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The numerical solution of a single, mixed, nonlinear equation with prescribed boundary data is discussed. A second order numerical procedure for solving the nonlinear equation and a shock fitting scheme was developed to treat the discontinuities that appear in the solution.
A zonal model for aerodynamic analysis of two-dimensional transonic circulation control airfoils has been developed. The present approach combines a transonic full potential method for the global flow field and an integral boundary layer method for regions of the airfoil excluding the wall jet with a parabolized Navier-Stokes code for resolving the wall jet region beyond the slot. Existing methods suffer from two deficiencies: the insensitivity of the calculation to small changes in the Coanda surface geometry; and the inability to predict the shock structure of the underexpanded supersonic wall jets. The present wall jet procedure involves a pressure-split approach in the streamwise sense to enable noniterative solution of the coupled continuity and normal momentum equations for increased surface sensitivity and allows for expansion of applications to sonic slot exit conditions. Encouraging results are obtained in comparison with experimental data for two circulation airfoils with subsonic wall jets.
We investigate the origin of a significant reduction in computed numerical “noise” in the spatial variation of computed wall heat flux observed when using a node-centered weighted least squares(WLSQ) gradient approach when solving the Reynolds-averaged Navier-Stokes (RANS) equations for hypersonic boundary layer flows on highly stretched tetrahedral grids. This investigation is conducted using a 2nd-order, cell-centered, finite-volume, discretization which we employ to contrast results obtained using two WLSQ gradient approaches: a conventional 3-D, cell-centered, node-neighbor, WLSQ gradient (NN-CCG) approach and a 3-D, face-averaged, node-centered gradient (F-ANG)approach. The F-ANG approach, is shown to produce significantly less “noise” in the spatial variation of wall heat flux, than the NN-CCG approach and we demonstrate the cause of this “noise” via a series of numerical experiments where we compute hypersonic laminar and turbulent boundary layer flows.We further investigate the level of grid resolution required for a tetrahedral grid to approach the fidelity of a grid resolved hexahedral grid solution obtained using an equivalent structured grid method.
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Presented by NETL at 2015 Fall AGU Meeting; 12/15
This work discusses methods for evaluating the Power Transfer Distribution Factor (PTDF) and Line Outage Distribution Factor (LODF) matrices by employing sparse linear algebra for large-scale computing applications. These matrices are critical in many power systems applications, such as the Unit Commitment Problem (UC), pre- and post-contingency power flow analysis, and transmission expansion. These matrices are typically dense, which means they require a significant amount of time and memory to be computed for large networks. However, by analyzing the structure of the matrices and their computation method, it is possible to use reduced memory methods based on sparse matrix operations. This paper shows that sparse linear algebra algorithms are faster and require less memory and time than traditional dense approaches. Additionally, we explore the effect of matrix sparsification by eliminating trailing digits on power flow calculations.
A boundary layer approach for the solution of the flow field induced over a two-dimensional surface obstruction, such as a building or other man-made structure, is proposed. Adopting a specific geometry in the form of a semi-elliptical cylinder, the characteristics of atmospheric shear flow over a rough terrain are coupled with the well-known boundary layer equations. Two approaches are presented to incorporate the pressure field and boundary conditions which exist within the large viscous region over the obstruction. The first considers a region in the immediate vicinity of the body in which the pressure distribution and outer boundary condition on the velocity are computed from potential theory for flow over the elliptical cylinder. The second approach considers a much larger region of influence, extending from the surface to the undisturbed flow at large heights above the obstruction. Methods which appear to provide an improved theoretical model of the flow over the ellipse, such as a technique for simulating the effect of the seperation regions upstream and downstream of the body, are also presented.
In this study, we introduce a data-driven machine learning framework for improving the accuracy of wind plant flow models by learning turbulence model corrections based on data from higher-fidelity simulations. First, a high-dimensional PDE-constrained optimization problem is solved using gradient-based optimization with adjoints to determine optimal eddy viscosity fields that improve the agreement of a medium-fidelity Reynolds-Averaged Navier Stokes (RANS) model with large eddy simulations (LES). A supervised learning problem is then constructed to find general, predictive representations of the optimal turbulence closure. A machine learning technique using Gaussian process regression is trained to predict the eddy viscosity field based on local RANS flow field information like velocities, pressures, and their gradients. The Gaussian process is trained on LES simulations of a single turbine and implemented in a wind plant simulation with 36 turbines. We show improvement over the baseline RANS model with the machine learning correction, and demonstrate the ability to provide accurate confidence levels for the corrections that enable future uncertainty quantification studies.
The nozzles described exhibit a flow field which is supersonic except for the initial flow region, and the secondary mass flow is typically about five percent of the primary core flow. The features to improve the accuracy of the performance calculations are discussed. A special calculation is made to get as realistic a sonic line as possible for this geometry, using an analysis developed by Brown. The mixing between the secondary and core flows is treated to account for entrainment of the secondary flow into core. Both of these phenomena directly affect the pressure distribution on the shroud and therefore, the thrust that the nozzle produces. The importance of using a realistic sonic line and a mixing analysis is stressed.
The mixing and atomization of propellants is often characterized by optically dense flow fields and complex breakup dynamics. In the development of propulsion systems, the complexity of relevant physics and the range of spatio-temporal scales often makes computational simulation impractical for full scale injector elements; consequently, continued research into improved systems for experimental flow diagnostics is ongoing. One area of non-invasive flow diagnostics which has seen widespread growth is using synchrotron based x-ray diagostics. Over the past 3 years, a series of water and cryogenic based experiments were performed at the Advanced Photon Source, Argonne National Lab, on a NASA in-house designed swirl co-axial rocket injector, designed for operation using liquid oxygen and liquid methane in support of Project Morpheus. A range of techniques, such as x-ray fluorescence and time-averaged radiography were performed providing qualitative and quantitative mass and phase distributions, and were complemented by investigations using time-resolved radiography and white beam imaging, which provided information on breakup and mixing dynamics. Results of these investigations are presented, and conclusions regarding the viability of x-ray based diagnostics are discussed.
