The effect of injector design on thrust- chamber erosion

Relation between injector design and erosion of ablative and pyrolytic graphite thrust chamber throa

Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in computational effort for the calculation of the reduced system, compared to a POD. The efficiency of the algorithm is tested on the one dimensional Burgers equations and a one dimensional equation of the Fisher type as nonlinear model systems.Comment: 12 pages, 12 figure

Study of the Three Component System Diethyl Ether-Water-Magnesium Bromide at 25 C. (Abstract)

Varying amounts of the three components were brought together in a tube and allowed to come to equilibrium at 25° C. and at atmospheric pressure. The composition of each of the condensed phases, solid and liquid, was determined by analysis and a triangular three component diagram of the phases in equilibrium was made. From the areas, lines and points of the phase diagram, the following information was obtained. Two independent pairs of partly miscible liquids were found: one consisting of a water and an ether layer with a small amount of magnesium bromide dissolved in the ether layer, the other pair consisting essentially of two ether layers, with considerable magnesium bromide in one of the layers. Two solids were found that can exist in equilibrium with liquid phases at 25° C., these being magnesium bromide hexahydrate and magnesium bromide di-ether ate. No evidence was found for the existence of a mixed solvate or the basic magnesium bromide di-etherate as claimed by Menschutkin

Application of the Van\u27t Hoff Equation to Adsorption Equilibria

Isothermal adsorption data for many gases and vapors on charcoal and other adsorbents have been shown by various investigators (1), (2), (3), (4), to agree satisfactorily with the Langmuir adsorption isotherm, except for deviations, possibly due to multilayer adsorption, as the pressure of the saturated vapor is approached. The Langmuir equation is derived on the hypothesis of a unimolecular adsorbed layer. The rate of adsorption, assumed proportional to the pressure p and the fraction of the surface unoccupied, (1 - ϑ), is equated to the rate of desorption which is assumed proportional to the fraction of the surface covered, ϑ, giving the equation below

Ethyl Etherates of Zinc Bromide

The salvation of solid zinc bromide in contact with diethyl ether solutions has been studied by vapor pressure measurements and solubility determinations from -10 to 35° C. The existence of two solvates, believed to be the dietherate of zinc bromide, ZnBr2, 2(C2H5)2O and the monoetherate of zinc bromide, ZnBr2. - (C2H5)2O, was indicated by the following results: Definite changes in slope occurred in the curves obtained by plotting the logarithm of the vapor pressure of ether for systems of varying mol ratios (mols (C2H5)2O/mols ZnBr2 ) against the reciprocal of the absolute temperature and by plotting the logarithm of the solubility of zinc bromide in ether against the reciprocal of the absolute temperature. These changes in slope, which are caused by changes in the solid phases, appear between 0 and 5° and between 15 and 25°C. Further, analyses of the wet solids in contact with the saturated solutions at 0, 15 and 25° C. indicate that the stable solid phases in equilibrium with the saturated solutions at these temperatures are the dietherate, the monoetherate and the unsolvated zinc bromide, respectively

The Solvating Power of Anhydrous Magnesium Bromide as a Possible Function of Its Preparation Temperature

Before undertaking a study of the solvates of magnesium bromide, a method for preparing a reproducibly active anhydrous salt must be found. A suitable method is by the direct union of magnesium and bromine in ether, according to the procedure of Zelinsky. This results in the formation of etherates, from which the anhydrous salt can be obtained by desolvating at a moderately high temperature in a vacuum. It is known that if too high a temperature is used in the preparation of anhydrous aluminum oxide or calcium sulfate, the resulting product will not recombine with water. It is conceivable that the solvating power of anhydrous magnesium bromide, prepared from its etherates, might in an analogous way be a function of the preparation temperature. To test the possible effect of temperature on the solvating property of magnesium bromide, samples were desolvated under reduced pressure at 100°, 200°, 300° and 400° C. A constant stream of air saturated with ether at 20° was then passed over the samples, which were kept at 25° and weighed at intervals. The rates of solvation for the various samples were found to be equal within experimental error. It is conceded that the necessity of using interchangeable ground-glass joints permitted the entrance of traces of moisture, but within the temperature ranges studied, we feel justified in stating that the solvating power of anhydrous magnesium bromide is not a function of its preparation temperature

The Solubility of Anhydrous Magnesium Perchlorate in Diethyl Ether

In the study of the physical properties of non-aqueous solvates considerable work has been done on the systems magnesium bromide-diethyl ether (1-3) and zinc bromide-diethyl ether (4). It is planned to extend these studies to the bromides of other elements in the same periodic group as well as to related compounds. One of the authors (R) during a study of the three component system, water-diethyl ether-magnesium bromide, tried to determine the amount of water in a sample of ether solution by use of the drying agent Dehydrite, which is anhydrous magnesium perchlorate. It was noted that the magnesium perchlorate appeared to retain considerable ether even when heated. Since other magnesium compounds form etherates, especially the halides, it was decided to investigate this phenomenon further by means of solubility measurements of anhydrous magnesium perchlorate in diethyl ether. Willard and Smith (5) had previously determined the solubility of this compound in numerous solvents including diethyl ether at 25°. The present work was done at 0°, 15° and 25°

Measurement of Adsorption Isotherms for Mixed Vapors

A great deal of work has been done in the measurement of adsorption isotherms of pure gases and vapors, but very little of the measurement of adsorption isotherms of mixed gases or vapors and much of this has been unintentional, being due to impurities in the adsorbate. Papers dealing with measurements of this type include those of Richardson and Woodhouse (2) and Bakr and King. (3) The method of Bakr and King has the objection that each experiment yields an isolated value. Richardson\u27s and Woodhouse’s method requires extensive gas analysis and yields an isotherm in which the composition of the adsorbate changes