Thesis (M.S.)--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 83-85).

M.S.

The object of this investigation was to develop a general solution for the thermal stresses and strains in a hollow cylindrical case-bonded solid propellant. The heat conduction equation, as solved by Carslaw and Jaeger, was applied to a hollow composite cylinder. The temperature distribution from this equation was used in conjunction with the stress and strain for an elastic solid propellant. The boundary conditions were employed to solve for the constants and the general solution for the stresses and strains were obtained. In order to study the predictions of the general expressions, a numerical example was presented. It was found that the maximum stress and strain appeared at the inner radius of the grain. It was also observed that the stress and strain increased with an increase in the radius ratio "m”. Failure criteria for the grain under consideration were discussed. A method for obtaining the maximum allowable temperature variation (from cure temperature) was investigated. Knowing the stress and strain characteristics of the grain the equations developed would indicate failure conditions and also allow calculations of the maximum allowable temperature variations prior to grain failure. / M.S.

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

This thesis contains investigations in the area of polymers herein propellants binders are modified functionally to meet the requirements of future energetic propellants. Chapter 1 contains a broad introduction to the area of recent advances in solid propellants and the numerous applications of ‘Click Chemistry’. Chapters 2 details the materials, characterization tools and the experimental techniques employed for the studies. This is followed by Chapter 3, 4, and 5 which deals with functional modification of various propellants binders, their characterisation and evaluation in propellant formulations. Chapter 6 details with the thermal decomposition of diazides and its reaction with alkenes. The advent of modern rockets has opened a new era in the history of space exploration as well as defence applications. The driving force of the rocket emanates from the propellant – either solid or liquid. Composite solid propellants find an indispensable place, in today’s rockets and launch vehicles because of the inherent advantages such as high reliability, easy manufacturing, high thrust etc. The composite propellant consisting of inorganic oxidiser like ammonium perchlorate, (AP), ammonium nitrate (AN) etc), metallic fuel (aluminium powder, boron etc) and polymeric fuel binder (hydroxyl terminated polybutadiene-HTPB, polybutadiene-acrylic acid-acrylonitrile PBAN, glycidyl azide polymer (GAP), polyteramethylene oxide (PTMO) etc. is used in igniters, boosters, upper stage motors and special purpose motors in large launch vehicles. Large composite solid propellant grains or rocket motors in particular, demand adequate mechanical properties to enable them to withstand the stresses imposed during operation, handling, transportation and motor firing. They should also have a reasonably long ‘potlife’ to provide sufficient window for processing operations such as mixing and casting which makes the selection of binder with appropriate cure chemistry more challenging. In all composite solid propellants currently in use, polymers perform the role of a binder for the oxidiser, metallic fuel and other additives. It performs the dual role of imparting dimensional stability to the composite, provides structural integrity and good mechanical properties to the propellant besides acting as a fuel to impart the required energetics. Conventionally, the terminal hydroxyl groups in the binders like GAP, PTMO and HTPB are reacted with diisocyanates to form a polyurethane network, to impart the necessary mechanical properties to the propellant. A wide range of diisocyantes such as tolylene diisocyanate (TDI) and isophorone diisocyanate (IPDI) are used for curing of these binders. However, the incompatability of isocyanates with energetic oxidisers like ammonium dinitramide (ADN), hydrazinium nitroformate (HNF), short ‘potlife’ of the propellant slurry and undesirable side reactions with moisture are limiting factors which adversely affect the mechanical properties of curing binders through this route. The objective of the present study is to evolve an alternate approach of curing these binders is to make use of the 1,3 dipolar addition reactions between azide and alkyne groups which is a part of ‘Click chemistry’. This can be accomplished by the reaction of azide groups of GAP with triple bonds of alkynes and reactions of functionally modified HTPB/PTMO (azide/alkyne) to yield 1,2,3 -triazole based products. This offers an alternate route for processing of solid propellants wherein, the cured resins that have improved mechanical properties, better thermal stability and improved ballistic properties in view of the higher heat of decomposition resulting from the decomposition of the triazole groups. GAP is an azide containing energetic polymer. The azide groups can undergo reaction with alkynes to yield triazoles. In, Chapter 3 the synthesis and characterisation of various alkynyl compounds including bis propargyl succinate (BPS), bis propargyl adipate (BPA), bis propargyl sebacate (BPSc.) and bis propargyl oxy bisphenol A (BPB) for curing of GAP to yield triazoles networks are studied. The mechanism of the curing reaction of GAP with these alkynyl compounds was elucidated using a model compound viz. 2-azidoethoxyethane (AEE). The reaction mechanism has been analysed using Density Functional Theory (DFT) method. DFT based theoretical calculations implied marginal preference for 1, 5 addition over the 1, 4 addition for the uncatalysed cycloaddition reaction between azide and alkyne group. The detailed characterisation of these systems with respect to the cure kinetics, mechanical properties, dynamic mechanical behaviour and thermal decomposition characteristics were done and correlated to the structure of the network. The glass transition temperature (Tg), tensile strength and modulus of the system increased with crosslink density which in turn is, controlled by the azide to alkyne molar stoichiometry. Thermogravimetic analysis (TGA) showed better thermal stability for the GAP-triazole compared to GAP based urethanes. Though there have been a few reports on curing of GAP with alkynes, it is for the first time that a detailed characterisation of this system with respect to the cure kinetics, mechanical, dynamic mechanical, thermal decomposition mechanism of the polymer is being reported. To extent the concept of curing binders through 1,3 dipolar addition reaction, the binder HTPB as chemically transformed to propargyloxy carbonyl amine terminated polybutadiene (PrTPB) with azidoethoxy carbonyl amine terminated polybutadiene (AzTPB) and propargyloxy polybutadiene (PTPB). Similarly, PTMO was convnerted to propargyloxy polytetramethylene oxide (PTMP). Triazole-triazoline networks were derived by the reaction of the binders with alkyne/azide containing curing agents. The cure characteristics of these polymers (PrTPB with AzTPB, PTPB with GAP and PTMP with GAP) were studied by DSC. The detailed characterisations of the cured polymers for were done with respect to the, mechanical, dynamic mechanical behaviour and thermal decomposition characteristics were done. Propellant level studies were done using the triazoles derived from GAP, PrTPB-AzTPB, PTPB and PTMP as binder, in combination with ammonium perchlorate as oxidiser. The propellants were characterised with respect to rheological, mechanical, safety, as well as ballistic properties. From the studies, propellant formulations with improved energetics, safety characteristics, processability and mechanical properties as well defect free propellants could be developed using novel triazole crosslinked based binders. Chapter 6, is aimed at understanding the mechanism of thermal decomposition of diazido compounds in the first section. For this, synthesis and characterisation of a diazido ester 1,6 –bis (azidoacetoyloxy) hexane (HDBAA) was done. There have been no reports on the thermal decomposition mechanism of diazido compounds, where one azide group may influence the decomposition of the other. The thermal decomposition mechanism of the diazido ester were theoretically predicted by DFT method and corroborated by pyrolysis-GC-MS studies. In the second section of this chapter, the cure reaction of the diazido ester with the double bonds of HTPB has been investigated. The chapter 6B reports the mechanism of Cu (I) catalysed azide-alkene reaction validated using density functional theory (DFT) calculations in isomers of hexene (cis-3-hexene, trans-3-hexene and 2-methy pentene: model compound of HTPB) using HDBAA. This the first report on an isocyanate free curing of HTPB using an azide. Chapter 7 of the thesis summarizes the work carried out, the highlights and important findings of this work. The scope for future work such as development of high performance eco-friendly propellants based on triazoles in conjunction with chlorine-free oxidizer like ADN, synthesis of compatible plasticisers and suitable crosslinkers have been described. This work has given rise to one patent, three international publications and four papers in international conferences in the domain.

