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Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics
We formulate and apply a non-replica equilibrium theory for the fluid-glass transition, glass thermodynamic properties, and jamming of hard spheres in three and all higher spatial dimensions. Numerical predictions for the zero complexity glass transition and jamming packing fractions, and a “densest” equilibrium glass, are made. The equilibrium glass equation of state is regarded as the practical continuation of its fluid analog up to jamming. The analysis provides a possible resolution to the inability of any fluid virial series re-summation based equation of state to capture jamming at a reasonable volume fraction. The numerical results are quantitatively compared with various simulation data for equilibrium hard sphere glasses in 3 to 12 dimensions. Although there are uncertainties in this comparison, the predicted zero complexity or configurational entropy and corresponding jamming packing fractions do agree well with two characteristic packing fractions deduced from the dynamic simulation data. The similarities and differences of our approach compared to the replica approach are discussed. Here, the high dimensional scaling of the equilibrium glass transition and jamming volume fractions are also derived. The developments in this paper serve as input to Paper II that constructs a self-consistent integral equation theory of the 3-dimensional hard sphere pair structure, in real and Fourier space, in the metastable regime up to jamming. The latter is employed as input to a microscopic dynamical theory of single particle activated barrier hopping.
Development of technology for fluid-structure interaction modeling of a 1/8-scale dynamic model of shuttle External Tank (ET). Volume i: Technical report
A NASTRAN analysis of the external tank (ET) substructure of the 1/8-scale space shuttle structural dynamics model is described. The NASTRAN hydroelastic procedures were used to form a model of the liquid oxygen portion of the ET. Large computer storage requirements and running times were required unless these procedures were modified. Several possibilities were demonstrated including the substitution of the real for the complex eigenvalue routine and the use of the OMIT capability to reduce the number of fluid coordinates. A NASTRAN model of the complete ET was formed and reduced to 252 degrees of freedom. A review of the eigenvector extracted, using the unsymmetrical inverse power method, indicated that the structural OMIT's resulted in unsatisfactory modal deflections. Modifications to the NASTRAN hydroelastic capability appeared necessary to generate a successful ET model. An approach is described which, by assuming incompressibility, reduces the fluid representation to a symmetric mass matrix which can be added to the structural mass. The problem is solved using faster and more efficient eigenvalue routines. Using this approach the ET NASTRAN model was analyzed for three separate weight conditions.
Computational fluid dynamics research in three-dimensional zonal techniques
Patched-grid algorithms for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver were investigated. Conservative and non-conservative approaches for performing zonal interpolations were implemented. The latter approach yields the most flexible technique in that it can handle both patched and overlaid grids. Results for a two-dimensional blunt body problem show that either approach yield accurate steady-state shock locations and jump conditions. In addition, calculations of the turbulent flow through a hypersonic inlet on a three-zone grid show that the numerical prediction is in good agreement with the experimental results. Through the use of a generalized coordinate transformation at the zonal interface between two or more blocks, the algorithm can be applied to highly stretched viscous grids and to arbitrarily-shaped zonal boundaries. Applications were made to the F-18 aircraft at subsonic, high-alpha conditions, in support of the NASA High-Alpha Research Program. The calculations were compared to ground-based and flight test experiments and were used as a guide to understanding the ground-based tests, which are laminar and transitional, and their relationship to flight. Calculations about a complete reconnaissance aircraft were also performed in order to further demonstrate the capability of the patched-grid algorithm.
Aeroelastic Analysis of Modern Complex Wings
A process is presented by which aeroelastic analysis is performed by using an advanced computational fluid dynamics (CFD) code coupled with an advanced computational structural dynamics (CSD) code. The process is demonstrated on an F/A-18 Stabilator using NASTD (an in-house McDonnell Douglas Aerospace East CFD code) coupled with NASTRAN. The process is also demonstrated on an aeroelastic research wing (ARW-2) using ENSAERO (an in-house NASA Ames Research Center CFD code) coupled with a finite element wing-box structures code. Good results have been obtained for the F/A-18 Stabilator while results for the ARW-2 supercritical wing are still being obtained.
