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Results from Second Round of Remediated Nitrate Salt Surrogate Formulation and Testing

High Explosives and Technology (M-7) completed the second round of formulation and testing of Remediated Nitrate Salt (RNS) surrogates on March 17, 2016. This report summarizes the results of the work and also includes additional documentation required under test plan PLAN-TA9-2443 Rev B, "Remediated Nitrate Salt (RNS) Surrogate Formulation and Testing Standard Procedure", released February 16, 2016. All formulation and testing was carried out according to PLAN-TA9-2443 Rev B. Results from the first round of formulation and testing were documented in memorandum M7-16-6042, "Results from First Round of Remediated Nitrate Salt Surrogate Formulation and Testing."

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

2016 Update of Hanford Glass Property Models and Constraints for Use in Estimating the Glass Mass to be Produced at Hanford by Implementing Current Enhanced Glass Formulation Efforts

Recent glass formulation and melter testing data have suggested that significant increases in waste loading in high-level waste (HLW) and low-activity waste (LAW) glasses are possible over current system planning estimates. In 2013 a set of models and constraints based on these data were developed and published (Vienna et al. 2013). Since that report roughly 200 additional glasses have been tested and lessons were learned in the application of the preliminary set of models and constraints. This report summarizes the advancements in glass formulation and glass property estimation since Vienna et al. 2013 (using the additional data and lessons learned) and updates the recommended set of enhanced glass property-composition models and constraints for use in River Protection Project (RPP) planning. The combined data (although limited in some cases) were evaluated to determine a set of constraints and models that could be used to estimate the maximum loading of specific waste compositions in glass. It is recommended that these models and constraints be used to estimate the likely HLW and LAW glass masses that would result if the current glass formulation studies are successfully completed. It is recognized that some of the models are preliminary in nature and will change in the coming years. In addition, the models do not currently address the prediction uncertainties that would be required before they could be used in plant operations. The models and constraints are only meant to give an indication of rough glass masses and are not intended to be used in quality-affecting activities or decisions. A current research program is in place to develop the data, models, and uncertainty descriptions for that purpose. A fundamental tenet underlying the research reported in this and the previous document is the attempt to be less conservative, but still realistic, than previous studies when developing constraints for the estimation of glass to be produced by implementing current enhanced glass formulation efforts. The less conservative approach documented herein should allow for the estimate of glass masses that may be realized if the current efforts in enhanced glass formulations are completed over the coming years, and are as successful as early indications suggest they may be. Because of this approach, there is an unquantifiable uncertainty in the ultimate glass mass projections due to model prediction uncertainties that must be considered, along with other system uncertainties, such as waste compositions and amounts to be immobilized, split factors between LAW and HLW, etc. A plan to estimate the impact of those uncertainties has been developed and a future update will document the results.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Glass Formulation and Testing with RPP-WTP HLW Simulants (Final Report)

This report presents the results from HLW glass formulation work that was conducted at the Vitreous State Laboratory of The Catholic University of America during Part B1 of the RPP-WTP Project (formally known as TWRS-P) in support of the Privatization contractor, BNFL, Inc. Glass formulation development is required to provide data that are essential for design of the vitrification facility in the near term and for safe and reliable operation of that facility in the longer-term. These data also form the bases from which contractually and technically acceptable immobilized high-level waste (IHLW) products will be devised. Glass formulation therefore impacts many aspects of the vitrification facility design, overall process economics, and contractual compliance. As an integral part of the overall system design, development of glass formulations requires input from many sources including tank waste characterization, pretreatment process definition, flow sheet development, and processing schedules. Accordingly, the glass formulation effort must be responsive to new information as the facility design basis evolves.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗

MCC level C formulation requirements. Entry guidance and entry autopilot, optional TAEM targeting

The level C software formulations requirements for the entry guidance and the simplified autopilot to be used by the Mission Control Center (MCC) entry processor are presented. The modifications required to functionally simulate optional Terminal Area Energy Management (TAEM) targeting capability (OTT) are incorporated. Implementation of this logic in the MCC must be coordinated with flight software OTT implementation and MCC TAEM guidance OTT. The entry guidance logic is based on the orbiter avionics entry guidance software. Descriptions of the entry guidance detailed formulation requirements, the detailed autopilot formulation requirements, and the targeting routine are given. Also included are a definition of coordinate systems, a list of parameter definitions for the software formulations, and a set of formulation flow charts.