Thesis (MScIng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: The emission spectrum measured in the middle infrared (IR) band from the plume of a rocket can be used to identify rockets and track inbound missiles. It is useful to test the stealth properties of the IR fingerprint of a rocket during its design phase without needing to spend excessive amounts of money on field trials. The modelled predictions of the IR spectra from selected rocket motor design parameters therefore bear significant benefits in reducing the development costs. In a recent doctorate study it was found that a fundamental approach including quantum-mechanical and computational fluid dynamics (CFD) models was not feasible. This is first of all due to the complexity of the systems and secondly due to the inadequate calculation speeds of even the most sophisticated modern computers. A solution was subsequently investigated by use of the ‘black-box’ model of a multi-layer perceptron feed-forward neural network with a single hidden layer consisting of 146 nodes. The input layer of the neural network consists of 18 rocket motor design parameters and the output layer consists of 146 IR absorbance variables in the range from 2 to 5 μm wavelengths. The results appeared promising for future investigations. The available data consist of only 18 different types of rocket motors due to the high costs of generating the data. The 18 rocket motor types fall into two different design classes, the double base (DB) and composite (C) propellant types. The sparseness of the data is a constraint in building adequate models of such a multivariate nature. The IR irradiance spectra data set consists of numerous repeat measurements made per rocket motor type. The repeat measurements form the pure error component of the data, which adds stability to training and provides lack-of-fit ANOVA capabilities. The emphasis in this dissertation is on comparing the feed-forward neural network model to the linear and neural network partial least squares (PLS) modelling techniques. The objective is to find a possibly more intuitive and more accurate model that effectively generalises the input-output relationships of the data. PLS models are known to be robust due to the exclusion of redundant information from projections made to primary latent variables, similarly to principal components (PCA) regression. The neural network PLS techniques include feed-forward sigmoidal neural network PLS (NNPLS) and radial-basis functions PLS (RBFPLS). The NNPLS and RBFPLS algorithms make use of neural networks to find non-linear functional relationships for the inner PLS models of the NIPALS algorithm. Error-based neural network PLS (EBNNPLS) and radial-basis function network PLS (EBRBFPLS) are also briefly investigated, as these techniques make use of non-linear projections to latent variables. A modification to the orthogonal least squares (OLS) training algorithm of radial-basis functions is developed and applied. The adaptive spread OLS algorithm (ASOLS) allows for the iterative adaptation of the Gaussian spread parameters found in the radial-basis transfer functions. Over-fitting from over-parameterisation is controlled by making use of leaveone- out cross-validation and the calculation of pseudo-degrees of freedom. After cross-validation the overall model is built by training on the entire data set. This is done by making use of the optimum parameterisation obtained from cross-validation. Cross-validation also gives an indication of how well a model can predict data unseen during training. The reverse problem of modelling the rocket propellant chemical compositions and the rocket physical design parameters from the IR irradiance spectra is also investigated. This problem bears familiarity to the field of spectral multivariate calibration. The applications in this field readily make use of PLS and neural network modelling. The reverse problem is investigated with the same modelling techniques applied to the forward modelling problem. The forward modelling results (IR spectrum predictions) show that the feedforward neural network complexity can be reduced to two hidden nodes in a single hidden layer. The NNPLS model with eleven latent dimensions outperforms all the other models with a maximum average R2-value of 0.75 across all output variables for unseen data from cross-validation. The explained variance for the output data of the overall model is 94.34%. The corresponding explained variance of the input data is 99.8%. The RBFPLS models built using the ASOLS training algorithm for the training of the radialbasis function inner models outperforms those using K-means and OLS training algorithms. The lack-of-fit ANOVA tests show that there is reason to doubt the adequacy of the NNPLS model. The modelling results however show promise for future development on larger, more representative data sets. The reverse modelling results show that the feed-forward neural network model, NNPLS and RBFPLS models produce similar results superior to the linear PLS model. The RBFPLS model with ASOLS inner model training and 5 latent dimensions stands out slightly as the best model. It is found that it is feasible to separately find the optimum model complexity (number of latent dimensions) for each output variable. The average R2-value across all output variables for unseen data is 0.43. The average R2-value for the overall model is 0.68. There are output variables with R2-values of over 0.8. The forward and reverse modelling results further show that dimensional reduction in the case of PLS does produce the best models. It is found that the input-output relationships are not highly non-linear. The non-linearities are largely responsible for the compensation of both the DB- and C-class rocket motor designs predictions within the overall model predictions. For this reason it is suggested that future models can be developed by making use of a simpler, more linear model for each rocket class after a class identification step. This approach however requires additional data that must be acquired. / AFRIKAANSE OPSOMMING: Die emissiespektra van die uitlaatpluime van vuurpyle in die middel-infrarooi (IR) band kan gebruik word om die vuurpyle te herken en om inkomende vuurpyle op te spoor. Dit is nuttig om die uitstralingseienskappe van ‘n vuurpyl se IR afdruk te toets, sonder om groot bedrae geld op veldtoetse te spandeer. Die gemodelleerde IR spektrale voorspellings vir ‘n bepaalde stel vuurpylmotor ontwerpsparameters kan dus grootliks bydra om motorontwikkelingskostes te bemoei. In ‘n onlangse doktorale studie is gevind dat ‘n fundamentele benadering van kwantum-meganiese en vloeidinamika-modelle nie lewensvatbaar is nie. Dit is hoofsaaklik as gevolg van die onvoldoende vermoë van selfs die mees gesofistikeerde moderne rekenaars. ‘n Moontlike oplossing tot die probleem is ondersoek deur gebruik te maak van ‘n multilaag perseptron voorwaartse neurale netwerk met 146 nodes in ‘n enkele versteekte laag. Die laag van invoer veranderlikes bestaan uit agtien vuurpylmotor ontwerpsparameters en die uitvoerlaag bestaan uit 146 IR-absorbansie veranderlikes in die reeks golflengtes vanaf 2 tot 5 μm. Dit het voorgekom dat die resultate belowend lyk vir toekomstige ondersoeke. Weens die hoë kostes om die data te genereer bestaan die beskikbare data uit slegs agtien verskillende tipes vuurpylmotors. Die agtien vuurpyl tipes val verder binne twee ontwerpsklasse, naamlik die dubbelbasis (DB) en saamgestelde (C) dryfmiddeltipes. Die yl data bemoeilik die bou van doeltreffende multiveranderlike modelle. Die datastel van IR uitstralingspektra bestaan uit herhaalde metings per vuurpyltipe. Die herhaalde metings vorm die suiwer fout komponent van die data. Dit verskaf stabilitieit tot die opleiding op die data en verder die vermoë om ‘n analise van variansie (ANOVA) op die data uit te voer. In hierdie tesis lê die klem op die vergelyking tussen die voorwaartse neurale netwerk en die lineêre en neurale netwerk parsiële kleinste kwadrate (PLS) modelleringstegnieke. Die doel is om ‘n moontlik meer