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Preliminary Enhanced LAW Glass Formulation Algorithm

This report summarizes the Preliminary Enhanced Low-Activity Waste Glass Formulation Algorithm (GFA), its background information, and the calculations it performs. The Preliminary Enhanced Low-Activity Waste GFA is a tool developed in MATLAB to formulate glass for a given waste composition while attempting to maximize waste loading. It is intended for use at the Waste Treatment and Immobilization Plant, where nuclear waste will be vitrified into glass. The formulated glass is required to satisfy several processing and product quality constraints. In addition, calculations must account for associated uncertainties in constraint prediction and measurement. The GFA adheres to Pacific Northwest National Laboratory nuclear quality assurance procedures and has been validated and verified. In this second revision to the report, two constraints: the lithium and zirconia target constraints were amended to Table 3.1 and programmed into the algorithm. Additionally, three sections were added. Section 3.2.1 includes the Enhanced LAW Correlation Rules, an addition to the glass optimality criteria. Section 4.0 discusses a stepped process approach taken to ensure the algorithm can adequately react to differences between its recommended output and the actual measurements and transfers made during plant operation, and calculation of specific radionuclide concentrations. Section 5.2 describes changes to the user interaction with the algorithm program including the addition of a graphical user interface and compilation of the software.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

LAW Glass Formulation to Support Melter Runs with Simulants

The major objective of this work was to prepare and characterize glass formulations in order to develop and select formulations that are compliant with contractual and processing requirements to support melter tests with each of the LAW Sub-Envelopes. Glasses that cover composition ranges of interest were prepared and characterized to ensure that selected glass compositions can tolerate expected composition variations resulting from process errors without adversely affecting processing characteristics or product quality. Glass compositions that are expected to result during transitions from one waste stream to another were also prepared and characterized. Other objectives of the work included preparation and characterization of glasses with respect to the properties of interest, optimization of sulfate loading in the glasses, evaluation of ability to achieve waste loading limits, testing to demonstrate compatibility of glass melts with melter materials of construction, and identification of glass formulation issues with respect to contract specifications and processing requirements.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Development of Magnesium Oxysulfate Formulation for SRPPF Aqueous Recovery Liquid Solidification

The liquid effluent from the Savannah River Plutonium Processing Facility (SRPPF) Aqueous Recovery Processes will be solidified into a stable form that is acceptable by Waste Isolation Pilot Plant (WIPP) for disposal. The current Aqueous Recovery flow sheet proposes to solidify the liquid effluent using a grout formula that was developed and tested for the former Waste Solidification Building process. This Portland cement based mixture results in a high pH (~13) leachate from the solidified waste form which is not acceptable to WIPP in the large quantities expected from production at SRPPF. Various cementitious materials were previously evaluated as alternative grout formulations to Portland cement and a MgO-based mix was identified as a promising alternative. A magnesium oxysulfate (MOS) cement formulation comprised of reactive magnesium oxide (MgO), anhydrous magnesium sulfate (MgSO 4 ), and sand, as a non-reactive heat sink provided good mixability, similar density to the original Portland-cement based mix, and a leachate pH of 9.4, within the assumed WIPP brine pH range. However, the MOS formulation exhibited an appreciable amount of heat generation, which resulted in premature setting of a large-scale test.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NMR Spectroscopy for Protein Higher Order Structure Similarity Assessment in Formulated Drug Products

Peptide and protein drug molecules fold into higher order structures (HOS) in formulation and these folded structures are often critical for drug efficacy and safety. Generic or biosimilar drug products (DPs) need to show similar HOS to the reference product. The solution NMR spectroscopy is a non-invasive, chemically and structurally specific analytical method that is ideal for characterizing protein therapeutics in formulation. However, only limited NMR studies have been performed directly on marketed DPs and questions remain on how to quantitively define similarity. Here, NMR spectra were collected on marketed peptide and protein DPs, including calcitonin-salmon, liraglutide, teriparatide, exenatide, insulin glargine and rituximab. The 1D 1 H spectral pattern readily revealed protein HOS heterogeneity, exchange and oligomerization in the different formulations. Principal component analysis (PCA) applied to two rituximab DPs showed consistent results with the previously demonstrated similarity metrics of Mahalanobis distance (D M ) of 3.3. The 2D 1 H- 13 C HSQC spectral comparison of insulin glargine DPs provided similarity metrics for chemical shift difference (Δδ) and methyl peak profile, i.e., 4 ppb for 1 H, 15 ppb for 13 C and 98% peaks with equivalent peak height. Finally, 2D 1 H- 15 N sofast HMQC was demonstrated as a sensitive method for comparison of small protein HOS. The application of NMR procedures and chemometric analysis on therapeutic proteins offer quantitative similarity assessments of DPs with practically achievable similarity metrics.

