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High-order discretizations have become increasingly popular across a wide range of applications, including reservoir simulation. However, the lack of stability and robustness of these discretizations for advection-dominant problems prevent them from being widely adopted. This paper presents work towards improving the stability and robustness of the discontinuous Galerkin (DG) finite element scheme, for advection-dominant two-phase flow problems in particular. A linearized analysis of the two-phase flow equations is used to show that a standard DG discretization of the two-phase flow equations in mass conservation form results in a neutrally stable semi-discrete system in the advection-dominant limit. Furthermore, the analysis is also used to propose additional terms to the DG method which linearly stabilize the discretization. These additional terms are derived by comparing the linearized equations in mass conservation form against an upwinded pressure-saturation form of the equations. Next, a partial differential equation-based artificial viscosity method is proposed for the Buckley-Leverett and two-phase flow equations, as a means of mitigating Gibbs oscillations in high-order discretizations and ensuring convergence to physical solutions. The modified DG method with artificial viscosity is demonstrated on a two-phase flow problem with heterogeneous rock permeabilities, where the high-order discretizations significantly outperform a conventional first-order approach in terms of computational cost required to achieve a given level of error in an output of interest.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015., Cataloged from PDF version of thesis., Includes bibliographical references (pages 147-152)., Variations in the geometry of compressor blades can be introduced by variability in the manufacturing process or by in-service erosion. Recent research efforts have focused on characterizing the impacts of this geometric variability on turbomachinery performance and designing blade geometries whose performance is robust to this variability. Relatively little work has been done to specify the appropriate level of variability by designing the manufacturing tolerances. This thesis presents new approaches for optimizing tolerances that can be applied to compliment existing geometry optimization techniques. Building upon previous research, a Gaussian random field model of manufacturing variability is developed and used to estimate the statistical performance impacts of geometric variability on compressor blade performance. Flow mechanisms that deteriorate the mean performance in the presence of geometric variability are analyzed for design and off-design conditions. A probabilistic, gradient-based optimization framework is presented and applied to optimize the tolerances of compressor blades, as well as to optimize the tolerances and blade geometry simultaneously. The effectiveness of simultaneous optimization of the geometry and manufacturing tolerances is compared to a sequential procedure where the nominal blade geometry is optimized first, followed by the tolerances. Single-point optimization, where the performance at a single flow incidence is optimized, is found to produce geometries that are not robust to manufacturing variations. Adopting a multi-point design strategy results in blades that are robust to both variations in the geometry and incidence, allowing a sequential design strategy to be used., by Eric Alexander Dow., Ph. D.

The manufacturing processes used to create compressor blades inevitably introduce geometric variability to the blade surface. In addition to increasing the performance variability, it has been observed that introducing geometric variability tends to reduce the mean performance of compressor blades. For example, the mean adiabatic efficiency observed in compressor blades with geometric variability is typically lower than the efficiency in the absence of variability. This “mean-shift” in performance leads to increased operating costs over the life of the compressor blade. These detrimental effects can be reduced by using robust optimization techniques to optimize the blade geometry. The impact of geometric variability can also be reduced by imposing stricter tolerances, thereby directly reducing the allowable level of variability. However, imposing stricter manufacturing tolerances increases the cost of manufacturing. Thus, the blade design and tolerances must be chosen with both performance and manufacturing cost in mind. This paper presents a computational framework for performing simultaneous robust design and tolerancing of compressor blades subject to manufacturing variability. The manufacturing variability is modelled as a Gaussian random field with non-stationary variance to simulate the effects of spatially varying manufacturing tolerances. The statistical performance of the compressor blade system is evaluated using the Monte Carlo method. A gradient based optimization scheme is used to determine the optimal blade geometry and distribution of manufacturing tolerances.

Many engineering systems are subject to spatially distributed uncertainty, i.e., uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will, in general, change the statistical distribution of the system outputs. We present an approach for computing the sensitivity of the statistics of system outputs with respect to the parameters describing the mean and covariance of the distributed uncertainty. This sensitivity information is then incorporated into a gradient-based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics. This framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade.

