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NASA NTRS2016

Augmenting Conceptual Design Trajectory Tradespace Exploration with Graph Theory

Within conceptual design changes occur rapidly due to a combination of uncertainty and shifting requirements. To stay relevant in this fluid time, trade studies must also be performed rapidly. In order to drive down analysis time while improving the information gained by these studies, surrogate models can be created to represent the complex output of a tool or tools within a specified tradespace. In order to create this model however, a large amount of data must be collected in a short amount of time. By this method, the historical approach of relying on subject matter experts to generate the data required is schedule infeasible. However, by implementing automation and distributed analysis the required data can be generated in a fraction of the time. Previous work focused on setting up a tool called multiPOST capable of orchestrating many simultaneous runs of an analysis tool assessing these automated analyses utilizing heuristics gleaned from the best practices of current subject matter experts. In this update to the previous work, elements of graph theory are included to further drive down analysis time by leveraging data previously gathered. It is shown to outperform the previous method in both time required, and the quantity and quality of data produced.

Dees, Patrick D.↗

NASA NTRS2016

Augmenting Conceptual Design Trajectory Tradespace Exploration with Graph Theory

Dees, Patrick D.↗

DOE OSTI2019

Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a deep learning framework for learning Koopman operators of nonlinear dynamical systems. We show that this novel method automatically selects efficient deep dictionaries, outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict quantitatively 100 steps into the future, using only a single timepoint, and qualitative oscillatory behavior 400 steps into the future.

koopman operators, machine learning, deep learning↗

DOE OSTI2016

A thermodynamic study of shear banding in polymer solutions

Although shear banding is a ubiquitous phenomenon observed in soft materials, the mechanisms that give rise to shear-band formation are not always the same. In this work, we develop a new two-fluid model for semi-dilute entangled polymer solutions using the generalized bracket approach of nonequilibrium thermodynamics. The model is based on the hypothesis that the direct coupling between polymer stress and concentration is the driving mechanism of steady shear-band formation. To obtain smooth banded profiles in the two-fluid framework, a new stress-diffusive term is added to the time evolution equation for the conformation tensor. The advantage of the new model is that the differential velocity is treated as a state variable. This allows a straightforward implementation of the additional boundary conditions arising from the derivative diffusive terms with respect to this new state variable. To capture the overshoot of the shear stress during the start of a simple shear flow, we utilize a nonlinear Giesekus relaxation. Moreover, we include an additional relaxation term that resembles the term used in the Rouse linear entangled polymer model to account for convective constraint release and chain stretch to generate the upturn of the flow curve at large shear rates. Numerical calculations performed for cylindrical Couette flow confirm the independency of the solution from the deformation history and initial conditions. Furthermore, we find that stress-induced migration is the responsible diffusive term for steady-state shear banding. Because of its simplicity, the new model is an ideal candidate for the use in the simulation of more complex flows.

42 ENGINEERING↗

NASA NTRS2010

Computational Analyses of Pressurization in Cryogenic Tanks

A comprehensive numerical framework utilizing multi-element unstructured CFD and rigorous real fluid property routines has been developed to carry out analyses of propellant tank and delivery systems at NASA SSC. Traditionally CFD modeling of pressurization and mixing in cryogenic tanks has been difficult primarily because the fluids in the tank co-exist in different sub-critical and supercritical states with largely varying properties that have to be accurately accounted for in order to predict the correct mixing and phase change between the ullage and the propellant. For example, during tank pressurization under some circumstances, rapid mixing of relatively warm pressurant gas with cryogenic propellant can lead to rapid densification of the gas and loss of pressure in the tank. This phenomenon can cause serious problems during testing because of the resulting decrease in propellant flow rate. With proper physical models implemented, CFD can model the coupling between the propellant and pressurant including heat transfer and phase change effects and accurately capture the complex physics in the evolving flowfields. This holds the promise of allowing the specification of operational conditions and procedures that could minimize the undesirable mixing and heat transfer inherent in propellant tank operation. In our modeling framework, we incorporated two different approaches to real fluids modeling: (a) the first approach is based on the HBMS model developed by Hirschfelder, Beuler, McGee and Sutton and (b) the second approach is based on a cubic equation of state developed by Soave, Redlich and Kwong (SRK). Both approaches cover fluid properties and property variation spanning sub-critical gas and liquid states as well as the supercritical states. Both models were rigorously tested and properties for common fluids such as oxygen, nitrogen, hydrogen etc were compared against NIST data in both the sub-critical as well as supercritical regimes.

