of concern in liquid rocket engines. Accurate modeling of the acoustic normal modes of the combustion chamber is important to understanding and preventing combustion instability. This study evaluates the effect of injector resistance on the mode shapes and complex eigen-frequencies of an injector/combustion chamber system by defining a high Mach-flow form of the convective wave equation (see Eq. 1) in COMSOL Multiphysics' Coefficient Form PDE Mathematics Module.

Morgan, C. J.↗

NASA NTRS2022

Validation of a High-Fidelity Supersonic Parachute Inﬂation Dynamics Model and Best Practice

The parachute inflation dynamics (PID) of a Disk-Gap-Band (DGB) parachute system travelling at supersonic velocities in the high-altitude Earth atmosphere is simulated using a high-fidelity, multiphysics, massively-parallel computational framework. The sensitivity of the simulation results with respect to critical modelling and simulation parameters, including the fluid mechanical governing equations (Euler vs Navier-Stokes with RANS turbulence closure vs Navier-Stokes with LES turbulence closer), the interaction between the flow and the suspension lines (accounted for vs not accounted for), the dynamics of the payload (restrained vs free), and the material model of the heterogeneous fabric canopy (Saint-Venant Kirchoff vs mechanics-informed multiscale neural network), is extensively investigated. The parameter investigation is enabled by advancements to the state-of-the-art in the modelling and simulation of the supersonic parachute inflation process, which are presented as part of the computational framework. The predictive quality of the computational framework in the context of supersonic PID is validated by comparison of the simulation results with the experimental results from NASA’s Advanced Supersonic Parachute Research (ASPIRE) project. Through the validation, best practices for the modelling and simulation of supersonic PID are developed and proposed.

Rabinovitch, Jason↗

NASA NTRSDate not supplied

System Modeling of a Lunar Molten Regolith Electrolysis Plant

Introduction: In-Situ Resource Utilization (ISRU) is the process of extracting local resources to produce commodities for propulsion, life support systems, and off-planet construction rather than transporting consumables from Earth. Molten Regolith Electrolysis (MRE) is a novel ISRU method of extracting oxygen gas and metal alloy from lunar regolith. The MRE process involves placing lunar regolith between two electrodes, through which current is passed, to melt the regolith and reduce the metal oxide constituents by direct electrolysis (e.g. FeO, SiO2, MgO, Al2O3) into oxygen gas and metal alloys. The oxygen is liquefied and used as propellant for landers, while the metals (e.g. Ferro-alloys) are further processed and used in structural building materials and parts manufacturing. A system model was developed that accounted for the major processes of an MRE plant (from excavation of raw materials to storage of products) to assess the feasibility of a lunar MRE plant. The System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team utilized its previously documented system sizing model, the Mission Analysis and Integration Tool (MAIT) [1] as framework of the system model. MAIT uses MATLAB/Simulink to integrate subsystem models into a complete system model of the MRE plant. Total mass, volume, and power requirements were computed for numerous iterations of a MRE plant. System Model: Figure 1: MRE Plant Block Diagram The regolith excavation model determines the mass and power needed to excavate sufficient regolith. The preheating auger initiates the regolith heating process before regolith enters the MRE re-actor to reduce the energy required to turn the solid into a molten liquid. The MRE reactor is modeled in COMSOL Multiphysics and based on the research by Dominguez, Sibille, and Schreiner [2, 3, 4]. This preliminary reactor model provides an accurate calculation of thermal equilibrium during electrochemical operation of the reactor system to assess the optimal mass and power required to process the inlet flow of regolith. The model also computes the outlet flowrates of oxygen and molten products. For this analysis, the primary components of the metal alloy considered were iron and silicon. The oxygen is then purified using an Yttrium Stabilized Zirconia (YSZ) electrode, followed by liquefaction using a 90K cryocooler to be stored as liquid oxygen in insulated cylindrical tanks. In future iterations of the system model, the molten metal tapped from the MRE reactor will undergo additional processing or refinement. However, downstream handling of metals is currently a technology gap that is missing a high TRL subsystem model. Therefore, for this analysis, the accumulated metal alloy stream terminates after leaving the MRE reactor. Study Goals: This analysis investigates multiple input variables to the system to determine the sensitivity of a (near) complete plant at full-scale. This preliminary investigation ran parametric sweeps on the MRE reactor geometry, electrical current supply, layers of multi-layer insulation (MLI) on the reactor, size of the electrodes in the oxygen purification model, and regolith composition (based on landing site location). Three production targets of oxygen (1,000, 10,000, and 50,000 kg/yr) were investigated for this analysis. The parametric sweeps conducted in this analysis provide valuable insight into the expected impact of the various model inputs on plant size. This information can be used to identify the most critical components of the plant and guide future decisions on allocating funding for research and development, providing subsystem developers with appropriate interfaces with downstream and upstream processes, and assessing the overall feasibility of MRE when compared to other ISRU plants. References: [1] Carlson, A. et al. (2024) ICES, ICES-2024-53. [2] Dominguez, D.A., and Sibille, L. (2011) AIAA, AIAA-2011-700. [3] Schreiner, S.S. (2015) MIT, Dissertation. [4] Schreiner, S.S. et al. (2016) ASR, 57(7), pp.1585-1603.