59 BASIC BIOLOGICAL SCIENCES↗

An Improved Formulation for Hybridizable Discontinuous Galerkin Fluid-Structure Interaction Modeling with Reduced Computational Expense

Here, this work presents two computational efficiency improvements for the hybridizable discontinuous Galerkin (HDG) fluid-structure interaction (FSI) model presented by Sheldon et al. A new formulation for the solid is presented that eliminates the global displacement, resulting in the velocity being the only global solid variable. This necessitates a change to the solid-mesh displacement coupling, which is accounted for by coupling the local solid displacement to the global mesh displacement. Additionally, the mesh basis and test functions are restricted to linear polynomials, rather than being equal-order with the fluid and solid. This change increases the computational efficiency dynamically, with greater benefit the higher order the computation, when compared to an equal-order formulation. These two improvements result in a 50% reduction in the number of global degrees of freedom for high-order simulations for both the fluid and solid domains, as well as an approximately 50% reduction in the number of local fluid domain degrees of freedom for high-order simulations. Finally, the new, more efficient formulation is compared against that from Sheldon et al. and negligible change of accuracy is found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Boundary lubrication of formulated C-ether in air to 300 deg C. 1: Phosphorus ester additives

Friction and wear measurements were made on CVM M-50 steel lubricated with three C-ether (modified polyphenyl ether) formulations in dry and wet air. Results were compared to those obtained with a formulated Type 2 ester and the C-ether base fluid. A ball-on-disk sliding friction apparatus was used. Experimental conditions were a 1-kilogram load, a 17-meter-perminute (100-rpm) surface speed, and a 25 to 300 C (77 to 572 F) disk temperature range. The C-ether base fluid and the three formulated C-ether fluids yielded lower wear than the Type 2 ester over the entire temperature range. All C-ether fluids exhibited slightly higher friction coefficients than the ester from 150 to 300 C (302 to 572 F) and similar values from 25 to 150 C (77 to 302 F). In general, lower wear rates were observed with the C-ethers when tested in wet air as compared to a dry air atmosphere.

Jones, W. R., Jr.↗

Formulation of image quality prediction criteria for the Viking lander camera

Image quality criteria are defined and mathematically formulated for the prediction computer program which is to be developed for the Viking lander imaging experiment. The general objective of broad-band (black and white) imagery to resolve small spatial details and slopes is formulated as the detectability of a right-circular cone with surface properties of the surrounding terrain. The general objective of narrow-band (color and near-infrared) imagery to observe spectral characteristics if formulated as the minimum detectable albedo variation. The general goal to encompass, but not exceed, the range of the scene radiance distribution within single, commandable, camera dynamic range setting is also considered.

Huck, F. O.↗

A new formulation of the conservation equations of fluid dynamics

The computation of time-dependent flows has inspired a new, higher-dimensional formulation of the conservation equations of fluid dynamics in which time is treated as a fourth coordinate. The formulation is derived for a constant-density flow, and then extended to a variable-density flow by introducing a fifth, fictitious coordinate. This new coordinate can also act as a source coordinate, so that external source terms can be included. The analysis is carried out for both incompressible, stratified flow, and compressible equilibrium flow. The results are then extended to non-equilibrium and magnetohydrodynamic flows. Several applications of the new formulation to the computation of time-dependent flows are discussed.