Techniques based on the Theory of Bottleneck Ordering can reveal the bottleneck structure of a network, and the Theory of Flow ordering can take advantage of the revealed bottleneck structure to manage and configure network flows so as to improve the overall network performance. These two techniques provide insights into the inherent topological properties of a network at least in three areas: (1) identification of the regions of influence of each bottleneck; (2) the order in which bottlenecks (and flows traversing them) may converge to their steady state transmission rates in distributed congestion control algorithms; and (3) the design of optimized traffic engineering policies.
Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. As a result, one of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.
Casting and welding of superalloys, stainless steel and titanium alloys are processes which can be improved through modeling of heat flow, fluid flow, residual stress development, and microstructural evolution. These simulations require inputs of thermophysical data, some of which involves the partially or totally liquid state. In particular, these processes involve melting, flow in the liquid, and solidification. Modeling of such processes can lead to an improved understanding of defects such as shrinkage, inclusions, cracks, incomplete filling (or penetration), macrosegregation, improper grain structure, and deviations from dimensional specifications. Effective modeling can shorten process development time and improve quality. An approach to these problems is to develop efficient models; validate through correlations with thermal, distortion, and microstructural data; run parametric studies; extract knowledge based rules; and apply to adaptive closed loop control systems. With the appropriate pre- and post-processing, such analyses can be made 'user friendly'. This would include graphical user interfaces as well as realistic images and color maps. In such form, these models can be used for sensitivity analyses, which are useful in defining appropriate sensors and in the development of control strategies. Such modeling can be done at several levels, e.g., the MARO level, modeling large scale phenomena such as heat and fluid flow or material deformation; the MICRO level, modeling the development of dendrites, grains or precipitates; or at the NANO level, modeling point defects, dislocations, stacking faults, etc. There are many computational issues associated with these simulations, e.g. computational efficiency and accuracy. In addition, there are many materials issues, not the least of which is the availability of accurate high temperature thermophysical data for complex alloys. This would include latent heat of fusion, temperature dependent heat capacity and thermal conductivity (for liquid and solid), viscosity, surface tension, thermal expansion, mechanical properties, etc. Preliminary data is frequently gathered from the literature; however, this is often not available for modern alloys. If additional data are required, measurements can be used; however, these are costly, time consuming and can be erroneous due to a lack of testing standards or impure materials. Microstructural predictors can be extracted from thermal information, e.g. cooling rate and thermal gradient; the prediction of microstructure is dependent on solidus and liquidus temperature, mushy zone permeability, the solidification curve, volume changes, phase transformations, alloying effects (such as surface tension or viscosity), mold/metal reactions, metal/environment reactions, etc. Defect maps may be needed to predict the onset of shrinkage, hot cracking or 'freckling'. Constants may be needed for stress relaxation, dendrite coarsening, vaporization, etc. Visualization was used as a tool to better comprehend complex data sets associated with the analysis of directional solidification (including crystal growth) and welding. Examples include not only isotherms, but also cooling rate, growth rate and thermal gradient. The latter two are not single valued scalars, but rather time and space dependent vector fields. Efficient models were developed for both casting and welding to predict heat flow and the relationship to dendrite and grain growth. These codes include many of the non-linear effects, e.g. radiation, which dominate these processes. The home-built FDM code(s) were designed to be useful not only to the scientist, but also to the process engineer. Special output can be requested to compare directly to experimental data. Visualization procedures were developed to visualize critical results, e.g. fusion zone width at the surface opposite that where the arc is applied ('penetration'). Both elaborate and simplified distortion analyses were carried out. It is clear that extensive mechanical property data are critical in order to accurately predict residual stress patterns. A scheme is currently being developed to integrate these modeling tools into a set of control algorithms; however, the success of this approach is critically dependent on the availability of accurate high temperature thermophysical data.
It has been suggested previously that the performance of scramjet propulsion system may be improved by the use of magnetohydrodynamic (MHD) energy bypass: an MHD generator could be made to decelerate the flow entering the combustor, thereby improving combustion efficiency, and the electrical power generated could be made to accelerate the flow exiting from the combustor prior to expanding through the nozzle. In one of such proposed schemes, the MHD generator is proposed to be operated at a low temperature and ionization is to be achieved under nonequilibrium by the application of an external power. In the present work, the required power of such an external source is calculated assuming a 100%-efficient nonequilibrium ionization scheme. The power required is that needed to prevent the degree of ionization from reaching equilibrium with the low gas temperature. The flow is seeded with potassium or cesium. Specific impulse is calculated with and without turbulent friction. The results show that, for typical intended flight conditions, the specific impulse obtained is substantially higher than that of a typical scramjet, but the required external-power is several times that of the power generated in the MHD generator.
Significant design changes to the Space Shuttle waste management system (WMS) and its related personal hygiene support provisions (PHSP) have been made recently to improve overall operational performance and human factors interfaces. The WMS design improvements involve increased urinal flow, individual urinals, and provisions for manually compacting feces and cleanup materials to ensure adequate mission capacity. The basic arrangement and stowage of the PHSP used during waste management operations were extensively changed to better serve habitability concerns and operations needs, and to improve the hygiene of WMS operations. This paper describes these changes and the design, development, and flight test evaluation. In addition, provisions for an eighth crewmember and a new four-tier sleep station are described.
MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.