ISRU↗

NASA NTRSDate not supplied

Modeling of a Solid Oxide Fuel Cell as Part of a Predictive Functional Model for Aerospace Fuel-Cell Systems

This paper will discuss initial efforts at modeling a solid oxide fuel cell (SOFC) for aerospace applications. Fuel cells historically have been used in spacecraft from the Gemini to the Shuttle era for providing spacecraft power with the added benefit of producing water for crew use. However, there are many potential applications for fuel cells and electrolyzers in spaceflight, including oxygen generation, in-situ resource utilization (ISRU) and propellant production. This proof-of-concept model has been developed using a commercial multiphysics modeling software package. Two-dimensional and one-dimensional isothermal models were created based on a certain SOFC design and results were compared to test data from the real system. Local Butler-Volmer kinetic relations were adjusted, and an effective porous medium approach was taken in order to capture how the many interconnects between cells in the gas channels affected fluid flow. The model was able to reproduce polarization curves derived from test data within around 0.02 Volts for a given current density. This model could be adapted to model a solid oxide electrolyzer, proton exchange membrane fuel cell, or other type of fuel cell technology in order to understand how these types of technologies could fit into broader spacecraft designs and advance the capabilities of spaceflight systems.

Mary Lou Nadeau↗

NASA NTRSDate not supplied

Modeling of a Solid Oxide Fuel Cell as Part of a Predictive Functional Model for Aerospace Fuel-Cell Systems

This paper will discuss initial efforts at modeling a solid oxide fuel cell (SOFC) for aerospace applications. Fuel cells historically have been used in spacecraft from the Gemini to the Shuttle era for providing spacecraft power with the added benefit of producing water for crew use. However, there are many potential applications for fuel cells and electrolyzers in spaceflight, including oxygen generation, in-situ resource utilization (ISRU) and propellant production. This proof-of-concept model has been developed using a commercial multiphysics modeling software package. Two-dimensional and one-dimensional isothermal models were created based on a certain SOFC design and results were compared to test data from the real system. Local Butler-Volmer kinetic relations were adjusted, and an effective porous medium approach was taken in order to capture how the many interconnects between cells in the gas channels affected fluid flow. The model was able to reproduce polarization curves derived from test data within around 0.02 Volts for a given current density. This model could be adapted to model a solid oxide electrolyzer, proton exchange membrane fuel cell, or other type of fuel cell technology in order to understand how these types of technologies could fit into broader spacecraft designs and advance the capabilities of spaceflight systems.

