Academic literature on the topic 'Hybrid propellant rockets – Combustion'

A rocket's engine usually uses fuel and oxygen as propellants to increase the rocket's projection during launch. Nowadays, metallic ingredients are commonly used in the rocket’s operation to increase its performance. Metallic ingredients have a high energy density, flame temperature, and regression rate that are important factors in the propulsion process. There is a wide range of additives have been reported so far as catalysts for rocket propulsion. The studies show that the presence of metal additives improves the regression rate, specific impulse and combustion efficiency. Herein, the common energetic additives for rocket propulsion such as metal and light metals are reviewed. Besides the effect of these energetic particles on the regression behaviors of base (hybrid) fuel has been exclusively discussed. This paper also proposed a new alloy namely high entropy alloys (HEAs) as a new energetic additive that can potentially increase the performance of the rocket propellant system.

High vapor pressure propellants such as nitrous oxide are widely used in experimental hybrid and liquid rockets as they can be used in a self-pressurization mode, eliminating the need for external pressurization or pumps and simplifying the design of the rocket system. This approach causes the two-phase flow in the feed system and the injector orifices, which cannot be easily modeled and accounted for in the design. A dedicated test stand has been developed to better understand how the two-phase flow of the self-pressurizing propellant impacts the mass flow characteristics, enabling the simulation of the operating conditions in the rocket engine. The injectors have been studied in the range of ΔP. The flow regimes have been identified, which can be predicted by the SPI and HEM models. It has been shown that the two-phase flow quality upstream of the injector may impact the discharge coefficient in the SPI region and the accuracy of the HEM model. It has been found that the transition to the critical flow region depends on the L/D ratio of the injector orifice. A series of conclusions can be drawn from this work to design the rocket injector with a self-pressurizing propellant to better predict the mass flow rate and ensure stable combustion.

Abstract Rocket motors are engines that create the necessary thrust for the rocket motion. There are different types of rocket motors based on the propellant state, such as solid propellant rocket motors, liquid propellant rocket motors, and hybrid propellant rocket motors. One of the biggest disadvantages of solid propellant rocket motors, in comparison to liquid and hybrid propellant rocket motors, is that they are extremely difficult to extinguish, necessitating the use of specific devices. This paper reviews various ways for thrust termination such as fluid injection, rapid increase in throat area, and sudden opening of an additional port at the forward section of the motor, which increases the depressurization rate (dp/dt) required for extinguishing. The rate of depressurization varies depending on propellant components, combustion pressure, and exhaust pressure, and may be investigated using experimental approaches. The change in the critical area for a motor can be predicted by using MATLAB code to ensure the complete extinguishing by decreasing the pressure under the deflagrationlimit with high depressurization rate.

The current research is focused on understanding the propulsive parameters of hybrid rocket motors. A comparative study is prepared from various research papers. The fuels paraffin wax, hydroxyl-terminated polybutadiene (HTPB) and polymethyl methacrylate (PMMA) with added additives (Al/Mg) were combined with two oxidizers, liquid oxygen (LOX), nitrous oxide (N2O). The propulsive parameters examined were the combustion efficiency, combustion or adiabatic flame temperature, characteristics velocity and regression rate. The propellant pair paraffin-N2O provided the highest performance for all parameters studied. This study provides an advantageous propellant option for future rocket propulsion based on a comparative investigation

A method for in-situ optical measurements of solid and hybrid propellant rocket plumes is developed, and results from proof of concept tests are presented. The developed method inserts fiber-optic cables acting as radiation conduits into the solid-fuel combustion port, allowing optical signals to be transmitted from the flame zone to externally-mounted spectrometers. Multiple hot-firings using a using a lab-scale gaseous-oxygen, thermo-plastic fueled hybrid rocket system were performed to validate the sensing method. Burn durations varied from 5 to 25 s, and the inserted fiber optic sensors survived for all of the hot fire tests. The obtained optical spectra were curve-fit to Planck’s black-body radiation law, and Wien’s displacement law was used to estimate the internal flame-temperature. Optically-sensed flame-temperatures are correlated to analytical predictions, and shown to generally agree within a few degrees. Additionally, local maxima in the optical spectra are shown to correspond to emission frequencies of atomic and molecular hydrogen, water vapor, and molecular nitrogen; all species known to exist in the hybrid combustion plume. Based on these preliminary test results, it is concluded that this simple in-situ measurement system operates as designed, and it shows considerable promise for future applications to a wide swath of gas-generator systems.