Harpold, J. C.↗

Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise

A new formulation is proposed for the problem of parameter estimation of dynamic systems with both process and measurement noise. The formulation gives estimates that are maximum likelihood asymptotically in time. The means used to overcome the difficulties encountered by previous formulations are discussed. It is then shown how the proposed formulation can be efficiently implemented in a computer program. A computer program using the proposed formulation is available in a form suitable for routine application. Examples with simulated and real data are given to illustrate that the program works well.

Maine, R. E.↗

Steady-state boundary lubrication with formulated C-ethers to 260 C

Steady state wear and friction studies were made at boundary lubrication conditions in a pin on disk (pure iron on rotating CVM M 50 steel) sliding friction apparatus with five C ether formulated fluids (modified polyphenyl ether containing phosphrous ester, organic acid, and other additives). Conditions included 20, 150, and 260 C disk temperatures, dry air test atmosphere, 1 kilogram load, 50 rpm disk speed, and test times to 130 minutes. Results were compared with those obtained with a formulated MIL L 27502 candidate ester and the C ether base fluid. Three of the C ether formulations gave better lubrication than both reference fluids under most conditions. The other two C ether formulations yielded higher wear rates and friction coefficients than the C ether base fluid for most of the temperature range. Only one C ether formulation showed consistently higher steady state wear rates than the ester.

Loomis, W. R.↗

Polyimides formulated from a partially fluorinated diamine for aerospace tribological applications

Preliminary tribological studies on polyimides formulated from the diamine 2,2-bis 4-(4-aminophenoxy)phenyl hexafluorapane (4-BDAF) indicate that polyimides formulated from this diamine have excellent potential for high temperature tribological applications. The dianhydrides used to make the polyimides were pyromellitic (PMDA) and benzophenonetetracarboxylic acid (BTDA). Friction and wear studies at 25 and 200 C indicate that polyimides formulated using 50 mole percent of the PMDA dianhydride and 50 mole percent of the BTDA dianhydride perform better than polyimides formulated solely with the BTDA dianhydride. Graphite fiber reinforced polyimide composites were formulated with the polyimide made from the BTDA dianhydride, both graphitic and non-graphitic fibers were evaluated. Graphitic fibers produced better tribological results, since thin, flowing, "layer-like' transfer films were produced which did not build-up with long sliding durations. Non-graphitic fibers did not produce this type of transfer.

Fusaro, R. L.↗

Polyimides formulated from a partially fluorinated diamine for aerospace tribological applications

Preliminary pribological studies on polyimides formulated from the diamine 2,2-bis 4-(4-aminophenoxy)phenyl hexafluoropane (4-BDAF) indicate that polyimides formulated from this diamine have excellent potential for high temperature tribological applications. The dianhydrides used to make the polyimides were pyromellitic (PMDA) and benzophenonetetracarboxylic acid (BTDA). Friction and wear studies at 25 and 200 C indicate that polyimides formulated using 50 mole percent of the PMDA dianhydride and 50 mole percent of the BTDA dianhydride perform better than polyimides formulated solely with the BTDA dianhydride. Graphite fiber reinforced polyimide composites were formulated with the polyimide made from the BTDA dianhydride and both graphitic and non-graphitic fibers were evaluated. Graphitic fibers produced better tribological results, since thin, flowing, 'layer-like' transfer films were produced which did not build up with long sliding durations. Non-graphitic fibers did not produce this type of transfer. Previously announced in STAR as N83-22423

Fusaro, R. L.↗

Comparison of two transonic noise prediction formulations using the aircraft noise prediction program

This paper addresses recently completed work on using Farassat's Formulation 3 noise prediction code with the Aircraft Noise Prediction Program (ANOPP). Software was written to link aerodynamic loading generated by the Propeller Loading (PLD) module within ANOPP with formulation 3. Included are results of comparisons between Formulation 3 with ANOPP's existing noise prediction modules, Subsonic Propeller Noise (SPN) and Transonic Propeller Noise (TPN). Four case studies are investigated. Results of the comparison studies show excellent agreement for the subsonic cases. Differences found in the comparisons made under transonic conditions are strictly numerical and can be explained by the way in which the time derivative is calculated in Formulation 3. Also included is a section on how to execute Formulation 3 with ANOPP.

Spence, Peter L.↗

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

Parallel computing using a Lagrangian formulation

A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.

Liou, May-Fun↗

Parallel computing using a Lagrangian formulation

This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.

Liou, May-Fun↗

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

Smith, Arlynn W.↗

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.

Winckelmans, G. S.↗

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Smith, A. W.↗

Higher Order Modeling In the BEM/FEM Hybrid Formulation

Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.

Fink, Patrick W.↗