Mary Lou Nadeau↗

NASA NTRSDate not supplied

Modeling of a Solid Oxide Fuel Cell as Part of a Predictive Functional Model for Aerospace Fuel-Cell Systems

This paper will discuss initial efforts at modeling a solid oxide fuel cell (SOFC) for aerospace applications. Fuel cells historically have been used in spacecraft from the Gemini to the Shuttle era for providing spacecraft power with the added benefit of producing water for crew use. However, there are many potential applications for fuel cells and electrolyzers in spaceflight, including oxygen generation, in-situ resource utilization (ISRU) and propellant production. This proof-of-concept model has been developed using a commercial multiphysics modeling software package. Two-dimensional and one-dimensional isothermal models were created based on a certain SOFC design and results were compared to test data from the real system. Local Butler-Volmer kinetic relations were adjusted, and an effective porous medium approach was taken in order to capture how the many interconnects between cells in the gas channels affected fluid flow. The model was able to reproduce polarization curves derived from test data within around 0.02 Volts for a given current density. This model could be adapted to model a solid oxide electrolyzer, proton exchange membrane fuel cell, or other type of fuel cell technology in order to understand how these types of technologies could fit into broader spacecraft designs and advance the capabilities of spaceflight systems.

Mary Lou Nadeau↗

NASA NTRSDate not supplied

Modeling of a Solid Oxide Fuel Cell as Part of a Predictive Functional Model for Aerospace Fuel-Cell Systems

This paper will discuss initial efforts at modeling a solid oxide fuel cell (SOFC) for aerospace applications. Fuel cells historically have been used in spacecraft from the Gemini to the Shuttle era for providing spacecraft power with the added benefit of producing water for crew use. However, there are many potential applications for fuel cells and electrolyzers in spaceflight, including oxygen generation, in-situ resource utilization (ISRU) and propellant production. This proof-of-concept model has been developed using a commercial multiphysics modeling software package. Two-dimensional and one-dimensional isothermal models were created based on a certain SOFC design and results were compared to test data from the real system. Local Butler-Volmer kinetic relations were adjusted, and an effective porous medium approach was taken in order to capture how the many interconnects between cells in the gas channels affected fluid flow. The model was able to reproduce polarization curves derived from test data within around 0.02 Volts for a given current density. This model could be adapted to model a solid oxide electrolyzer, proton exchange membrane fuel cell, or other type of fuel cell technology in order to understand how these types of technologies could fit into broader spacecraft designs and advance the capabilities of spaceflight systems.

Mary Lou Nadeau↗

NASA NTRS2012

Piezocomposite Actuator Arrays for Correcting and Controlling Wavefront Error in Reflectors

Three reflectors have been developed and tested to assess the performance of a distributed network of piezocomposite actuators for correcting thermal deformations and total wave-front error. The primary testbed article is an active composite reflector, composed of a spherically curved panel with a graphite face sheet and aluminum honeycomb core composite, and then augmented with a network of 90 distributed piezoelectric composite actuators. The piezoelectric actuator system may be used for correcting as-built residual shape errors, and for controlling low-order, thermally-induced quasi-static distortions of the panel. In this study, thermally-induced surface deformations of 1 to 5 microns were deliberately introduced onto the reflector, then measured using a speckle holography interferometer system. The reflector surface figure was subsequently corrected to a tolerance of 50 nm using the actuators embedded in the reflector's back face sheet. Two additional test articles were constructed: a borosilicate at window at 150 mm diameter with 18 actuators bonded to the back surface; and a direct metal laser sintered reflector with spherical curvature, 230 mm diameter, and 12 actuators bonded to the back surface. In the case of the glass reflector, absolute measurements were performed with an interferometer and the absolute surface was corrected. These test articles were evaluated to determine their absolute surface control capabilities, as well as to assess a multiphysics modeling effort developed under this program for the prediction of active reflector response. This paper will describe the design, construction, and testing of active reflector systems under thermal loads, and subsequent correction of surface shape via distributed peizeoelctric actuation.

