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At least 523 records · Page 29

Constrained optimization using design of experiment surfaces

An algorithm for solving constrained optimization problems is presented. First, design of experiment techniques are used to survey the design space. After evaluating the objective and constraint functions, as specified by Taguchi orthogonal arrays, analytical models of these functions are generated using a least-squares regression analysis. Next, a nonlinear programming package is used to optimize the analytical model. Based on the optimization information, the design space is reduced so as to close in around the minimum, and the entire procedure is repeated until convergence. An important feature of the algorithm is that function gradients are not required; therefore, for problems in which gradients would have to be estimated using finite-differences the number of function evaluations required for the optimization is significantly reduced, when compared with traditional nonlinear programming techniques. In addition, there is no requirement that the gradients must be smooth and continuous.

Bolt, Marvin Vance↗

Evaluating Crystallinity in Thermoplastic Composites for Aerospace Applications

Polymer matrix composites (PMCs) offer many benefits for the aerospace industry due to their potential for weight reduction when compared to metal or ceramic based materials. Most PMCs currently in flight use thermoset matrices, however, thermoplastic resins are being explored as alternatives due to their ability to be remelted, which is of particular interest due to the potential for in-situ repair and faster production. Most thermoplastic resins are semicrystalline polymers. The properties of semicrystalline thermoplastics are directly influenced by their crystallinity, which can vary due to many factors including thermal treatments, environmental conditions, and mechanical deformation. Within thermoplastic PMC parts, crystallinity gradients can arise due to variations in part geometry, across part thicknesses, and along bonded joints. Monitoring the crystallinity of thermoplastic composites is key to ensuring these materials meet the high demands required for aerospace. Several different analytical techniques exist that can be used to characterize the bulk crystallinity of thermoplastic materials. However, many existing methods lack the specificity required to identify the subtle variations in crystallinity that may play a significant role in the performance and durability of PMC parts. Because of this, a significant amount of work is still required to fully characterize and understand the crystallinity profiles of thermoplastic PMCs and the resulting impact to material properties. This talk discusses the use of multiple techniques such as Differential Scanning Calorimetry, Polarized Light Optical Microscopy, and Fourier-Transform Infrared Spectroscopy to characterize the crystallinity in carbon fiber/thermoplastic composites. Samples of different crystallinity profiles were manufactured using various cooling procedures. This work aims to provide the fundamental data necessary to understand the effects of crystallinity on thermoplastic PMCs, which is key to advancing their use in aerospace applications.

Thermoplastics↗

Preliminary Cryogenic Cold Test Results of the First 9-Cell LSF Shape Cavity

Following successful prototyping and testing of single- & 5-cell LSF shape cavities *, **, the first 9-cell LSF shape cavity LSF9-1 was successfully constructed using an innovative process at JLab with the in-house facilities. The cavity was then shipped to KEK for post-fabrication mechanical adjustment and ILC TDR style treatment and surface processing. Cold testing was carried out at the JLab VTA facility, instrumented with a suite of Kyoto instruments. Favorable values for the bath pressure detuning sensitivity and Lorentz force detuning coefficient were experimentally measured, validating the design improvement in cell stiffeners. Pass-band measurements indicate 4 out of 9 cells reaching gradient capability of > 45 MV/m, including 2 cells reaching 51 MV/m. Cornell OST detectors identified the cell and location responsible for the current hard quench limit. Multipacting-like barriers observed in end cells are investigated both analytically and numerically. The cavity was shipped to FNAL and received a light EP at the joint ANL/FNAL facility for further cold testing at Jlab. Two new 9-cell LSF cavities are being constructed including one made of large-grain niobium material.