Ahuja, Vineet↗

DOE OSTI2014

Integrated Lift- and Wall-Force Closures in Computational Fluid Dynamics (CMFD)

In this report, we provide the necessary background to put this work in context and for a more detailed background, the reader is referred to CASL 2013 report. Central constraints on the design of LWRs are thermal-structural limits, e.g., maximum fuel pin temperature and maximum allowable working pressure in a pressure vessel. In both of these cases, the knowledge of the spatially and temporally varying two-phase flow is required to make accurate predictions as the distribution of both the phases have an impact on heat extraction as well as neutron moderation. Engineered two-phase flow systems have complex geometry and often high Reynolds numbers which increase the computational cost of an analysis, and generally make direct numerical simulations of the flow field impossible even on the fastest computers today. Consequently, a number of models which seek to reduce this computational cost have been created over the years. One of these called the two-fluid model has become the standard in three dimensional CFD (Computational Fluid Dynamics) codes and is and is also referred to as CMFD (Computational Multiphase Fluid Dynamics). The two-fluid model splits each conserved quantity into two fields, one for each phase that is treated as interspersed continua. Splitting one field into two requires additional interfacial closure relationships. In the two-fluid model, the momentum flux between the phases is governed by a number of these closure relationships. Generally, the net force on the dispersed phase is decomposed into inertial, added mass, buoyancy, drag, lift, and wall forces. In addition, there is a time-dependent Basset force, as well as turbulent dispersion effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1999

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗

DOE OSTI2019

In situ transformation of ethoxylate and glycol surfactants by shale-colonizing microorganisms during hydraulic fracturing

In the last decade, extensive application of hydraulic fracturing technologies to unconventional low-permeability hydrocarbon-rich formations has significantly increased natural gas production in the United States and abroad. The injection of surface-sourced fluids to generate fractures in the deep subsurface introduces microbial cells and substrates to low-permeability rock. A subset of injected organic additives has been investigated for their ability to support biological growth in shale microbial community members; however, to date, little is known on how complex xenobiotic organic compounds undergo biotransformations in this deep rock ecosystem. Here, high-resolution chemical, metagenomic, and proteomic analyses reveal that widely-used surfactants are degraded by the shale-associated taxa Halanaerobium, both in situ and under laboratory conditions. These halotolerant bacteria exhibit surfactant substrate specificities, preferring polymeric propoxylated glycols (PPGs) and longer alkyl polyethoxylates (AEOs) over polyethylene glycols (PEGs) and shorter AEOs. Enzymatic transformation occurs through repeated terminal-end polyglycol chain shortening during co-metabolic growth through the methylglyoxal bypass. Furthermore, this work provides the first evidence that shale microorganisms can transform xenobiotic surfactants in fracture fluid formulations, likely affecting the efficiency of hydrocarbon recovery, and demonstrating an important association between injected substrates and microbial growth in an engineered subsurface ecosystem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2015

Finite Element Modeling Techniques for Analysis of VIIP

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a major health concern for long-duration space missions. Currently, it is thought that a cephalad fluid shift in microgravity causes elevated intracranial pressure (ICP) that is transmitted along the optic nerve sheath (ONS). We hypothesize that this in turn leads to alteration and remodeling of connective tissue in the posterior eye which impacts vision. Finite element (FE) analysis is a powerful tool for examining the effects of mechanical loads in complex geometries. Our goal is to build a FE analysis framework to understand the response of the lamina cribrosa and optic nerve head to elevations in ICP in VIIP.

eye (anatomy)↗

DOE OSTI2021

Subsurface Characterization of Hydraulic Fracture Test Site-2 (HFTS-2), Delaware Basin

