This work presents a preliminary design of a liquid rocket engine test platform to support research into liquid propulsion systems and rocket engine components, including injectors, ignition systems, combustion chambers and engine cooling systems. The liquid propellants, specifically liquid oxygen and ethanol, are pressure-fed using gaseous nitrogen. The test platform supports engine thrust values up to 1 kN, as well as varying oxidizer/fuel ratios up to 4.0 and varying ethanol concentrations between 70 and 100%. The test platform will integrate with a mobile control centre, which was designed concurrently, and provides remote control of the test procedures and data acquisition of all relevant pressure, temperature, mass flow and thrust data. The propellant feed assembly can support both cold and hot fire testing campaigns and is equipped with numerous safety features including inert gas purge lines, emergency drain lines and emergency shut-down and de-pressurization procedures.

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

The ADP rocket pump inducer was studied computationally using a 3-D Navier-Stokes solver, The Moore Elliptic Flow Program. Design and off-design flow rates were simulated to qualitatively and quantitatively study the effects of flow rate on the flow and performance. Several views of the results were created to aid flow visualization. The 3-D laser measurements made by Rocketdyne were used for comparison. The velocity magnitudes as well as the flow patterns within the inducer match well between the calculated and measured results. The axial velocity distribution and the rotary stagnation pressure, losses, are predicted very well by the calculation. The internal flow patterns developed in the simulation as expected, with radial outflow in the blade boundary layers. The tip leakage flow formed a recirculation region, a toroidal shaped vortex at the tip leading edge of the blades. The associated backflow forms a blockage that varies with flow rate. The thermodynamic performance was evaluated by calculating the contributions to pressure rise, the pump characteristic, the contributions to moment of momentum, and the efficiency. The centrifugal effect and relative velocity effect were found to vary with flow rate. The effective inlet throat radius, which governs these two effects, changes with flow rate because of the recirculation blockage. The shear on the blades was found to produce a small fraction of the work in the inducer, and most was produced by the pressure difference across the blade. The inducer efficiency was about 89%, and increased with decreasing flow rate in the range of flow rates considered, from 89% to 110% of the design flow rate. / Master of Science

A nonlinear programming technique is applied to the optimization of the thrust and lift control histories for missiles. The first problem considered is that of determining the thrust history which maximizes the range of a continuously-variable (non-pulsed) thrust rocket in horizontal lifting flight. The optimal control solution for this problem is developed. The problem is then approximated by a parameter optimization problem which is solved using a second-order, quasi-Newton method with constraint projection. The two solutions are found to compare well. This result allows confidence in the use of the nonlinear-programming technique to solve optimization problems in flight mechanics for which no analytical optimal-control solutions exist. Such a problem is to determine the thrust and lift histories which maximize the final velocity of a multiple-pulse missile. This problem is solved for both horizontal- and elevation-plane trajectories with and without final time constraints. The method is found to perform well in the solution of these optimization problems and to yield substantial improvements in performance over the nominal trajectories. / M.S.

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

A mixed variational statement and corresponding finite element model are developed for an axisymmetric solid body under external symmetric loads using the updated Lagrangian formulation. The mixed finite element formulation treats the nodal displacements and stresses as the variables that can be approximated independently. The method of static condensation is used to keep some stresses across interfaces of a solid of revolution discontinuous. The stiffness matrix is transformed from semi-positive definite to positive definite. A rocket motor is composed of (1) case (2) propellant and (3) hollow air core and is modelled as an axisymmetric solid. The propellant of a rocket motor is treated as a viscoelastic material. Static and dynamic analyses are performed under (1) two opposite line loads (2) two opposite patch loads and (3) one line and one patch load combination. The modified Newton-Raphson method is used in the solutions of nonlinear algebraic equations. The analysis of free vibration is executed first and then the Newmark direct integration method is used in a transient analysis. Results of these analyses are compared with solutions obtained from different methods that are independent of the finite element method. / Ph. D.

Thesis (M.S.)--Mississippi State University. Department of Physics and Astronomy. / Title from title screen. Includes bibliographical references.