Geng, Rong-Li↗

Consequences of magnetotail ion dynamics

The trajectories of a large ensemble of particles are calculated in a modified Tsyganenko magnetic field model with a uniform cross-tail electric field. The model magnetotail can be divided into several distinct dynamical regimes of ion motion. Near Earth, where the field lines are dipolar the adiabatic formalism is adequate. In the mid-tail and distant tail, guiding-center theory breaks down and must be replaced by a quasi-adiabatic formalism. There is an important transition region between the adiabatic and quasi-adiabatic regions where ion trajectories become more complicated and no simple analytical description holds. This wall region is characterized by rapid ion acceleration and a major loss of particles to the dusk flank. The moments of the ion distribution function are constructued from the ion trajectories, including density, temperature, and pressure in the x-z and x-y planes. In the noon-midnight meridian plane, parameters are relatively constant except near the Earth, while the x-y plots show strong gradients across the magnetotail. Magnetotail plasma convects earthward, drifts toward dusk, and is squeezed out of the tail in the near-Earth region. A thin current sheet forms in the quasi-adiabatic region, and the pressure tensor has significant off-diagonal terms at its edges. These terms are the result of quasi-adiabatic ion trajectories which lead to azimuthally asymmetric distribution functions capable of maintaining approximate stress balance across the current sheet. Simplified analytical descriptions provide further physical insight into ion dynamics that are observed.

Ashour-Abdalla, Maha↗

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of Hydrocyclone Geometry via Rapid Optimization Based on Computational Fluid Dynamics

Abstract Hydrocyclones exploit density gradients for the centrifugal separation of dispersions in a continuous liquid. Selection of the geometrics for optimal separation is case specific, like the media characteristics. The existing optimization method based on computational fluid dynamics (CFD) provides a powerful analytical tool but requires long computational times. The most common praxis for CFD optimization is via the single‐factor optimization method (SFOM). In this study, a novel approach is presented as an improved rapid optimization method that implements a dynamic‐mesh and user‐defined function optimization method (DUOM). The DUOM adapts the dynamic‐mesh approach from other applications to the optimization analysis of hydrocyclones. The DUOM reduced the computational time by 31.1 %, compared to the SFOM.

Liu, Lin↗

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN 4 for an IBM 360/91 computer.

Wing, L. D.↗

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN IV for an IBM 360/91 computer.

Wing, L. D.↗

The influence of centrifugal forces on the B field structure of an axially symmetric equilibrium magnetosphere

A model is presented of an axially symmetric pole-on magnetosphere in MHD force balance, in which both plasma thermal pressure gradients and centrifugal force are taken into account. Assuming that planetary rotation leads to differentially rotating magnetotail field lines, the deformation of magnetotail field lines under the influence of both thermal plasma pressure and centrifugal forces was calculated. Analytic solutions to the Grad-Shafranov equation are presented, which include the centrifugal force term. It is shown that the nonrotational magnetosphere with hot thermal plasma leads to a field configuration without a toroidal B(phi) component and without field-aligned Birkeland currents. The other extreme, a rapidly rotating magnetosphere with cold plasma, leads to a configuration in which plasma must be confined within a thin disk in a plane where the radial magnetic field component B(r) vanishes locally.

Ye, Gang↗

Microwave Scattering Model for Grass Blade Structures

In this paper, the electromagnetic scattering solution for a grass blade with complex cross-section geometry is considered. It is assumed that the blade cross section is electrically small, but its length is large compared to the incident wavelength. In a recent study it has been shown that the scattering solution for such problems, in the form of a polarizability tensor, can be obtained using the low-frequency approximation in conjunction with the method of moments. In addition, the study shows that the relationship between the polarizability tensor of a dielectric cylinder and its dielectric constant can be approximated by a simple algebraic expression. The results of this study are used to show that this algebraic approximation is valid also for cylinders with cross sections the shape of grass blades, providing that proper values am selected for each of three constants appearing in the expression. These constants are dependent on cylinder shape, and if the relationship between the constants and the three parameters describing a grass blade shape can be determined, an algebraic approximation relating polarizability tensor to blade shape, as well as dielectric constant, can be formed. Since the elements of the polarizability tensor are dependent on only these parameters, this algebraic approximation can replace the cumbersome method of moments model. A conjugate gradient method is then implemented to correctly determine the three constants of the algebraic approximation for each blade shape. A third-order polynomial fit to the data is then determined for each constant, thus providing a complete analytic replacement to the numerical (moment method) scattering model. Comparisons of this approximation to the numerical model show an average error of less than 3%.

