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Molten salts thermodynamic properties, discussing pure salts corresponding states and binary mixtures conformal solution theories, using model ionic melt
The isothermal processes of membrane separation, supercritical extraction and chromatography were examined using availability analysis. The general approach was to derive equations that identified where energy is consumed in these processes and how they compare with conventional separation methods. These separation methods are characterized by pure work inputs, chiefly in the form of a pressure drop which supplies the required energy. Equations were derived for the energy requirement in terms of regular solution theory. This approach is believed to accurately predict the work of separation in terms of the heat of solution and the entropy of mixing. It can form the basis of a convenient calculation method for optimizing membrane and solvent properties for particular applications. Calculations were made on the energy requirements for a membrane process separating air into its components.
The shock interaction produced when an incident shock impinges on an inlet cowl lip is investigated for a cowl lip radius of 0.1 in. and flight conditions of Mach 15 and 35-km altitude. This problem is of interest in the design of hypersonic flight vehicles because the interference heating at the cowl lip surface from such a shock interaction is expected to be very high and the design of adequate thermal protection in this region will be challenging. Noncontinuum effects may be significant at this combination of altitude and small dimensions. If this is so, a computational solution based on the Navier-Stokes equations could significantly overpredict the surface heating on the cowl lip. Therefore, a kinetic theory solution technique, direct simulation Monte Carlo (DSMC), is used to predict the flowfield and surface heating. The details of modeling this problem and some preliminary results are presented. The same qualitative flow patterns are seen with DSMC and a continuum solution of the shock interference case, but the peak heating predicted with DSMC is somewhat lower.
Modeling of multicomponent trace contaminant adsorption on activated carbon for spacecraft life support applications presents challenges due to the very low contaminant concentrations in cabin air coupled with very strong adsorption of heavier components such as cyclic polydimethylsiloxanes. Both gas-phase and solid-phase micropore mass transfer resistances can be important, and competitive interactions between adsorbed components can result in behavior such as roll-up where lighter components displaced by heavier components have a higher concentration at the outlet than at the inlet. This paper describes the further development of a dynamic trace contaminant adsorption model based on Ideal Adsorbed Solution Theory (IAST). Alternative 1-dimensional and 2-dimensional versions of the model are described with different mass transfer resistance and driving force assumptions. Optimization of solution methods for speed and stability is also described. Mass balance equations are scaled to provide sensitivity over the wide range of component concentrations in cabin air. Model parameters are estimated from isotherm and breakthrough test data on single adsorbate and binary adsorbate systems. Multicomponent results are compared against predictions of a heritage model used extensively by NASA for trace contaminant control system (TCCS) carbon bed sizing. Finally, efforts to implement the model in a second software platform for wider access are described.
The computer code LTRAN2 has been extended to compute unsteady transonic flows about oscillating airfoils with supersonic freestreams. The LTRAN2 code uses an alternating direction implicit (ADI) algorithm to solve the two-dimensional, nonlinear, low-frequency, transonic small-disturbance (LF-TSD) equation. The modified code, LTRAN2-SS, includes a 'high-frequency' option. Steady solutions are checked against those computed by the steady TSD code, TSFOIL; unsteady computations of the linear LF-TSD equation are compared with known linear theory solutions; and new unsteady nonlinear solutions are presented. These cases include standard AGARD test cases for the NLR 7301, MBB-A3, and DO Al supercritical airfoils, as well as several NACA airfoils. The modified code enables aerodynamicists to quickly and efficiently compute transonic flows for both subsonic and supersonic freestreams, and thus resolve flutter boundaries through the full extent of the transonic dip phenomenon.