Thesis (MScEng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: The focus of this thesis is on the investigation of the functioning of a liquefied-gas thruster. Such a thruster could be used to provide secondary propulsion to a microsatellite in orbit. A general overview of the need for thrusters in micro-satellites is put forward in the introduction. Motivation for deciding to investigate a liquefied-gas system is presented. Recent developments in the field of micro-satellites are discussed as well as their relevance to the project undertaken. Fundamental background theory relevant to the engineering problems associated with the development and analysis of such a system is also presented. Computer programs were written to simulate such a liquefied-gas thruster system. The experimental work carried out to analyse the system from a practical view-point is documented. Attention is also given to the measurement and calibration techniques used to obtain experimental data. One-dimensional fully explicit transient mathematical models of the thruster system were developed to model the system using both compressed air and butane as propellants. These models were incorporated into computer programs used to simulate the transient behaviour of the system. Although it is intended to use butane as the propellant onboard a satellite, the reason for modelling and simulating a system using compressed air is because air is a convenient fluid to work with from both a theoretical and practical point of view. An experimental model of a thruster system was designed, built and tested using air and butane as propellants. Most of the model was built using perspex to allow for the observation of the two-phase behaviour of the propellant inside the system. Locally purchased components were used for the solenoid and fill valves. Readily available butane lighter fluid was used for butane testing. Self-made heating elements were used to provide heat input to the propellant. Testing was done at different back pressures ranging from 100 kPa down to 20 kPa in a vacuum chamber. Good comparison between theoretical and experimental results was obtained for air. Theoretical results for peak thrusts tended to over predict experimental results by approximately 15 % for a system exhausting to a pressure of 100 kPa. Peak thrusts as high as 0.2 N were obtained for vacuum tests conducted at an absolute pressure of 20 kPa. Peak thrusts of approximately 50 mN were achieved for experimental testing III atmospheric conditions using butane with a starting pressure of between 270 and 290 kPa. Typical average thrusts of between 20 mN and 30 mN were noted for butane testing with initial pressure of between 200 to 300 kPa. Peak thrusts of over 0.1 N were observed for vacuum testing at an absolute pressure of 20 kPa. An equation to correlate the experimentally determined average thrust as a function of pulse duration and starting pressure was developed. This correlated most of the experimental data to within ±25 %. Theoretical results for butane testing are able to predict peak thrusts within approximately 20 % for starting pressures in the range of 200 to 300 kPa. Since the project was an exploratory investigation into a liquefied-gas thruster, some additional aspects relating to such systems were also given attention. The effect of liquid propellant motion or sloshing was considered and recommendations regarding the design and placement of the propellant tanks were made. The use of heat pipes as an alternative to electrical heating elements was investigated and some elementary design aspects are presented graphically. The management of the liquid propellant using surface tension devices was examined qualitatively. Recommendations relating to future projects in the field of simple, low-cost propulsion systems for micro-satellites are put forward. More specifically these recommendations are with regard to: thermo-fluid modelling of the propellant, future experimental work to be done, techniques to measure small thrusts and vacuum chamber testing. / AFRIKAANSE OPSOMMING: Die tesis ondersoek die funksionering van 'n vervloeidegas stuwer. So 'n stuwer kan gebruik word om sekondêre aandrywing aan 'n mikro-satelliet in 'n wentelbaan te verskaf. 'n Algemene oorsig oor die behoeftes van stuwers vir mikro-satelliete word voortgesit in die inleiding. Redes vir die gebruik van 'n vervloeidegas stuwer word bespreek. Onlangse ontwikkelinge in die veld van mikro-satelliet aandrywing word bespreek asook die toepaslikheid daarvan. Fundamentele teoretiese agtergrond verbonde aan die ontwikkeling en analise van so 'n stuwer stelsel word ook gegee. Rekenaarprogramme is geskryf om die gedrag van so 'n stuwer stelsel te simuleer. Eksperimentele werk is gedoen om die stelsel vanuit 'n praktiese oogpunt te analiseer. Aandag word ook gegee aan die metings- en kalibrasietegnieke soos toegepas vir die eksperimentele werk. Eendimensionele volle eksplisiete wiskundige modelle is ontwikkelom die oorgangsgedrag van die stuwer-stelsel te simuleer met beide lug en butaan as dryfmiddel. Hierdie modelle is geïnkorporeer in die rekenaar programme om die stuwer stelsel te simuleer. Alhoewel dit beoog word om butaan as die dryfmiddel aan boord die satelliet te gebruik, is lug ook gebruik vir simulasie weens sy gerieflikheid as 'n vloeier uit beide 'n teoretiese en 'n praktiese oogpunt. 'n Eksperimentele model van die stuwer stelsel is ontwerp, gebou en getoets met beide lug en butaan as dryfmiddels. Die model is hoofsaaklik uit perspex gebou sodat die twee-fase gedrag van die butaan uitgebeeld kon word. Vrylik beskikbare butaan aansteker vloeistof IS gebruik VIr butaan toetsing. Selfvervaardigde verhittingselemente is gebruik om hitte aan die dryfmiddel te verskaf. Toetse is gedoen deur verskeie omgewingsdrukke varieërend van 100 kPa af tot 20 kPa in 'n vakuumtenk te gebruik. Goeie ooreenstemming tussen die teoretiese en eksperimentele resultate vir die toetsing van lug is verkry. Die teoretiese resultate neig om die piek stukrag 15 % hoër te voorspel as die eksperimentele resultate vir 'n stelsel wat tot 'n omgewingsdruk van 100 kPa by die uitlaat. Piek stukragte van meer as 0.2 N is gekry vir vakuum toetse wat gedoen is by 'n omgewingsdruk van 20 kPa. Tydens eksperimentele toetsing met butaan teen 'n aanvanklike druk tussen 270 en 290 kPa, in atmosferiese toestande, is piek stukragte van ongeveer 50 mN behaal. Tipiese gemiddelde stukragte van tussen 20 en 30 mN is waargeneem vir butaan toetsing teen 'n aanvanklike druk tussen 200 en 300 kPa. Piek stukragte van meer as 0.1 N is behaal vir vakuum toetse met 'n absolute druk van 20 kPa. 'n Vergelyking om die gemiddelde stukrag, wat eksperimenteel bepaal is, as 'n funksie van puls tydsduur en aanvanklike druk te korreleer, is ontwikkel. Die meeste eksperimentele data se afwyking van die korrelasie-vergelyking was minder as 25 %. Teoretiese resultate vir butaantoetse het piek stukragte binne 20 % van die eksperimenteel metings korrek voorspel vir aanvanklike drukke tussen 200 tot 300 kPa. Weens die feit dat die projek 'n oorhoofse ondersoek in In vervloeidegas stuwer behels, is aandag ook gegee aan addisionele aspekte wat verband hou met sulke stelsels. Die effek van die vloeistof-dryfmiddel se onstabiele beweging in sy tenke is in ag geneem en voorstelle vir die ontwerp en plasing van die dryfmiddel tenke is gemaak. Die gebruik van hitte pype as 'n alternatief vir elektriese verhittingselemente is ondersoek. Verskeie ontwerp aspekte word grafies voorgestel. Die bestuur van die vloeistof-dryfmiddel deur van oppervlak spannings apparaat gebruik te maak, is kwalitatief ondersoek. Voorstelle vir verdere navorsing in die veld van eenvoudige, lae-koste stuwer stelsels vir mikro-satelliete is gemaak. Meer spesifiek is hierdie voorstelle gerig op die termo-vloeidinamiese modellering van die dryfmiddel, verdere eksperimentele navorsing, tegnieke om klein stukragte te meet en vakuumtenk toetse.