Stiles, James M.↗

Thermal Examination of an Orbiting Cryogenic Fuel Depot

For many years NASA has been interested in the storage and transfer of cryogenic fuels in space. Lunar, L2 and other chemical propulsive space vehicle missions now have staged refueling needs that a fuel depot would satisfy. The depot considered is located in lower earth orbit. Many considerations must go into designing and building such a station. Multi-layer insulation systems, thermal shielding and low conductive structural supports are the principal means of protecting the system from excessive heat loss due to boiloff. This study focuses on the thermal losses associated with storing LH2 in a passively cooled fuel depot in a lower earth equatorial orbit. The corresponding examination looks at several configurations of the fuel depot. An analytical model has been developed to determine the thermal advantages and disadvantages of three different fuel depot configurations. Each of the systems consists of three Boeing rocket bodies arranged in various configurations. The first two configurations are gravity gradient stabilized while the third one is a spin-stabilized concept. Each concept was chosen for self-righting capabilities as well as the fuel settling capabilities, however the purpose of this paper is to prove which of the three concepts is the most efficient passively cooled system. The specific areas to be discussed are the heating time from the fusion temperature to the vaporization temperature and the amount of boiloff for a specific number of orbits. Each of the previous points is compared using various sun exposed surface areas of the tanks.

Hull, Patrick V.↗

Generation and Life Cycle of Solar Spicules

The physical mechanism for the creation of solar spicules is proposed with three stages of their life cycle. It is assumed that at stage I the density hump is formed locally in the x-y plane in the lower chromosphere in the presence of temperature gradients of electrons and ions along the z-axis (the vertical direction). In this region, the density structure of quasi-neutral (n i ≃ n e = n) plasma after taking birth is accelerated in the vertical direction owing to the thermal force F th ∝ ∇n(x, y, t) × (∇T e + ∇T i ). The exact time-dependent analytical solution of two-fluid plasma equations is presented assuming that density is maximum at the center of the density structure and decays away from it gradually. The 2D density structure is created as a step function H(t) in time at the bottom of the chromosphere, and consequently, the vertical plasma velocity turns out to be the ramp function of time R(t) = tH(t), whereas the source term S(x, y, t) for the density follows the delta function δ(t) form. The upward acceleration a = a(x, y) $\hat{z}$ produced in this density structure is greater than the downward constant solar acceleration −g ⊙ in the chromosphere. In the transition region, the temperature gradients are steeper; therefore, the upward acceleration increases in magnitude g ⊙ ≪ a and the density hump spends less time there. This is stage II of its life cycle. In stage III, the density structure enters into the corona, where the gradients of temperatures vanish and the structure decelerates to zero velocity under the action of the solar gravitational force.

79 ASTRONOMY AND ASTROPHYSICS↗

Enhancing the cooling performance of thermocouples: a power-constrained topology optimization procedure

Abstract Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form $$p_k=p_{\sigma }>p_{\alpha }=1$$ p k = p σ > p α = 1 for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

Gutiérrez, G. Reales↗

Electrically Driven Ion Separations in Permeable Membranes

Ion separations are critical for producing materials such as Li and rare-earth element salts that are essential for applications including energy storage and production. This research aimed to develop and understand separations of singly and multiply charged ions as well as separations among different singly charged ions such as Li + and Na + . Thin layers of polyelectrolytes on membranes allow passage of singly charged ions at rates 1000 times faster than those for multiply charged ions. This allows purification of mixtures with equal concentrations of Li + and Mg 2+ to create a permeate solution with >99% Li + . Such membranes may also effectively isolate rare earth elements. To separate Li + and K + , this work developed opposing flow and current in membranes. The current overcomes the flow of K + to allow Li + to selectively pass through the membrane, leading to Li + /K + selectivities around 70. All of the research employs modelling to better understand the mechanism of these separations, which includes transport driven by gradients in electrical potential, concentration, and pressure. The interplay of these driving forces can create highly selective separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytical solutions of a class of multidimensional Fokker-Planck equations

Analytical representations of the solutions of Kolmogorov's forward (i.e., Fokker-Planck) and backward partial differential equations are obtained by employing Girsanov's (1960) transformation. The equations considered are restricted to those with the drift vector being the gradient of a function and the diffusion matrix being nonsingular and dependent upon time only.

Zhang, Weijian↗

Supervised learning of probability distributions by neural networks

Supervised learning algorithms for feedforward neural networks are investigated analytically. The back-propagation algorithm described by Werbos (1974), Parker (1985), and Rumelhart et al. (1986) is generalized by redefining the values of the input and output neurons as probabilities. The synaptic weights are then varied to follow gradients in the logarithm of likelihood rather than in the error. This modification is shown to provide a more rigorous theoretical basis for the algorithm and to permit more accurate predictions. A typical application involving a medical-diagnosis expert system is discussed.

Baum, Eric B.↗