M.S.

The experimental apparatus employed in this investigation permitted a fuel droplet and an oxidizer droplet to collide in a nitrogen atmosphere at temperatures from 50°C to 430°C. The resulting phenomena were photographed with a 16mm Fastax camera. Experimentation was completed in three series of tests. The first series consisted of impacting hydrazine droplets with white fuming nitric acid droplets at an impact velocity of 35 cm/sec and at temperatures from 200°C to 425°C. The second series utilized the same fuel and oxidizer at an impact velocity of 122 cm/sec and at temperatures ranging from 50°C to 430°C. The third series employed an alcohol-aniline mixture as the fuel droplets, and white fuming nitric acid as the oxidizer droplets. The impact velocity was 35 cm/sec and the nitrogen temperature ranged from 50°C to 415°C. Ignition was not obtained in the two series employing hydrazine as a fuel. The droplets, upon colliding, underwent a chemical reaction and were blown apart. With the series utilizing an alcohol-aniline mixture as the fuel, the droplets, after collision, formed one large drop which vaporized rapidly. The vapors ignited with flame at temperatures over 200°C. / Master of Science

The problem of maximizing the altitude of a rocket in vertical flight has been extensively analyzed by many writers since the early days of rocketry. In the beginning, solutions were obtained using the classical theory of the Calculus of Variations, and later using Optimal Control theory. For strict assumptions on the drag law and the thrust, solutions were found, even in a closed, analytic form. Nevertheless, for more realistic conditions, the problem becomes a very complex one, and the solution is far from complete. In addition to this, complexity increases if an isoperimetric constraint is added to the problem. Such a case is, for example, the problem of extremizing the rise in altitude for a given time. In the present work an attempt is made to treat the problem under the most realistic assumptions used so far, for both the system of equations and the drag model. The analysis of the problem reveals that a more complex thrust history exists than the classical sequence of full-singular-coast subarcs, for both the time-constrained case, and for the case of a drag model with a sharp rise in the transonic region. In the first case, a second full-thrust subarc is generated at the end of the singular subarc, owing to the boundedness of the thrust, while, in the second case, a full-thrust subarc appears in transition from the subsonic to the supersonic branch of the singular path. Both are new results, at least for the bounded-thrust case, and the drag law assumed, insofar as the author knows. Discussion is also provided for the limitations of such a switching structure, and it is shown that the composition of an optimal trajectory is heavily dependent on the assumed drag law. / Master of Science

Ph. D.

Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained. / Master of Science

The analysis of nitrate-ester propellants and explosives has been performed extensively by gas chromatography for the past decade. As capillary GC technology has advanced, new opportunities for the improvement of existing methods have developed. This investigation probes several of these possibilities. The effect on quantitation of: the solvent, the analysis time, and the use of splitless injection were investigated. Precision was shown to be improved by: 1. using a non-volatile solvent (toluene) rather than CH₂Cl₂, 2. using the most time-efficient method that will allow adequate resolution of the components, 3. using splitless injection (0.80 min. splitless time). After these potential improvements of method were investigated, the mechanism employed in splitless injection was investigated. This mechanism is known as the SOLVENT EFFECT. The investigation showed that: 1. non-volatile components required less splitless time to achieve 100% sample transfer to the column; 2. using splitless injection improved precision over split injection; 3. injector liner design had no effect on precision; 4. column overload did not hurt precision, as long as all peaks remain baseline-resolved; 5. the initial column temperature must be below the boiling point of the solvent (how far below did not appear to be very significant); 6. quantitation is improved by using a solvent that is as non-volatile as possible; 7. varying the split ratio after the split vent has reopened (within the range of 20:1 to 500:1) has no effect on resolving peaks that occur extremely close to the solvent peak. / Master of Science