piezoelectric actuation↗

NASA NTRS2023

Analytical Design and Performance Estimation Methods for Aircraft Permanent Magnet Synchronous Machines

The design of an electric motor drivetrain is a complex multiphysics problem. Low fidelity motor drivetrain sizing can be a key tool in the design cycle of an electric motor drivetrain and for system level studies of aircraft configurations. However, low fidelity sizing can lead to misleading results if all the physics involved in a motor design are not properly accounted for. This paper provides details on modeling approaches for initial design and sizing of permanent magnet synchronous electric machines. The goal of this paper is to provide the reader an understanding of the key principles of motor design and some modeling approaches to perform initial sizing of an electric motor and its inverter.

Thomas F. Tallerico↗

NASA NTRSDate not supplied

Silver Electrolysis for Disinfection of Spacecraft Potable Water: 2024 Update

Anodic dissolution of silver electrodes, or “silver electrolysis,” is being investigated as a means of introducing biocidal silver into potable water on exploration spacecraft. This paper provides an update on the effort to implement this technology into a spacecraft potable water system. Previous papers reported on the feasibility of the technology for this application, strategies to prevent a potential fault condition termed “electrode bridging,” results from a preliminary investigation into the cathode reaction, and preliminary multiphysics modeling of the reactor. Since then, work has begun on the design of a next-generation silver electrolysis reactor prototype that will incorporate improvements identified in previous testing and package the reactor in a more flight-like configuration. This development effort has included additional testing to optimize the reactor design for prevention of electrode bridging, further investigation into the cathode reaction (including the use of a dissolved hydrogen sensor), and an assessment of the feasibility of using the reactor in other applications, such as for microbial shock and preparation for system dormancy.

silver biocide↗

NASA NTRSDate not supplied

Silver Electrolysis for Disinfection of Spacecraft Potable Water: 2024 Update

Anodic dissolution of silver electrodes, or “silver electrolysis,” is being investigated as a means of introducing biocidal silver into potable water on exploration spacecraft. This paper provides an update on the effort to implement this technology into a spacecraft potable water system. Previous papers reported on the feasibility of the technology for this application, strategies to prevent a potential fault condition termed “electrode bridging,” results from a preliminary investigation into the cathode reaction, and preliminary multiphysics modeling of the reactor. Since then, work has begun on the design of a next-generation silver electrolysis reactor prototype that will incorporate improvements identified in previous testing and package the reactor in a more flight-like configuration. This development effort has included additional testing to optimize the reactor design for prevention of electrode bridging, further investigation into the cathode reaction (including the use of a dissolved hydrogen sensor), and an assessment of the feasibility of using the reactor in other applications, such as for microbial shock and preparation for system dormancy.

silver biocide↗

NASA NTRS2019

Numerical Model of the Mars Electrostatic Precipitator

NASA's future human exploration missions will require chemical processing plants to convert local resources into consumables to support astronaut activities. The thin and mostly carbon dioxide atmosphere of Mars is estimated to have 1 - 10 particles/cu.cm with diameters of 1 - 10 m and up to 1000 particles/cu.cm during storms. The dust in the Martian atmosphere can foul chemical reactors and pose a risk to life support systems. Electrostatic precipitation (ESP) removes dust particles from the Martian atmosphere. The Electrostatics and Surface Physics Laboratory at NASA's Kennedy Space Center has developed a COMSOL Multiphysics(Registered Trademark) model of an ESP for dust filtration on Mars. The fundamental principles of an ESP can be simulated by four physics modules: plasma, AC/DC electromagnetics, computational fluid dynamics (CFD), and particle tracing. In the ESP model presented here, the plasma module was solved to estimate particle charge. The AC/DC and CFD module were solved for the electrostatic force and fluid force. The particle-tracing module was solved for particle collection efficiency.

Wang, Jerry J.↗