The process of fused deposition material (FDM) was used to manufacture propellant grains of Acrylonitrile Butadiene Styrene (ABS) as novel rocket fuel grain, with three types of geometry in the burning port. These solid fuel grains were used to measure the typical characteristics of combustion in rocket motors such as thrust and pressure inside the combustion chamber, seeking to obtain preliminary characteristics of operation and analyze the effect of combustion port geometry on pressure and thrust, using Multivariate Analysis of Variance (MANOVA) as statistical method. Two of the three geometries were manufactured with a helical-finocyl configuration, specially designed to be fabricated by Direct Digital Manufacturing (DDM), the other one was a straight-bore geometry also by DDM. This characterization experiment was performed on a static hybrid rocket engine, designed to inject 99.98% pure nitrous oxide into a combustion chamber with capacity to withstand 6.9 MPa of pressure, with an easy-to-exchange nozzle, avoiding erosive behavior in the throat. Statistical analyses made with the ABS fuel grains, suggest a significant effect on rocket motor pressure and thrust, due to helical geometric changes made to the combustion port of solid fuel grains made by FDM manufacture process.

A novel fuel grain configuration comprising two star-segmented grains is proposed. The effect of the rotation, mid-chamber length, and segmented position on the fuel regression rate and the combustion efficiency in hybrid rocket motors with star-segmented grains is investigated in this paper. To this end, 90% hydrogen peroxide (H2O2) and hydroxyl-terminated polybutadiene (HTPB) are selected as the propellant combination in this research. Three-dimensional numerical simulations of the star-segmented grain configuration are conducted. A firing test of a lab-scale hybrid rocket motor was conducted to verify the accuracy of the numerical model, and the errors between simulation data and experimental results are no more than 4.5%. The case without segmented grain configuration is regarded as the base case. The simulation results demonstrate that the combustion flow field structure of the motor could be ameliorated by the segmented rotation grain configuration. Compared with the base case, the rotation of aft-section grain has little effect on the regression rate in the fore-section grain, while the average regression rate in aft-section grain increases, with a maximum increase of 25.04%. The combustion efficiency of the motor with the segmented rotation grain configuration is higher than the base case. Compared with the base case, the combustion efficiency of segmented rotation grain case with mid-chamber length 40 mm and segmented position of 1/2 is raised by 4.06%. The average fuel regression rate and the combustion efficiency of hybrid rocket motors with segmented rotation grains are higher than those in the base case during the entire period of operation, and the combustion efficiency is increased by 1.40–4.21% during the motor operation. The research findings of this paper can provide valuable guidance for the performance improvement of hybrid rocket motors with star grain.

The present work focuses on the development of new mathematical and numerical tools to deal with wave propagation problems in a realistic liquid rocket chamber environment. A simplified real fluid equation of state is here derived, starting from the literature. An approximate Riemann solver is then specifically derived for the selected conservation laws and primitive variables. Both the new equation of state and the new Riemann solver are embedded into an in-house one-dimensional CFD solver. The verification and validation of the new code against wave propagation problems are then performed, showing good behavior. Although such problems might be of interest for different applications, the present study is specifically oriented to the low order modeling of high-frequency combustion instability in liquid-propellant rocket engines.

