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DOE OSTI2018

Lagrangian particle method for compressible fluid dynamics

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Final Scientific/Technical Report: Correlations and Fluctuations in Weakly Collisional Plasma

Plasma is a state of matter that exhibits a very rich range of phenomena. To begin with, plasma is both electrical and mechanical - bringing together theories of particle motion and the electromagnetic field. Furthermore, and especially important for this project, a weakly-collisional plasma, such as is found in high-temperature (fusion energy) experiments on earth and the majority of contexts in space and astrophysics, has many moving parts. For example, sitting in earth’s atmosphere we are immersed in a mechanical wave field (sound), a possibly turbulent fluid motion (wind), and an electromagnetic vector wave field with two polarizations (light). This is already enough to produce a rich range of possibilities. In plasma, the electromagnetic field is coupled to the mechanical motion of the medium because it is ionized. Furthermore, a weakly-collisional plasma supports an infinite number of mechanically independent fluids. Thus, plasmas support an infinite number of independent electromechanical waves. Much has been done to describe plasmas with "reduced models" of various kinds. The goal of this project was to both explore the validity of reduced plasma models that are in use, and to propose and validate new models of plasma motion. The primary means to his end was laboratory experiments employing both electrical probes and laser spectroscopy. Laser spectroscopy enables many techniques which can separate the spectrum of independent fluid motions in the ion phase-space. The choice was to focus on low frequency electrostatic waves because the electron motion is relatively simple, the experiments can be on a spatial scale of a few meters, and all the relevant parameters can be measured with a few lasers systems. No study of this kind had previously been undertaken for the study of plasmas. The validation of theories required that the experimental descriptions be compared with theory and simulation in detail. It was found that even multi-fluid theories leave out a large part of the complexity of plasma motion. Reduced descriptions were found to fail under most circumstances. A new technique was developed that enabled a measurement of the phase-space resolved ion correlation function for the first time. The wide range of plasma dynamics possible became clear through this technique. It was found that collisionless (Vlasov) theory has a large field of application even when the plasma is weakly-collisional. A new approach, the kinetic wave expansion, was proposed, tested and found to be very useful for describing electrostatic ion waves. This project demonstrated a new way of looking at the "degrees-of-freedom" of plasmas and provided significant validation tests of fluid and kinetic plasma descriptions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Evidence for Carbonate Surface Complexation during Forsterite Carbonation in Wet Supercritical Carbon Dioxide

Continental flood basalts are attractive formations for geologic sequestration of carbon dioxide because of their reactive divalent-cation containing silicates, such as forsterite (Mg2SiO4), suitable for long-term trapping of CO2 mineralized as metal carbonates. The goal of this study was to investigate at a molecular level the carbonation products formed during the reaction of forsterite with supercritical CO2 (scCO2) as a function of the concentration of H2O adsorbed to the forsterite surface. Experiments were performed at 50 °C and 90 bar using an in situ IR titration capability, and post-reaction samples were examined by ex situ techniques, including SEM, XPS, FIB-TEM, TGA-MS, and MAS-NMR. Carbonation products and reaction extents varied greatly with adsorbed H2O. We show for the first time evidence of Mg-carbonate surface complexation under wet scCO2 conditions. Carbonate is found to be coordinated to Mg at the forsterite surface in a predominately bidentate fashion at adsorbed H2O concentrations below 27 µmol/m2. Above this concentration and up to 76 µmol/m2, monodentate coordinated complexes become dominant. Beyond a threshold adsorbed H2O concentration of 76 µmol/m2, crystalline carbonates continuously precipitate as magnesite, and the particles that form are hundreds of times larger than the estimated thicknesses of the adsorbed water films of about 7 to 15 Å. At an applied level, these results suggest that mineral carbonation in scCO2 dominated fluids near the wellbore and adjacent to caprocks will be insignificant and limited to surface complexation, unless adsorbed H2O concentrations are high enough to promote crystalline carbonate formation. At a fundamental level, the surface complexes and their dependence on adsorbed H2O concentration give insights regarding forsterite dissolution processes and magnesite nucleation and growth.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2015

Modeling the Interaction Between Hydraulic and Natural Fractures Using Dual-Lattice Discrete Element Method

The interaction between hydraulic fractures (HF) and natural fractures (NF) will lead to complex fracture networks due to the branching and merging of natural and hydraulic fractures in unconventional reservoirs. In this paper, a newly developed hydraulic fracturing simulator based on discrete element method is used to predict the generation of complex fracture network in the presence of pre-existing natural fractures. By coupling geomechanics and reservoir flow within a dual lattice system, this simulator can effectively capture the poro-elastic effects and fluid leakoff into the formation. When HFs are intercepting single or multiple NFs, complex mechanisms such as direct crossing, arresting, dilating and branching can be simulated. Based on the model, the effects of injected fluid rate and viscosity, the orientation and permeability of NFs and stress anisotropy on the HF-NF interaction process are investigated. Combined impacts from multiple parameters are also examined in the paper. The numerical results show that large values of stress anisotropy, intercepting angle, injection rate and viscosity will impede the opening of NFs.