Numerical Modeling of Fluid Transient in Cryogenic Fluid Network of Rocket Propulsion System
Fluid transients, also known as water hammer, can have a significant impact on the design and operation of both spacecraft and launch vehicles propulsion systems. These transients often occur at system activation and shut down. For ground safety reasons, many spacecrafts are launched with the propellant lines dry. These lines are often evacuated by the time the spacecraft reaches orbit. When the propellant isolation valve opens during propulsion system activation, propellant rushes into lines creating a pressure surge. During propellant system shutdown, a pressure surge is created due to sudden closure of a valve. During both activation and shutdown, pressure surges must be predicted accurately to ensure structural integrity of the propulsion system fluid network. The method of characteristics is the most widely used method of calculating fluid transients in pipeline [ 1,2]. The method of characteristics, however, has limited applications in calculating flow distribution in complex flow circuits with phase change, heat transfer and rotational effects. A robust cryogenic propulsion system analyzer must have the capability to handle phase change, heat transfer, chemical reaction, rotational effects and fluid transients in conjunction with subsystem flow model for pumps, valves and various pipe fittings. In recent years, such a task has been undertaken at Marshall Space Flight Center with the development of the Generalized Fluid System Simulation Program (GFSSP), which is based on finite volume method in fluid network [3]. GFSSP has been extensively verified and validated by comparing its predictions with test data and other numerical methods for various applications such as internal flow of turbo-pump [4], propellant tank pressurization [5,6], chilldown of cryogenic transfer line [7] and squeeze film damper rotordynamics [8]. The purpose of the present paper is to investigate the applicability of the finite volume method to predict fluid transient in cryogenic flow circuits.
Characterization of Slosh Damping for Ortho-Grid and Iso-Grid Internal Tank Structures
Grid stiffened tank structures such as Ortho-Grid and Iso-Grid are widely used in cryogenic tanks for providing stiffening to the tank while reducing mass, compared to tank walls of constant cross-section. If the structure is internal to the tank, it will positively affect the fluid dynamic behavior of the liquid propellant, in regard to fluid slosh damping. As NASA and commercial companies endeavor to explore the solar system, vehicles will by necessity become more mass efficient, and design margin will be reduced where possible. Therefore, if the damping characteristics of the Ortho-Grid and Iso-Grid structure is understood, their positive damping effect can be taken into account in the systems design process. Historically, damping by internal structures has been characterized by rules of thumb and for Ortho-Grid, empirical design tools intended for slosh baffles of much larger cross-section have been used. There is little or no information available to characterize the slosh behavior of Iso-Grid internal structure. Therefore, to take advantage of these structures for their positive damping effects, there is much need for obtaining additional data and tools to characterize them. Recently, the NASA Marshall Space Flight Center conducted both sub-scale testing and computational fluid dynamics (CFD) simulations of slosh damping for Ortho-Grid and Iso-Grid tanks for cylindrical tanks containing water. Enhanced grid meshing techniques were applied to the geometrically detailed and complex Ortho-Grid and Iso-Grid structures. The Loci-STREAM CFD program with the Volume of Fluid Method module for tracking and locating the water-air fluid interface was used to conduct the simulations. The CFD simulations were validated with the test data and new empirical models for predicting damping and frequency of Ortho-Grid and Iso-Grid structures were generated.
Progress on Computational Modeling of Water-Based NSTF (FY2021)
This report documents the FY21 progress and achievements made in the computational analyses of the water-based NSTF. Both system-level and high-fidelity Computational Fluid Dynamics (CFD) analyses were performed to gain a complete understanding of the complex flow and heat transfer phenomena in natural convection systems. The progress on the waterbased NSTF experimental testing is summarized in a companion report (ANL-ART-230). As a continuation of progress from previous years, in FY21 the RELAP5 model of the NSTF was first updated to include a representative heated cavity that incorporated convection and conduction means of heat transfer. Two different cavity models were developed, one that models the radiation heat exchange among all surfaces in one enclosure (Cavity Model 1), and another that employs multiple radiation enclosures with each considering the surfaces at one axial level (Cavity Model 2). This updated RELAP5 deck was benchmarked with single-phase test data to tune form loss coefficients of the elbows and tees, along with heat transfer coefficients within the cavity and off the external insulation panels. This tuned model was then found to accurately predict fluid temperatures within 2.5% and both system and riser flow rates within 6% during single-phase, steady-state simulations. For transient simulations, there is a slight over prediction of the flow rate, fluid temperatures, and heater temperatures during the heat-up period, which indicate that