Rarefied gas dynamics - kinetic theory, solutions of boltzmann equation, molecular beams and surface interactions
A limited number of lifting-surface-theory solutions for wings with chordwise loadings resulting from angle of attack, parabolic-ac camber, and flap deflection are now available. These solutions were studied with the purpose of determining methods of extrapolating the results in such a way that they could be used to determine lifting-surface-theory values of the aspect-ratio corrections to the lift and hinge-moment parameters for both angle-of-attack and flap-deflection-type loading that could be used to predict the characteristics of horizontal tail surfaces from section data with sufficient accuracy for engineering purposes. Such a method was devised for horizontal tail surfaces with full-span elevators. In spite of the fact that the theory involved is rather complex, the method is simple to apply and may be applied without any knowledge of lifting-surface theory. A comparison of experimental finite-span and section value and of the estimated values of the lift and hinge-moment parameters for three horizontal tail surfaces was made to provide an experimental verification of the method suggested. (author)
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Growth of vapor bubble in liquid mixtures and growth and collapse of noncondensing, nonsoluble gas in pure liquid determined by approximate solutions derived from forster source theory
Solutions of impact of a rigid prismatic float connected by a massless spring to a rigid upper mass are presented. The solutions are based on hydrodynamic theory which has been experimentally confirmed for a rigid structure. Equations are given for defining the spring constant and the ratio of the sprung mass to the lower mass so that the two-mass system provides representation of the fundamental mode of an airplane wing. The forces calculated are more accurate than the forces which would be predicted for a rigid airframe since the effect of the fundamental mode on the hydrodynamic force is taken into account. In a comparison of the theoretical data with data for a severe flight-test landing impact, the effect of the fundamental mode on the hydrodynamic force is considered and response data are compared with experimental data.
Absorption induced embrittlement of solid metals by certain liquid metals is analyzed through an Engel-Brewer calculation of the solid-liquid interaction energy, and of the effect of the latter in reducing fracture surface energy. The reduction in fracture surface energy is estimated by comparison of the electronic contribution to the solid-liquid interaction energy with solid-solid bond energy for some 40 liquid-solid couples. Regular solution theory is used to estimate mutual solubility as the relative difference in parameter values. Embrittlement can be predicted by using reduction in fracture surface energy and solubility parameter difference as critical variables. The effect of solute additions to the liquid on the degree of embrittlement is interpreted via the same two variables; the principal effect of solutes is to modify solubility relationships at the solid-liquid interface.
A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.
The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.
In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.
Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.
We show that the Killing tensor of the Kerr spacetime has an analogue in the $\sqrt{Kerr}$ gauge theory solution related to it by the classical double copy. This hidden symmetry of $\sqrt{Kerr}$ leads to an additional constant of motion for color-charged point particles moving in it, implying integrability of the equation of motion. These are the gauge theory counterparts to the Carter constant and the integrability of the geodesic equation in a Kerr background.
By utilizing linear stability theory, solutions for elastic buckling of short and moderate length orthotropic cylinders under axial compression are presented and correlated with experimental results on circumferentially stiffened cylinders. The plastic buckling of short and moderate length isotropic and orthotropic cylinders is also investigated and the theoretical results correlated with available experimental data. A discussion of the effects of finite deflection and initial imperfection is presented in order to explain the correlation obtained between the theory and the experimental data.
The behavior of highly concentrated electrolytes departs radically from the dilute-solution theory, yet the molecular origin of this transformation remains unresolved. Here, we identify the conformational isomerization of molecular ions as a decisive, previously unrecognized control parameter governing structure and transport in crowded aqueous electrolytes. Across a series of fluorosulfonimide anions, we show that increasing concentration drives a collective shift from extended transoid to compact cisoid conformers, revealed by small-angle X-ray scattering, vibrational spectroscopy, pulsed-field gradient NMR, and molecular dynamics simulations. This conformational transition triggers a collapse of the hydrogen-bonded water network and the emergence of densely packed ionic domains with confined water, producing a qualitative change in Li+ transport from solvent-mediated diffusion to network-confined hopping. Anion size and asymmetry systematically tune the onset of this transition, demonstrating that molecular geometry dictates mesoscale organization and dynamics in the ion-rich regime. Our results establish ion conformation, not merely composition or coordination, as a fundamental thermodynamic variable in concentrated solutions, providing a chemical framework that unifies solvation structure and transport in water-in-salt electrolytes and suggesting new principles for designing dense ionic media.