02 PETROLEUM↗

DOE OSTI2022

Continued Verification of MOOSE Structural Mechanics Tools for Modeling Core Bowing Phenomena in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY22, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21. Several benchmark verification examples were selected from the IAEA verification and validation report. These examples involve clusters of ducts representative of a sector of a hexagonal reactor core which bow into each other and cause contact and load pad elevations, as well as single ducts subjected to irradiation fields undergoing swelling and subsequent bowing. The MOOSE-based results were compared to both IAEA benchmark participants’ results, analytic equations as available, and NUBOW-3D, a beam model code developed by Argonne National Laboratory. In every case, the MOOSE results agreed with other simulations results, providing additional verification basis of the tools for this particular physics application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

FY23 Status Report on MOOSE-Based Approaches to Modeling Core Bowing in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY23, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21 and FY22. Several benchmark verification examples were selected from the IAEA verification and validation report with increased number of ducts and more complex contact interaction behavior. These examples involve a full symmetric sector with restraint rings at multiple load pad locations to simulate a limited free-bow restraint system concept, as well as irradiation induced swelling and creep effects in a sector. In addition, improvements to the contact module sideset assignment were assessed and compared with previous MOOSE results to verify the contact behavior. The MOOSE-based results were compared to IAEA benchmark participants’ results. In every case, the MOOSE results agreed with other simulations results for estimating bowing behavior, providing additional verification basis of the tools for this particular physics application. Estimation of contact forces were mostly in agreement, with a few outlier results. A plan was suggested for dealing with the discrepancies with estimating contact force values. In addition, a 1-way coupling demonstration was performed using subchannel analysis code Pronghorn-SC and MOOSE on an ABR-1000-design sodium-cooled fast reactor assembly to evaluate coolant and duct wall temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2019

Extrusion of Complex Surface Meshes Utilizing Face Offsetting and Mean Curvature Smoothing

Grids for three-dimensional Computational Fluid Dynamics problems frequently require a prismatic layer of cells, typically extruded in the off-body direction from a two-dimensional surface mesh to properly resolve boundary layers. When the surface geometry is complex, the extrusion process can fail, resulting in the physical boundary layer being thicker than the prismatic layer, leading to under-resolved boundary layers. To address the shortcomings of existing grid generation tools, a new tool has been developed as part of the Mesh Tools suite, that is capable of extruding complex surface meshes. The new tool uses a face offsetting method to preserve surface curvature and a mean curvature smoothing algorithm to prevent the cells from self-intersecting in concave regions. Testing of the new tool found that not only were complex surface meshes able to be extruded to the desired thickness, but extrusion of simple surface meshes was also improved, due to the face offsetting method.

mesh extrusion↗

DOE OSTI2024

Catalytic resonance theory: Circumfluence of programmable catalytic loops

Chemical reactions on heterogeneous catalyst surfaces exhibit complex networks of elementary reactions with multiple pathways to fluid phase products, sometimes leading to surface reaction loops consisting of a closed cycle reaction pathway. While conventional catalysts at steady state exhibit zero net flux in either direction around a catalytic loop, the loop turnover frequency of three-species surface loops was evaluated in this work via microkinetic modeling to assess the reaction loop behavior resulting from a catalytic surface oscillating between two or more surface energy states. For dynamic heterogeneous catalysts undergoing applied oscillations of surface energy (i.e., programs), surface reaction loops of three species were shown to exhibit non-zero net flow of molecules around the loop, with the extent of loop turnover frequency varying with the applied frequency and amplitude of a sinusoidal or square wave oscillation. Alternatively, some dynamic surface reactions exhibited oscillations only between two surface species or resulted in surfaces covered by a single species at all times. Here, more complex behavior was observed for dynamic surface programs of three distinct electronic states, with the temporal order of applied states controlling the direction of flow of molecules within a three-molecule surface loop. Catalytic loops have the potential to limit overall catalytic reaction rates and use energy in programmable catalysts, while some applications could purposely impose non-zero loop turnover frequency for improved surface reaction control.