insiggewende en akkurate model te vind wat effektief die in- en uitvoer verhoudings kan veralgemeen. Dit is bekend dat PLS modelle meer robuus kan wees weens die weglating van oortollige inligting deur projeksies op hoof latente veranderlikes. Dit is analoog aan hoofkomponente (PCA) regressie. Die neurale netwerk PLS-tegnieke sluit in voorwaartse sigmoïdale neurale netwerk PLS (NNPLS) en radiale-basis funksies PLS (RBFPLS). Die NNPLS en RBFPLS algoritmes maak gebruik van die neurale netwerke om nie-lineêre funksionele verbande te kry vir die binne PLS-modelle van die nie-lineêre iteratiewe parsiële kleinste kwadrate (NIPALS) algoritme. Die fout-gebaseerde neurale netwerk PLS (EBNNPLS) en radiale-basis funksies PLS (EBRBFPLS) is ook weens hulle nie-lineêre projeksies na latente veranderlikes kortiliks ondersoek. ‘n Aanpassing tot die ortogonale kleinste kwadrate (OLS) opleidingsalgoritme vir radiale-basis funksies is ontwikkel en toegepas. Die aangepaste algoritme (ASOLS) behels die iteratiewe aanpassing van die verspreidingsparameters binne die Gauss-funksies van die radiale-basis transformasie funksies. Die oormatige parameterisering van ‘n model word beheer deur kruisvalidering met enkele weglatings en die berekening van pseudo-vryheidsgrade. Na kruisvalidering word die algehele model gebou deur opleiding op die volledige datastel. Dit word gedoen deur van die optimale parameterisering gebruik te maak wat deur kruisvalidering bepaal is. Kruisvalidering gee ook ‘n goeie aanduiding van hoe goed ‘n model ongesiende data kan voorspel. Die modellering van die vuurpyle se chemiese en fisiese ontwerpsparameters (omgekeerde probleem) is ook ondersoek. Hierdie probleem is verwant aan die veld van spektrale multiveranderlike kalibrasie. Die toepassings in die veld maak gebruik van PLS en neurale netwerk modelle. Die omgekeerde probleem word dus ondersoek met dieselfde modelleringstegnieke wat gebruik is vir die voorwaartse probleem. Die voorwaartse modelleringsresultate (IR voorspellings) toon dat die kompleksiteit van die voorwaartse neurale netwerk tot twee versteekte nodes in ‘n enkele versteekte laag gereduseer kan word. Die NNPLS model met elf latente dimensies vaar die beste van alle modelle, met ‘n maksimum R2-waarde van 0.75 oor alle uitvoer veranderlikes vir die ongesiende data (kruisvalidering). Die verklaarde variansie vir die uitvoer data vanaf die algehele model is 94.34%. Die verklaarde variansie van die ooreenstemmende invoer data is 99.8%. Die RBFPLS modelle wat gebou is deur van die ASOLS algoritme gebruik te maak om die PLS binne modelle op te lei, vaar beter in vergelyking met die K-gemiddeldes en OLS opleidingsalgoritmes. Die toetse wat ‘n ‘tekort-aan-passing’ ANOVA behels, toon dat daar rede is om die geskiktheid van die NNPLS model te wantrou. Die modelleringsresultate lyk egter belowend vir die toekomstige ontwikkeling van modelle op groter, meer verteenwoordigde datastelle. Die omgekeerde modellering toon dat die voorwaartse neurale netwerk, NNPLS en RBFPLS modelle soortgelyke resultate produseer wat die lineêre PLS model s’n oortref. Die RBFPLS model met ASOLS opleiding van die PLS binne modelle word beskou as die beste model. Dit is lewensvatbaar om die optimale modelkompleksiteite van elke uitvoerveranderlike individueel te bepaal. Die gemiddelde R2-waarde oor alle uitvoerveranderlikes vir ongesiende data is 0.43. Die gemiddelde R2-waarde vir die algehele model is 0.68. Daar is van die uitvoer veranderlikes wat R2-waardes van 0.8 oortref. Die voor- en terugwaartse modelleringsresultate toon verder dat dimensionele reduksie in die geval van PLS die beste modelle lewer. Daar is ook gevind dat die nie-lineêriteite grootliks vergoed vir die voorspellings van beide DB- en Ctipe vuurpylmotors binne die algehele model. Om die rede word voorgestel dat toekomstige modelle ontwikkel kan word deur gebruik te maak van eenvoudiger, meer lineêre modelle vir elke vuurpylklas nadat ‘n klasidentifikasiestap uitgevoer is. Die benadering benodig egter addisionele praktiese data wat verkry moet word.