Hydraulic Fracturing Test Site-2 (HFTS-2) is a field-based research experiment performed in the Wolfcamp Formation of the Permian (Delaware) Basin. This paper focuses on integration, advanced geological characterization, and 3D subsurface modeling of the comprehensive HFTS-2 dataset. The study showcases a multidisciplinary reservoir characterization approach that incorporates geology, petrophysics, geochemistry, geomechanics, microseismic, and subsurface engineering analysis. Subsurface characterization of organic-rich mudstone formations requires understanding complex hydraulic fracture network growth in relation to inherent lithology, geomechanical properties, and interaction with pre-existing natural fractures. This paper presents a characterization workflow incorporating pre- and post-stimulation subsurface data, unique to the HFTS-2 dataset. The study integrated: (1) rock properties from logs, cores, and thin sections; (2) natural and hydraulic fracture descriptions from cores and image logs; (3) local and regional stresses; (4) geomechanics; (5) microseismic; (6) fiber optic (FO) and bottomhole pressure gauge (BHPG) response; and (7) produced fluids analysis. During a stimulation treatment, creation of the stimulated rock volume (SRV) is influenced by several subsurface factors. Key contributing factors include structural context, stress conditions, lithology, facies architecture, pre-existing natural fractures, and geomechanical properties. The HFTS-2 subsurface data integration indicates that the SRV is comprised of a complex juxtaposition of hydraulic fracture swarms, as evidenced by image logs analysis, core description, and microseismic monitoring. The HFTS-2 microseismic event density was used to generate 3D heat maps that serve as a representative SRV footprint, corroborated by secondary datasets. These maps were further integrated with petrophysical and geomechanical characteristics, as well as responses from FO and BHPG, to estimate the lateral and vertical dimensions of the effective fractures. The geological characterization for the HFTS-2 dataset combined with 3D modeling for petrophysical and geomechanical properties provides a strong foundation for subsurface simulation and optimization studies. Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/1-21URTC/D011S005R001/2477501/urtec-2021-5243-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5243 The workflow improved our understanding of HFTS-2 hydraulic fracture propagation and characteristics in relation to offset pressure depletion and interaction with pre-existing natural fractures. Analysis showed that fracture geometry varies by stage and by well, and a complex fracture network is generated with varying fracture density. The multidisciplinary workflow presented herein for integration and characterization serves as a foundation to evaluate completion efficiency and estimate areal and vertical stimulation and depletion extent for the project. Furthermore, the workflow and learnings can also be transferred to other unconventional plays.

58 GEOSCIENCES↗

DOE OSTI2016

Experimental investigation of flow induced dust acoustic shock waves in a complex plasma

We report on experimental observations of flow induced large amplitude dust-acoustic shock waves in a complex plasma. The experiments have been carried out in a Π shaped direct current glow discharge experimental device using kaolin particles as the dust component in a background of Argon plasma. A strong supersonic flow of the dust fluid is induced by adjusting the pumping speed and neutral gas flow into the device. An isolated copper wire mounted on the cathode acts as a potential barrier to the flow of dust particles. A sudden change in the gas flow rate is used to trigger the onset of high velocity dust acoustic shocks whose dynamics are captured by fast video pictures of the evolving structures. The physical characteristics of these shocks are delineated through a parametric scan of their dynamical properties over a range of flow speeds and potential hill heights. The observed evolution of the shock waves and their propagation characteristics are found to compare well with model numerical results based on a modified Korteweg-de-Vries-Burgers type equation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1997

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

Sun, Xian-He↗

DOE OSTI2024

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Enhanced Laser-Induced Graphene Microfluidic Integrated Sensors (LIGMIS) for On-Site Biomedical and Environmental Monitoring

The convergence of microfluidic and electrochemical biosensor technologies offers significant potential for rapid, in-field diagnostics in biomedical and environmental applications. Traditional systems face challenges in cost, scalability, and operational complexity, especially in remote settings. Addressing these issues, laser-induced graphene microfluidic integrated sensors (LIGMIS) are presented as an innovative platform that integrates microfluidics and electrochemical sensors both comprised of laser-induced graphene. This study advances the LIGMIS concept by resolving issues of uneven fluid transport, increased hydrophobicity during storage, and sensor biofunctionalization challenges. Key innovations include Y-shaped reservoirs for consistent fluid flow, hydrophilic polyethyleneimine coatings to maintain wettability, and separable microfluidic and electrochemical components enabling isolated electrode nanoparticle metallization and biofunctionalization. Multiplexed electrochemical detection of the neonicotinoid imidacloprid and nitrate ions in environmental water samples yields detection limits of 707 nm and 10 -5.4 m with wide sensing ranges of 5–100 µm and 10 -5 –10 -1 m, respectively. Similarly, uric acid and calcium ions are detected in saliva, demonstrating detection limits of 217 nm and 10 -5.3 m with sensing ranges of 10–50 µm, and 10 -5 –10 -2.5 m, respectively. Overall, this biosensing demonstrates the capability of the LIGMIS platform for multiplexed detection in biologically complex solutions, with applications in environmental water quality monitoring and oral cancer screening.