A method for developing an erosive burning model for use in solid propellant design-and-analysis interior ballistics codes is described and evaluated. Using Direct Numerical Simulation, the primary mechanisms controlling erosive burning (turbulent heat transfer, and finite rate reactions) have been studied independently through the development of models using finite rate chemistry, and infinite rate chemistry. Both approaches are calibrated to strand burn rate data by modeling the propellant burning in an environment with no cross-flow, and adjusting thermophysical properties until the predicted regression rate matches test data. Subsequent runs are conducted where the cross-flow is increased from M=0.0 up to M=0.8. The resulting relationship of burn rate increase versus Mach Number is used in an interior ballistics analysis to compute the chamber pressure of an existing solid rocket motor. The resulting predictions are compared to static test data. Both the infinite rate model and the finite rate model show good agreement when compared to test data. The propellant considered is an AP/HTPB with an average AP particle size of 37 microns. The finite rate model shows that as the cross-flow increases, near wall vorticity increases due to the lifting of the boundary caused by the side injection of gases from the burning propellant surface. The point of maximum vorticity corresponds to the outer edge of the APd-binder flame. As the cross-flow increases, the APd-binder flame thickness becomes thinner; however, the point of highest reaction rate moves only slightly closer to the propellant surface. As such, the net increase of heat transfer to the propellant surface due to finite rate chemistry affects is small. This leads to the conclusion that augmentation of thermal transport properties and the resulting heat transfer increase due to turbulence dominates over combustion chemistry in the erosive burning problem. This conclusion is advantageous in the development of future models that can be calibrated to heat transfer conditions without the necessity for finite rate chemistry. These results are considered applicable for propellants with small, evenly distributed AP particles where the assumption of premixed APd-binder gases is reasonable.