This paper presents a computational approach for optimal robust design and tolerancing of turbomachinery compressor blades that are subject to geometric variability. This approach simultaneously determines the optimal blade geometry and manufacturing tolerances to minimize the overall cost of producing and operating the resulting compressor blades. A pathwise sensitivity method is used to compute gradient information that is in turn used to optimize the design and tolerances. Results for a two-dimensional subsonic compressor are presented, demonstrating the significant performance improvements that can be achieved using the proposed approach., Pratt & Whitney Aircraft Company, Boeing Company

Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011., Cataloged from PDF version of thesis., Includes bibliographical references (p. 69-70)., This thesis presents an approach for building a statistical model for the structural uncertainties in Reynolds averaged Navier-Stokes (RANS) turbulence models. This approach solves an inference problem by comparing the results of RANS calculations to direct numerical simulation. The adjoint method is used to efficiently solve an inverse problem to determine the RANS turbulent viscosity field that most accurately reproduces the mean flow field computed by direct numerical simulation. The discrepancy between the inferred turbulent viscosity and the turbulent viscosity predicted by RANS is modeled as a Gaussian random field. Finally, the uncertainty in the turbulent viscosity field is propagated to the quantities of interest. Results are first presented for turbulent flow through a straight channel. To model the uncertainty in more complex flows, the procedure is repeated for a collection of flows through randomly generated geometries., by Eric Alexander Dow., S.M.

An electrochemical cell system and methods for controlling the system are provided that are operated to produce an amount of current based upon power draw. The cell utilizes a solution phase catholyte introduced into a cell containing a metallic anode and a catalytic surface. A cathodic species is introduced into the space between the anode and the surface as a liquid along with electrolyte and liquid caustic. The mixture of caustic, electrolyte and liquid catholyte is continuously recirculated through the space, and a portion of the recirculation stream is exhausted in order to control the concentration of reaction products in each cell. Controllable injection mechanisms are used to inject the liquids from storage sources based upon the monitored power draw. The control mechanism independently controls each injection mechanism to inject appropriate amounts of caustic, electrolyte and catholyte to achieve the desired concentrations.

It is a general purpose and object of the present invention to eliminate the parasitic direct reaction of the catholyte with the metal anode in a semi-fuel cell, thereby improving the overall energy yield of the semi-fuel cell. This general purpose and object is accomplished with the present invention by using a semi-permeable membrane capable of ion exchange placed between the anode and cathode compartment of a semi-fuel cell in order to isolate the anolyte and catholyte solutions.

This patent application discloses an improved semi-fuel cell and an improved cathode used therein. The semi-fuel cell stack comprises a housing, an anode within the housing, a porous cathode within the housing, an aqueous catholyte within the housing, an aqueous anolyte stream flowing in the housing, and a membrane for preventing migration of the catholyte through the porous cathode and into the anolyte stream. In a preferred embodiment of the present invention, the catholyte comprises an aqueous hydrogen peroxide solution, the anolyte comprises a NaOH/seawater solution, and the membrane permits passage of OH ions while inhibiting the passage of hydrogen peroxide. The membrane is attached to a surface of the cathode or, alternatively, impregnated into the cathode. (3 figures)

The present invention relates to a method of producing an electrocatalytic cathode for use in an electrochemical cell system comprising the steps of providing a carbon substrate and simultaneously depositing palladium and iridium on the carbon substrate by cyclic voltammetry or by controlled potential coulometry. The simultaneous deposition of the palladium and iridium is preferably carried out using a solution containing 1.0mM palladium chloride, 2.0mM sodium hexachloroiridate, 0.2M potassium chloride, and 0.1M hydrochloric acid.

The present invention relates to an improved magnesium semi-fuel cell which has a magnesium anode, a seawater/catholyte electrolyte, preferably containing acid to solubilize solid precipitates, and an electrocatalyst composed of palladium and iridium catalyzed onto carbon paper. The acid added to the electrolyte is preferably selected from the group consisting of sulfuric acid, hydrochloric acid, phosphoric acid, acetic acid and mixtures thereof.

The present invention relates to a dry composition of materials to be used in a battery system. The dry composition comprises a mixture consisting of sodium hydroxide and sodium oxide. In a first reservoir in the battery system, the mixture is present in an amount sufficient to form with water a heated sodium hydroxide electrolyte solution having a 15% by weight concentration of sodium hydroxide. In a second reservoir in the battery system, the mixture is present in an amount sufficient to form with water a heated sodium hydroxide electrolyte solution having to up to about 75% by weight concentration of sodium hydroxide. The present invention also relates to a battery system and a method for generating electrical power which utilize the aforementioned dry composition of materials., Supersedes PAT-APPL-797 765-97, AD-D018 414

This report contains a summary of the ONR projects concerned with semi-fuel cell power systems.