Catalysis↗

NASA NTRS2001

B-spline Method in Fluid Dynamics

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier↗

DOE OSTI2017

Verification of the Coupled Neutronics/Thermal-Hydraulics Code TANSY against the MSFR Benchmark

The MSRs is a liquid-fuel reactor in which uranium, fission products and actinides are dissolved in the molten salt. The molten salt reactors are featured by circulating fuel, low pressure and high temperature. The MSRs meets many of the future goals of nuclear technology, in particular for what concerns as improved sustainability and unique characteristics in terms of actinide burning. The fluid nature of fuel in MSRs gives extra flexibility in reactor design, fuel fabrication and recycling. But because of the application of fluid fuel, MSRs have several special characteristics compared with the traditional solid-fuel reactors. Firstly, the transport of the delayed neutron precursors by the fluid flow reduces the contribution of delayed neutrons to the chain reaction.. Secondly, the fact that the fuel is dissolved in the coolant rather than separated from the coolant by the claddings results in a much stronger coupling phenomenon between the neutronics and thermal-hydraulics. Thirdly, the shape of the fuel is determined by the container because of the characteristics of fluid, the unstructured meshes are required to model the complex geometry accurately. However most of the conventional reactor codes were developed for solid-fuel reactor and therefore not capable of taking liquid fuel flow into account. To address all these particular modeling issues of MSRs, a multi-physics code named TANSY has been developed in our laboratory. In this paper, the benchmark problem based on the MSFR design was calculated to verify the code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

A reduced set of gyrofluid equations for plasma flow in a diverging magnetic field

Plasmas are often generated in a small diameter source with a strong magnetic field and subsequently flow into a region with greater diameter and smaller field. The magnetic mirror force that accelerates plasma in a diverging magnetic field appears in the gyrofluid equations developed for applications to toroidal devices, but this force is often absent from fluid equations. A set of gyrofluid equations with reduced complexity is developed in which drifts are assumed negligible and the mirror force is retained. The Chew–Goldberger–Low equations of state are used for a simple closure. These reduced gyrofluid equations are applied to plasma equilibrium in a magnetic mirror, to acceleration of plasma in a magnetic nozzle, and to space charge neutralization of an ion beam by electrons in a diverging magnetic field. The results from gyrofluid theory are compared with results from drift kinetic theory to find the accuracy of the gyrofluid approximation in these applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

NdPO 4 solubility and aqueous Neodymium speciation in supercritical fluids: An experimental study at 500–700 °C and 1.7 kbar

A key aspect in the formation of rare earth elements (REE) deposits is the role of REE transport as aqueous REE complexes in supercritical hydrothermal solutions, where the nature of the aqueous complex is controlled by solution composition, temperature and pressure. Despite chloride being considered as one of the most abundant transporting ligands in magmatic-hydrothermal fluids, experimental investigations on the stability of aqueous REE chloride complexes are scarce above 300 °C. In this study, synthetic NdPO 4 crystals were reacted with non-saline and saline (0, 0.05 and 0.5 mNaCl), acidic (0.01 mHCl) aqueous solutions in a series of solubility experiments conducted at 500–700 °C and 1.7 kbar, where the solubilities were determined using a stable Nd isotope ( 145 Nd isotope spike) dilution technique. NdPO 4 solubility ranges between 28 ppm and 10,858 ppm, where solubility increases with both temperature and salinity. At 500 °C, log mNdPO 4 increases from –3.93 to –1.60 and there is a strong correlation between NdPO 4 solubility and NaCl concentrations (slope of 1.2 ± 0.3), indicating stabilization of the Nd chloride aqueous complexes with a stoichiometry corresponding to NdCl 2+ . At 600 °C, this correlation is weaker (slope of 0.4, log mNdPO 4 increases from –2.63 to –1.88) indicating the stabilization of both Nd chloride and hydroxyl species controlling solubility. At 700 °C, NdPO 4 solubility is largely independent of NaCl concentration indicating that solubility is controlled by Nd hydroxyl complexes, where stoichiometry suggests the neutral Nd(OH) 3 0 species is dominant. The solubility product (Ksp) of NdPO4 is derived from experimental data with the relation: log K sp = -41.81 – 0.057T – 20987/T, with T temperature in Kelvin. Comparison of the measured Nd phosphate solubility to thermodynamic predictions using the available Helgeson-Kirkham-Flowers equation of state parameters for aqueous Nd complexes indicate that predictions are up to three orders of magnitude lower compared to experimental observations. This discrepancy is most pronounced in saline solutions, suggesting that thermodynamic properties of the REE chloride species in supercritical fluids require revision. Numerical simulations of fluid-rock interaction between acidic, saline fluids and a Strange Lake felsic mineral assemblage demonstrates that NdPO 4 solubility predictions from models are four to six orders of magnitude lower than those calculated based on empirical fits from experiments, which suggests that acidic, saline fluids may play an important role in mobilizing large amounts of light REE from 450 to 700 °C.