Vinokur, M.↗

The formulation of simulation models of aeronautical systems

Recent developments in formula-manipulation compilers have led to a significant reduction in the time spent in formulating models of complex multi-degrees-of-freedom dynamical systems. MACSYMA, a computer system that can be used to perform symbolic manipulations in an interactive mode, is applied to the problem of formulating models of aeronautical systems for simulation studies. An example demonstrates that once the procedure is established, the formulation and modification of the models can be reduced to a series of routine computer operations.

Howard, J. C.↗

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response: (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate dependent aerodynamic phenomena characteristic of airfoils in low speed dynamic stall; the second permits a description of the double valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies.

Tobak, M.↗

An element formulation for perturbed motion about the center of mass

The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements: l, the magnitude of the angular momentum vector; h, the total energy; delta and epsilon, two linear functions of the independent variable; and psi(1) and theta (1), two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body.

Donaldson, J. D.↗

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate-dependent aerodynamic phenomena characteristic of airfoils in low-speed dynamic stall; the second permits a description of the double-valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies.

Tobak, M.↗

CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Lee, C. H.↗

Dynamic loads analysis system (DYLOFLEX) summary. Volume 1: Engineering formulation

The DYLOFLEX computer program system expands the aeroelastic cycle from that in the FLEXSTAB computer program system to include dynamic loads analyses involving active controls. Two aerodynamic options exist within DYLOFLEX. The analyst can formulate the problem with unsteady aerodynamics calculated using the doublet lattice method or with quasi-steady aerodynamics formulated from either FLEXSTAB or doublet lattice steady state aerodynamics with unsteady effects approximated by indicial lift growth functions. The equations of motion are formulated assuming straight and level flight and small motions. Loads are calculated using the force summation technique. DYLOFLEX consists of nine standalone programs which can be linked with each other by magnetic files used to transmit the required data between programs.

Miller, R. D.↗

The computation of isentropic atmospheric trajectories using a 'discrete model' formulation

An explicit technique for calculating atmospheric trajectories is presented as an alternative method to the standard implicit scheme of Danielsen (1961). The technique uses the inviscid equations of motion and the discrete model formulation derived by Greenspan (1972, 1973) to compute trajectories on isentropic surfaces, assuming adiabatic flow. The discrete model formulation is designed specifically for a Lagrangian system and objectively accounts for the geostrophic departures, local psi-tendencies, and the subsequent accelerations along the entire length of the trajectory. Application of the discrete formulation to a diagnostic case study yielded favorable results.

Petersen, R. A.↗

A general and computationally fast formulation for radiative transfer with scattering

A general formulation of monocromatic radiative transfer with scattering has been developed for plane-parallel geometry. The inhomogeneous and nonisothermal medium absorbs, emits, and anisotropically scatters radiation. Surfaces can emit and scatter radiation in any specified manner. The solution procedure uses the fact that phase incoherent scattering is linear in radiative sources. Certain basic scattering functions are then defined and calculated by an adding computer code using matrix algebra. These scattering functions are weighted by the temperature field and summed (superimposed) to obtain the solution for any specific problem. Numerical results for exiting intensities and one-sided heat fluxes from general media bound by one arbitrary surface are presented. These parametric studies demonstrate the effects of scattering particles and surfaces on radiative transfer from inhomogeneous and nonisothermal media. Application of the formulation to radiative equilibrium is also discussed. The conclusion is that all problems in plane-parallel radiative transfer with scattering can be solved by a common and computationally fast algorithm based on this formulation.

Cogley, A. C.↗

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗

An analytic formulation for heating source memory in the thermospheric composition

Numerical calculations from a spectral circulation model are utilized to construct an analytic Green's function formulation describing the meridional, time-dependent thermospheric composition and temperature response during magnetic storms. The purpose is to develop a formulation that embodies source memory while being sufficiently simple to serve as a heuristic guide for empirical modeling. By passing from the discrete Fourier series representation, utilized for the numerical circulation model, to a continuous Fourier integral representation, explicit waves are obtained for the thermospheric response times. The response times are altitude and species dependent and can exceed two days below 200 km. Thus, for certain storm scenarios, pronounced source memory signatures for the composition and temperature are predicted. Response times obtained from the formulation are shown to give a response consistent with previously published neutral composition data from AE-C for the February 1974 storm when an ap dependent heat source is employed.

Porter, H. S.↗