the transient heat loss may be underestimated. Following, the capabilities of RELAP5-3D were examined, which feature a conduction enclosure model that is not present in the current version of RELAP5-MOD3.3 used for all previous NSTF simulations. As an initial comparison of the two codes, single-phase simulations were run that used similar input decks. The results indicate that the single-phase flow predicted by the two codes was very similar, however RELAP5-3D appears to predict a higher system flow during the two-phase transient when compared to the flow rates predicted by RELAP5-MOD3.3. Furthermore, RELAP5-3D run did not capture the density wave oscillations or geysering phenomena, which are large oscillation flow instabilities observed in the experimental facility. To further the prediction capabilities for capturing two-phase instabilities, Options 55, 57, 58, 61, which are implemented by default in RELAP5-MOD3.3 but not in RELAP5-3D, were investigated. When enabling Option 61, RELAP5-3D agrees well with MOD3.3 in predicting the total system flow, while other options have negligible effect on the predicted total system flow by RELAP5-3D. However, none of these options enables RELAP5-3D to produce the same flow instabilities. For future steps, efforts are currently underway to investigate RELAP5-3D’s different behavior in predicting low-pressure two-phase instabilities. STAR-CCM+ was used to perform CFD analysis of the water-based test facility and provide simulation results for comparisons to experimental data. Efforts first focused on describing the characteristics of flow within the heated cavity. A study was performed on whether possible leakage flow between the two sides of the cavity could substantially impact and explain the results. An additional second assumption was examined which defined adiabatic side walls, so physical insulation structures were added to the models to allow conduction across this outer insulation. The results suggest that potential porosity of the insulation could be a major factor in the temperature distribution within the cavity and should be considered in any studies where it is desirable to know the cavity wall temperatures to higher accuracy.
Annual Research Briefs
This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.
The Plant Water Management Experiments: Soil
A simple means of watering plants in the low-g environment aboard orbiting spacecraft is not obvious. Since the beginning of spaceflight, numerous approaches have been pursued to water plants that seek to maximize plant viability and system reliability, while minimizing crew time and system complexity. We are not there yet. The Plant Water Management (PWM) Soil experiments seek to apply recent advances in low-g capillary fluidics phenomena to the challenges faced by plant growth operations aboard spacecraft. The primary challenge is to establish earth-like flows minimizing low-g specific adaptations required of the plants. This is difficult due to the ever-present fluid physics challenges of poorly-wetting multiphase inertial-visco-capillary flows in geometrically complex conduits and containers. In this paper, we present recent flight results for the PWM Soil experiments where arcillite ‘soil reservoirs’ are arranged in a non-wetting host soil that serves as an O2-breathing wetting barrier. In this way, a largely terrestrial water-soil environment is mimicked where, as liquid is evapo-transpired through the growing plant foliage, the effective water table passively ‘falls’ reducing viscous lengths and increasing water uptake for the plant. We present data from 6 days of 24-7 experiments on the ISS testing 3 different plant root models. We also present and correlate a capillary flow model which captures the primary features of the flow. Our summary is valued for the assessment of current and future low-g plant watering systems employing soil media.
Investigating the Role of VR in a Simulation-Based Medical Planning System for Coronary Interventions
Virtual reality (VR) based computational fluid dynamics (CFD) simulations are emerging as a viable solution to guide complex surgical or invasive procedures, such as percutaneous coronary intervention (PCI), as they enable a realistic first-person experience of underlying patient anatomy and physiology. Realistic VR experience can be assessed by immersion, an objective VR property. However, it remains unclear how immersion influences virtual PCI procedures and what level of immersion is required. This study answers both these questions by evaluating the application of a CFD-based VR system and comparing semi-immersive and fully immersive VR displays. Nine patient-specific arterial models were simulated using CFD and used to conduct a quantitative user evaluation (n = 31) with both types of VR displays. The findings of this study reveal that VR immersion significantly improves the accuracy of simulated stent placement in complex arterial geometries, relative to traditional desktops with no immersion (p < 0.05). Higher accuracy is noted by the use of semi-immersive VR display, which offers higher display fidelity as compared to the fully immersive VR display (p < 0.05). Interestingly, CFD data mapped on to arterial geometries strongly influences the location of stent placement. This finding is demonstrated by the lack of significant accuracy deviation between the two immersive displays when CFD data is shown. This study provides compelling evidence that a CFD-based VR system rendered on semi-immersive displays can enable more accurate and efficient stent placement.