With an increase of interest in space flight and vacuum research, there has been a corresponding increase in the need for values of outgassing rates of many materials. In space flight the knowledge of the outgassing rates of components and materials used in construction of space vehicles allow the determination of pressures within sections of the vehicle, the contamination level of critical components, and the reliability of vehicle components. In the construction of an ultra high vacuum facility, the knowledge of the value of the outgassing rates of construction materials allows the chamber to be constructed of low outgassing materials, minimizing the amount of gas evolving from the chamber walls. With the initiation of a research program, the outgassing rates of the chamber, test objects, and instrumentation are needed to determine the level of vacuum obtainable during the investigation.<br /> With the increased need for outgassing rates, more emphasis has been placed on the measurement of outgassing rates. The literature reports several techniques for the measurement of outgassing rates. Of these techniques, the rate of rise method is simple and convenient to apply, and hence of much interest. Because it is simple and easily applied, the rate of rise technique has been used by many experimenters to measure the outgassing rates of various materials. However, some experimenters have rejected its use as they felt that the dynamic nature of the technique introduced large errors into the outgassing measurements. There is presently in the literature no technical evaluation of the rate of rise method as to the suitability or unsuitability for measuring outgassing rates. / Master of Science

The accuracy of the calculated drag force in OpenRocket was examined in this investigation for a rocket traveling at subsonic, transonic and supersonic speeds. The idea was to compare the computed drag coefficients in OpenRocket to the drag coefficients obtained by running multiple computational fluid dynamics (CFD) simulations in Ansys Fluent. Specifically, the freestream Mach number and altitude parameters were varied for a geometric model of the Mjöllnir rocket. The results obtained converged several orders of magnitude and were exceptionally stable. Both the physical accuracy and numerical independence of the results was verified through examining the solutions' contour plots and conducting multiple sensitivity analyses. The conclusion was that OpenRocket overpredicts the Mjöllnir rocket's drag coefficients by 12 % to 73 % for all examined freestream Mach numbers and altitudes. Additionally, an empirical relationship was found for how the Mjöllnir rocket's drag coefficient changes with altitude and the freestream Mach number. In particular, it is a multivariate function that can be considered valid for an altitude of h ≤ 10 km and a freestream Mach number of 0.2 ≤ M ≤ 3.0. The empirical relationship fitted exceedingly well with simulation data and merits further investigation.

Star grain configuration design has been widely used in solid rocket applications for several decades. Although a large number of surface cracks are detected in the rocket motor propellants, the mechanism of these cracks is sull not well known due to the complex geometry of the grain. A stress-freezing photoelastic investigation has been performed to study the deep cracks which emanate from the fingertips of the star-shaped cutout cylinders. Using three-dimensional photoelasticity and proper algorithms in fracture mechanics, the stress intensity factors (SIF's) and the stress singularity orders along the crack front have been calculated. A surface effect on the dominant singularity order is observed and some analytical results are employed as a comparison. Meanwhile, three-dimensional finite element solution to the circular cylinder is used to find the “equivalent” inner radius for the internal star cylinder and the variation of SIF's along the crack border shows a very similar trend to the experimental results once the "equivalent" radius is adopted. / Master of Science

In order to gain a fundamental understanding of actual solid propellant thermal stress problems, the geometry of the solid propellant baa been idealized as a short, circular cylinder with flat ends. It is felt that the consideration of actual curved ends would only unduly have complicated the analysis. The method of solution for the thermal stresses in the finite cylinder, that has been presented in this thesis, utilizes an arbitrarily selected set of cylinder end-conditions. Therefore, different end conditions than the ones employed here might have been considered just as easily. The fundamental difficulties encountered in the thermoelastic analysis of short cylinders are that firstly the problem is at least two-dimensional and secondly, it has mixed boundary conditions since displacements and/or stresses specified along at least four distinct boundaries. It is relatively simple to solve the governing differential equation by the method of separation of variables. The greatest difficulties are encountered in satisfying the various boundary conditions. As a matter of fact the method of solution for the thermal stresses that has been presented in this thesis is applicable only when the temperature distribution throughout the propellant and casing exhibits a particular variation in the axial direction, as shown by Eqs. (39) and (43). With such temperature fields, however the elastic analytic solutions that have been presented are significant since the simultaneous linear algebraic equations, for the arbitrary constants, are easily solved. It is true that, in principle, an infinite number of these arbitrary constants must be determined. From a practical point of view, however, the arbitrary constants can always be reduced to a finite number by truncating the obtained series solutions for the thermal displacements and stresses. / Master of Science