environmental monitoring↗

NASA NTRS2022

Design of Hypervelocity Flow Generator (HFG) and Its Diagnostics

Ground facilities for hypersonic research are a key element for successful development of aerodynamically proven hypervelocity vehicles. Design concepts and diagnostics of a hypervelocity flow generator (HFG) were made as a test platform for hypersonic/hypervelocity spacecraft models at the NASA Langley Research Center. The HFG is a hypersonic flow field generator using optically heated gas which is blown into an 80 cu m vacuum chamber. The vacuum chamber is kept at a stable vacuum pressure with a combination of three large vacuum pumps, while the HFG is in the test mode. The HFG provides a relatively small test section with approximately a 20 cm window. This facility was designed to generate 2.45 km/sec of flow speed, and potentially generate a continuous flow with the nozzle and vacuum system. The window in test section provides a direct view of the shock wave around a model in order to measure temperature, pressure, and density profile within the shock layer. One of the key test goals under this project is to understand why the emission spectra from the standing shockwave plasma predicted by Lora-Loran codes are significantly different from the measured emission spectra from the Flight Investigation Reentry Environment (FIRE II) Flight. The correct estimate of the thermal loading on the leading edge of hypersonic vehicles greatly affects the aerodynamic design, the material selection for the vehicle, and the cooling requirement and can be obtained by the precise modeling of emission spectra from shockwave plasma. However, the estimation of thermal loading is not an easy task due to complex non-equilibrium radiative process within high temperature shock layers that still falls into a category of cold plasma. Direct flight experiments are the most desirable, but not a cost-effective approach. Analysis by computational fluid dynamics (CFD) offers many test flexibilities. However, the CFD codes must be fully tested and validated with experimental data before the codes are effectively used for practical design. Large discrepancies between experiments and codes appear in hypersonic/hypervelocity flow regimes at high altitudes of 60 km ~ 90 km. This HFG facility offers some important parameters for CFD code validation, such as collision cross-sections, relaxation times, reaction rate coefficients and transportation coefficients. The HFG test facility is based on the ejection flow of high temperature gas heated over to 3500 K through a nozzle. The tungsten gas chamber of the HFG is heated up to a desired temperature by a 60 kW optical power beam source. This system consists of an optical power source, a thermal chamber, an expansion nozzle, a test section, and an 80 cu m vacuum tank. 60 kW optical input power is obtained from the 150 kW Vortek arc lamp system (by Vortek Industries, Vancouver, Canada). This optical beam is focused to heat the gas chamber within which a flow media is heated. The maximum achievable temperature of the flow medium reached approximately 3500 K or even higher but is limited by the melting point of the chamber material used. The exhaust velocity through the nozzle was determined by the stagnation temperature and the molecular weight of the working medium at the test section. To provide design parameters, a NASA Chemical Equilibrium with Application (CEA) computer program is used for the simulation of aerothermal data. This CEA program can calculate chemical equilibrium and properties of complex mixtures using shock tube parameters. For nitrogen gas at 2666 K stagnation temperature, the maximum achievable velocity at the test section is approximately 2.45 km/sec which is within the range of the thermal velocity of 8000 K shock layer. Based on the calculation through the CEA program, the design parameters of a HFG were determined and implemented for the test section that includes an expansion nozzle. The installed test section of the experimental facility can sustain a condition of a re-entry vehicle from the Space at an altitude of 60-90 km. After installation of the HFG, the system was fully tested and its operational parameters were measured. An 80 cu m vacuum chamber of HFG was set at 1 torr level to keep a stable downstream condition. The pumping time to reach the minimum vacuum pressure (~ 1 torr) at the test chamber from atmospheric pressure was approximately an hour using Kinney (MBV-14000/MB -1600/KT-300) and Stokes (Model 1772 and 412) pumps. Such a setup condition allowed a continued stable operation of the HFG experiment with flowrates through 1-, 3-, or 5-mm diameters of nozzle throat. The flow characteristics of the HFG for various operating conditions were performed using a focused Schlieren method. At 0.8 torr chamber pressure, a barrel shock was observed at the test section. With a sphere obstacle of 12 mm diameter in the flow, a bow shock (~ 2-mm thickness) was observed by a focused Schlieren visualization method.