Band-Like Distribution of Grains in Selective Laser Melting Track Under Keyhole Mode
Grain structure in the melt pool under keyhole mode is complex due to complicated solidified conditions, especially in consideration of the intense fluid flow. This paper aims to clarify grain structure and grain growth mechanism in melt pool under keyhole mode in selective laser melting. The microstructure from transverse cross section and longitudinal cross section near the centerline of 316L single tracks was characterized. In the longitudinal cross section, band-like grain structure formed. It is found that fluid flow can refine the grains, and large columnar grains grow towards crystallographic 〈110〉 direction.
Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications
Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.
Direct numerical simulation of reactor two-phase flows enabled by high-performance computing
Nuclear reactor two-phase flows remain a great engineering challenge, where the high-resolution two-phase flow database which can inform practical model development is still sparse due to the extreme reactor operation conditions and measurement difficulties. Owing to the rapid growth of computing power, the direct numerical simulation (DNS) is enjoying a renewed interest in investigating the related flow problems. A combination between DNS and an interface tracking method can provide a unique opportunity to study two-phase flows based on first principles calculations. More importantly, state-of-the-art high-performance computing (HPC) facilities are helping unlock this great potential. This paper reviews the recent research progress of two-phase flow DNS related to reactor applications. The progress in large-scale bubbly flow DNS has been focused not only on the sheer size of those simulations in terms of resolved Reynolds number, but also on the associated advanced modeling and analysis techniques. Specifically, the current areas of active research include modeling of sub-cooled boiling, bubble coalescence, as well as the advanced post-processing toolkit for bubbly flow simulations in reactor geometries. A novel bubble tracking method has been developed to track the evolution of bubbles in two-phase bubbly flow. Also, spectral analysis of DNS database in different geometries has been performed to investigate the modulation of the energy spectrum slope due to bubble-induced turbulence. In addition, the single-and two-phase analysis results are presented for turbulent flows within the pressurized water reactor (PWR) core geometries. The related simulations are possible to carry out only with the world leading HPC platforms. Furthermore, these simulations are allowing more complex turbulence model development and validation for use in 3D multiphase computational fluid dynamics (M-CFD) codes.
Second order upwind Lagrangian particle method for Euler equations
A new second order upwind 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 / multiphase 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) an upwind second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.
The Complicated Link Between Material Properties and Microfracture Density for an Underground Explosion in Granite
Geophysical techniques are often implemented as quick and inexpensive ways to locate and characterize fractures in the subsurface, which is important for a number of geoscience fields. Seismic velocities are the most widely used proxies for identification of fractures, but the correlation is not always well-defined. In this study we present material property data: unconfined compressive strength (UCS), bulk density (ρ), Young's modulus (E), Poisson's ratio (ν), P wave velocity (V p ), and S wave velocity (V s ), in conjunction with microfracture densities measured on samples of granite collected before and after underground chemical explosions. Results indicate the relationship between fractures and material properties is complex, even in this single-lithology environment. We interpret that this complexity arises from varying fracture mechanisms (e.g. dilation-inducing fractures vs compression-inducing fractures) in different parts of the core, due to differences in stress conditions. Additional complexity may result from chemical interactions between the fresh fractures and the fluids in the area. Water content appears to have a significant, if not dominant, role in the unconfined compressive strength (UCS) of the samples. We suggest caution when using elastic property measurements as a proxy for fracturing in areas of explosion-induced damage, or in other areas where a variety of mechanisms induce fracturing.
Mixed convection flow of nanofluid in a square enclosure with an intruded rectangular fin
Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid’s thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.
Updated Thermofluid Performance of the Simplified Flat Variant of the HEMJ
Our group has recently developed and studied “finger”-type divertors that are a simplified version of the helium-cooled modular divertor with multiple jets (HEMJ) using coupled computational fluid dynamics and thermal stress simulations. Such a simplified geometry could reduce complexity and cost given the large number of fingers required to cover the total divertor target area. Previous experimental studies for this simplified flat design reported lower heat transfer coefficients and higher pressure drops than the HEMJ, contrary to numerical predictions. Subsequent measurements determined that the original test section had significant dimensional variations in the jet exit holes. A new test section was therefore manufactured and tested in the Georgia Tech (GT) helium loop. The experimental results presented here for this test section at maximum heat flux of 7.1 MW/m 2 are in good agreement with numerical predictions. Correlations developed from these experimental data are extrapolated to predict the maximum heat flux that can be accommodated by the flat design and the coolant pumping power requirements under prototypical conditions. Lastly, numerical simulations are used to estimate the sensitivity of the flat design to geometric variations typical of manufacturing tolerances and variations in the gap width.