Propõe-se aqui uma metodologia de projeto aero-termo-estrutural de motores foguete a propelente sólido. O projeto de um motor foguete deve ser realizado com o objetivo de cumprir requisitos de uma missão. Para cada veículo espacial, com uma nova missão, um novo motor pode ser projetado, necessitando para isso de uma série de ferramentas robustas, capazes de compreender todas as combinações de esforços existentes no funcionamento de um motor, sob condições de altas pressões e temperaturas. A metodologia aqui proposta é testada e validada em bancada de ensaios desenvolvida para este fim. Os resultados obtidos mostram que a metodologia utilizada se aproxima bastante dos resultados teóricos e pode ser ajustada por coeficientes de eficiência com grande facilidade. / It is proposed here an aero-thermo-structural design methodology for solid propellant rocket motors. The design of a rocket motor must be carried out in order to fulfill requirements of a mission. For each new space vehicle, with a new mission, a new motor can be designed, requiring for it a variety of robust tools, able to comprise all combinations of load existing in the operation of a motor under high pressures and temperatures. The methodology proposed here is tested and validated in bank of tests developed for this purpose. The results show that the methodology is very close to the theoretical results and can be adjusted by coefficients of efficiency with great ease.

A one-dimensional, steady-state numerical model of the combustion of homogeneous solid propellant has been developed. The combustion processes is modeled in three regions: solid, two-phase (liquid and gas) and gas. Conservation of energy and mass equations are solved in the two-phase and gas regions and the eigenvalue of the system (the mass burning rate) is converged by matching the heat flux at the interface of these two regions. The chemical reactions of the system are modeled using a global kinetic mechanism in the two-phase region and an elementary kinetic mechanism in the gas region. The model has been applied to RDX, HMX and GAP. There is very reasonable agreement between experimental data and model predictions for burning rate, temperature sensitivity, surface temperature, adiabatic flame temperature, species concentration profiles and melt-layer thickness. Many of the similarities and differences in the combustion of RDX and HMX are explained from sensitivity analysis results. The combustion characteristics of RDX and HMX are similar because of their similar chemistry. Differences in combustion characteristics arise due to differences in melting temperature, vapor pressure and initial decomposition steps. A reduced mechanism consisting of 18 species and 39 reactions was developed from the Melius-Yetter RDX mechanism (45 species, 232 reactions). This reduced mechanism reproduces most of the predictions of the full mechanism but is 7.5 times faster. Because of lack of concrete thermophysical property data for GAP, the modeling results are preliminary but indicate what type of experimental data is necessary before GAP can be modeled with more certainty.

In this study, a detailed service life assessment procedure for solid propellant rockets under random environmental temperature and transportation loads is introduced. During storage and deployment of rocket motors, uncontrolled thermal environments and random vibratory loads due to transportation induce random stresses and strains in the propellant which provoke mechanical damage. In addition, structural capability degrades due to environmental conditions and induced stresses and strains as well as material capability parameters have inherent uncertainties. In this proposed probabilistic service life prediction, uncertainties along with degradation mechanisms are taken into consideration. Vibration loads are accounted by utilizing acceleration spectral density values which are induced during various deployment scenarios of ground, air and sea transportation. Furthermore, thermal loads are represented with a mathematical model being a harmonic function of time. Throughout the finite element analyses, a linear viscoelastic material model is to be used for the propellant. Change in the structural capability of the propellant with time is calculated using Laheru&#039 / s cumulative damage model. Moreover, to include aging effect of the propellant, Layton model is used. To determine the effects of induced stress and strains under variations and uncertainties in the random loads and material constants, mathematical surrogate models are constructed using response surface method. Limit state functions are utilized to predict failure modes of the solid rocket motor. First order reliability method is used to calculate reliability and probability of failure of the propellant grain. With the proposed methodology, instantaneous reliability of the propellant grain is determined within a confidence interval.