Hypervelocity flow↗

DOE OSTI2023

Physics-based Induced Earthquake Forecasting: Process Understanding, and Hazards Mitigation

Disposal of saltwater co-produced with oil and gas is linked to elevated seismicity in the Central and Midwest US. There is a concern that these events may lead to widespread damage and an overall increase in seismicity. Thus an improved understanding of the spatially and temporally variable deformation and stress field associated with fluid injection operation is critically necessary for evaluating time-varying seismic hazards. Despite the improvements in seismic monitoring capacity and the resulting decrease in the magnitude detection threshold, estimates of induced earthquake probability remain elusive due to insufficient models incapable of accounting for the complex physics governing the process of induced seismicity. The proposed research effort will comprehensively analyze, integrate, and interpret geodetic, injection, and seismic data in the vicinity of the injection sites in Oklahoma to resolve the 4-dimensional distribution of pore pressure and stress in the shallow crust. This project, in particular, is focused on exploring the statistical relation between injection operation and increased earthquake hazard. The amplitude of and the extent to which pore pressure changes are determined by some factors, in particular, the hydrogeological properties of the rocks, such as diffusivity. Thus the available deformation data will be used to constrain hydrogeological properties of the medium, to accurately resolve the evolution of crustal stresses due to fluid injection. Having the time-varying models of stress changes, a statistical framework will be implemented to estimate the time-dependent probability of large earthquakes on the nearby fault systems. These data and models help to improve seismic hazard estimates and aid in constructing operational-induced earthquake forecast models. This information can also be integrated into the updated U.S. National Seismic Hazard Map, which local communities and authorities use in their earthquake risk estimates and mitigation efforts.

58 GEOSCIENCES↗

DOE OSTI2019

A Review of Physical and Numerical Approaches for the Study of Gas Stirring in Ladle Metallurgy

This article presents a review of the research into gas stirring in ladle metallurgy carried out over the past few decades. Herein, the physical modeling experiments are divided into four major areas: (1) mixing and homogenization in the ladle; (2) gas bubble formation, transformation, and interactions in the plume zone; (3) inclusion behavior at the steel–slag interface and in the molten steel; and (4) open eye formation. Several industrial trials have also been carried out to optimize gas stirring and open eye formation. Approaches for selecting criteria for scaling to guarantee flow similarity between industrial trials and physical modeling experiments are discussed. To describe the bubble behavior and two-phase plume structure, four main mathematical models have been used in different research fields: (1) the quasi-single-phase model, (2) the volume of fluid (VOF) model, (3) the Eulerian multiphase (E–E) model, and (4) the Eulerian–Lagrangian (E–L) model. In recent years, the E–E model has been used to predict gas stirring conditions in the ladle, and specific models in commercial packages, as well as research codes, have been developed gradually to describe the complex physical and chemical phenomena. Furthermore, the coupling of turbulence models with multiphase models is also discussed. For physical modeling, some general empirical rules have not been analyzed sufficiently. Based on a comparison with the available experimental results, it is found that the mathematical models focusing on the mass transfer phenomenon and inclusion behaviors at the steel-slag interface, vacuum degassing at the gas–liquid interface, dissolution rate of the solid alloy at the liquid–solid interface, and the combination of fluid dynamics and thermodynamics need to be improved further. To describe industrial conditions using mathematical methods and improve numerical modeling, the results of physical modeling experiments and industrial trials must offer satisfactory validations for the improvement of numerical modeling.

36 MATERIALS SCIENCE↗

NASA NTRS2015

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