This thesis explores how an Asteroid Sample Return Mission might make use of solar electric propulsion to send a spacecraft on a journey to the asteroid 1989ML and back. It examines different trajectories that can be used to get an asteroid sample return or similar spacecraft to an interplanetary destination and back in the most fuel-efficient manner. While current plans call for keeping such a spacecraft on the asteroid performing science experiments for approximately 90 days, it is prudent to inquire how lengthening or shortening this time period may affect mission fuel requirements. Using optimal control methods, various mission scenarios have been modeled and simulated. The results suggest that the amount of time that the spacecraft may spend on the asteroid surface can be approximated as a linear function of the available fuel mass. Furthermore, It can be shown that as maximum available thrust is decreased, the radial component of the optimal thrust vector becomes more pronounced.

Approved for public release, distribution is unlimited / This thesis explores using a direct pseudospectral method for the solution of optimal control problems with mixed dynamics. An easy to use MATLAB optimization package known as DIDO is used to obtain the solutions. The modeling of both low thrust interplanetary trajectories as well as aerocapture trajectories is detailed and the solutions for low thrust minimum time and minimum fuel trajectories are explored with particular emphasis on verification of the optimality of the obtained solution. Optimal aerocpature trajectories are solved for rotating atmospheres over a range of arrival Vinfinities. Solutions are obtained using various performance indexes including minimum fuel, minimum heat load, and minimum total aerocapture mass. Finally, the problem formulation and solutions for the mixed dynamic problem of low thrust trajectories with a terminal aerocapture maneuver is addressed yielding new trajectories maximizing the total scientific mass at arrival. / Lieutenant, United States Navy