58 GEOSCIENCES↗

NASA NTRSDate not supplied

Time-History Statistics of Soot Formation in A Model Gas Turbine Combustor

Soot formation is a complex dynamic and intermittent process determined by properties of the fuel, combustor design, and combustor operation. Although the major steps in soot formation (i.e., formation of precursors, inception, growth and evolution) are similar for a variety of carbonaceous fuels, applications, and operating conditions, it remains unclear when the temporal transition between these steps occurs. An engineering prediction tool coupled with computational fluid physics (CFD), therefore needs to accurately model all these complex steps. To develop such a model, we propose the time-history concept for understanding the time dependency of soot formation as a function of local properties (i.e., temperature, velocity, local fuel air ratio, etc.). We continue our previous work with modeling the DLR aero-combustor [1] with our updated in-house CFD code, Open National Combustion Code (OpenNCC), that now includes a Multiple Time-Scale Flamelet Progress Variable approach and a the semi-empirical two-equation soot model. We injected massless tracer particles upstream of the injector region of the combustor to collect time-history statistics of the solution variables. The correlations between the collected statistics with respect to the experimental soot volume fraction data showed that time-history effect of certain flow variables, including turbulent kinetic energy (TKE), and multiple species is indeed important for soot formation. We then conducted a time-history based correlation analysis to determine the key species and the concentration ranges critical for soot formation (C6H5-based nucleation, acetylene-based surface growth, and oxidation with OH and O2). Based on the time-history correlation coefficient (THCC) analysis, we propose possible modifications to improve the current two-equation model.

LES↗

DOE OSTI2019

Using Ultrafast X-ray Spectroscopy To Address Questions in Ligand-Field Theory: The Excited State Spin and Structure of [Fe(dcpp) 2 ] 2+

We have employed a range of ultrafast X-ray spectroscopies in an effort to characterize the lowest energy excited state of [Fe(dcpp) 2 ] 2+ (where dcpp is 2,6-(dicarboxypyridyl)pyridine). This compound exhibits an unusually short excited-state lifetime for a low-spin Fe(II) polypyridyl complex of 270 ps in a room-temperature fluid solution, raising questions as to whether the ligand-field strength of dcpp had pushed this system beyond the 5 T 2 / 3 T 1 crossing point and stabilizing the latter as the lowest energy excited state. Kα and Kβ X-ray emission spectroscopies have been used to unambiguously determine the quintet spin multiplicity of the long-lived excited state, thereby establishing the 5 T 2 state as the lowest energy excited state of this compound. Geometric changes associated with the photoinduced ligand-field state conversion have also been monitored with extended X-ray absorption fine structure. The data show the typical average Fe-ligand bond length elongation of ~0.18 Å for a 5 T 2 state and suggest a high anisotropy of the primary coordination sphere around the metal center in the excited 5 T 2 state, in stark contrast to the nearly perfect octahedral symmetry that characterizes the low-spin 1 A 1 ground state structure. This study illustrates how the application of time-resolved X-ray techniques can provide insights into the electronic structures of molecules—in particular, transition metal complexes—that are difficult if not impossible to obtain by other means.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2014

Science Goals and Mission Concept for the Future Exploration of Titan and Enceladus

Saturn׳s moons, Titan and Enceladus, are two of the Solar System׳s most enigmatic bodies and are prime targets for future space exploration. Titan provides an analogue for many processes relevant to the Earth, more generally to outer Solar System bodies, and a growing host of newly discovered icy exoplanets. Processes represented include atmospheric dynamics, complex organic chemistry, meteorological cycles (with methane as a working fluid), astrobiology, surface liquids and lakes, geology, fluvial and aeolian erosion, and interactions with an external plasma environment. In addition, exploring Enceladus over multiple targeted flybys will give us a unique opportunity to further study the most active icy moon in our Solar System as revealed by Cassini and to analyse in situ its active plume with highly capable instrumentation addressing its complex chemistry and dynamics. Enceladus׳ plume likely represents the most accessible samples from an extra-terrestrial liquid water environment in the Solar system, which has far reaching implications for many areas of planetary and biological science. Titan with its massive atmosphere and Enceladus with its active plume are prime planetary objects in the Outer Solar System to perform in situ investigations. In the present paper, we describe the science goals and key measurements to be performed by a future exploration mission involving a Saturn-Titan orbiter and a Titan balloon, which was proposed to ESA in response to the call for definition of the science themes of the next Large-class mission in 2013. The mission scenario is built around three complementary science goals: (A) Titan as an Earth-like system; (B) Enceladus as an active cryovolcanic moon; and (C) Chemistry of Titan and Enceladus - clues for the origin of life. The proposed measurements would provide a step change in our understanding of planetary processes and evolution, with many orders of magnitude improvement in temporal, spatial, and chemical resolution over that which is possible with Cassini-Huygens. This mission concept builds upon the successes of Cassini-Huygens and takes advantage of previous mission heritage in both remote sensing and in situ measurement technologies.

future missions↗

NASA NTRS1959

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array

The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Sparrow, E. M.↗

NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗

DOE OSTI2023

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

42 ENGINEERING↗