Thesis (MScIng)--University of Stellenbosch, 2003.
ENGLISH ABSTRACT: It was shown in an earlier study that it is possible to predict the spectral radiance of rocket combustion plumes directly from the propellant composition and motor parameters. Little is published in the open literature on this subject, but the current trend is to use determinative methods like computational fluid dynamics and statistical techniques to simulate wide band radiance based on blackbody temperature assumptions. A limitation of these methods is the fact that they are computationally expensive and rather complex to implement. An alternative modeling approach was used which did not rely on solving all the nonlinearities and complex relationships applicable to a fundamental model. A multilayer perceptron based Neural Network was used to develop a parametric functional mapping between the propellant chemical composition and the motor design and the resulting spectral irradiance measured in a section of the plume. This functional mapping effectively models the relationship between the rocket design and the plume spectral radiance. Two datasets were available for use in this study: Emission spectra from solid propellant rockets and flare emission spectra. In the case of the solid rocket propellants, the input to the network consisted of the chemical composition of the fuels and four motor parameters, with the output of the network consisting of 146 scaled emission spectra points in the waveband from 2-5 microns. The four motor parameters were derived from equations describing the mass flow characteristics of rocket motors. The mass flow through the rocket motor does have an effect on the shape of the plume of combustion gases, which in turn has an effect on the infrared signature of the plume. The characteristics of the mass flow through the nozzle of the rocket motor determine the thermodynamic properties of the combustion process. This then influences the kind of chemical species found in the plume and also at what temperature these species are radiating energy.The resultant function describing the plume signature is: Plume signature f {p T A fuel composition} t , , , , 1 1 = ε It was demonstrated that this approach yielded very useful results. Using only 18 basic variables, the spectra were predicted properly for variations in all these parameters. The model also predicted spectra that agree with the underlying physical situation when changing the composition as a whole. By decreasing the Potassium content for example, the model demonstrated the effect of a flame suppressant on the radiance in this wavelength band by increasing the predicted output. Lowering the temperature, which drives the process of molecular vibration and translation, resulted in the expected lower output across the spectral band. In general, it was shown that only a small section of the large space of 2 propellant classes had to be measured in order to successfully generate a model that could predict emission spectra for other designs in those classes. The same principal was then applied to predicting the infrared spectral emission of a burning flare. The brick type flare considered in this study will ignite and the solid fuel will burn on all surfaces. Since there are no physical parameters influencing the plume as in the case of the rocket nozzles it was required to search for parameters that could influence the flare plume. It was possible to calculate thermodynamic properties for the flare combustion process. These parameters were then reduced to 4 parameters, namely: the oxidant-fuel ratio, equilibrium temperature, the molar mass and the maximum combustion temperature. The input variables for the flares thus consisted of the chemical composition and 4 thermodynamic parameters described above. The network proposed previously was improved and optimised for a minimum number of variables in the system. The optimised network marginally improved on the pevious results (with the same data), but the training time involved was cut substantially. The same approach to the optimization of the network was again followed to determine the optimal network structure for predicting the flare emission spectra. The optimisation involved starting out with the simplest possible network construction and continuouslyincreasing the variables in the system until the solution predicted by the network was satisfactory. Once the structure of the network was determined it was possible to optimise the training algorithms to further improve the solution. In the case of the solid rocket propellant emission data it was felt that it would be important to be able to predict the chemical composition of the fuel and the motor parameters using the infrared emission spectra as input. This was done by simply reversing the optimised network and exchanging the inputs with the outputs. The results obtained from the reversed network accurately predicted the chemical composition and motor parameters on two different test sets. The predicted spectra of some of the solid propellant rocket test sets and flare test sets did not compare well with the expected values. This was due to the fact that these test sets were in a sparsely populated area of the variable space. These outliers are normally removed from training data, but in this case there wasn’t enough data to remove outliers. To obtain an indication of the strength of the correlation between the predicted and measured line spectra two parameters were used to test the correlation between two line spectra. The first parameter is the Pearson product moment of coefficient of correlation and gives an indication of how good the predicted line spectra followed the trend of the measured spectral lines. The second parameter measures the relative distance between a target and predicted spectral point. For both the solid propellants and the flares the correlation values was very close to 1, indicating a very good solution. Values for the two correlation parameters of a test set of the flares were 0.998 and 0.992. In order to verify the model it was necessary to prove that the solution yielded by the model is better than the average of the variable space. Three statistical tests were done consisting of the mean-squared-error test, T-test and Wilcoxon ranksum test. In all three cases the average of the variable space (static model) and the predicted values (Neural Network model) were compared to the measured values. For both the T-test and the Wilcoxon ranksum test the null hypothesis is rejected when t < -tα = 1.645 and then thealternative hypothesis is accepted, which states that the error of the NN model will be smaller than that of the static model. The mean squared error for the static model was 0.102 compared to the 0.0167 of the neural net, for a solid propellant rocket test set. A ttest was done on the same test set, yielding a value of –2.71, which is smaller than – 1.645, indicating that the NN model outperforms the static model. The Z value for this test set is Z = -11.9886, which is a much smaller than –1.645. The results from these statistical tests confirm that neural network is a valid conceptual model and the solutions yielded are unique.
AFRIKAANSE OPSOMMING: In ‘n vroeër studie is bewys hoe dit moontlik is om die spektrale irradiansie van ‘n vuurpyl se verbrandingspluim te voorspel vanaf slegs die dryfmiddelsamestelling en vuurpylmotoreienskappe. In die literatuur is daar min gepubliseer oor hierdie onderwerp. Dit wil voorkom asof meer deterministiese metodes gebruik word om die probleem op te los. Metodes soos CFD simulasies en statistiese analises word tans verkies om wyeband radiansie te voorspel gebaseer op perfekte swart ligaam teorie. ‘n Groot beperking van hierdie metodes is die feit dat die berekeninge kompleks is en baie lank neem om te voltooi. ‘n Alternatiewe benadering is gebruik, wat nie poog om al die nie-liniêre en komplekse verbande uit eerste beginsels op te los nie. ‘n Neurale netwerk is gebruik om ‘n funksionele verband te skep tussen die chemiese samestelling van die dryfmiddel, vuurpylmotor ontwerp en die spektrale irradiansie van die vuurpyl se pluim. Die funksionele verband kan nou effektief die afhanklikheid van die dryfmiddelsamestelling, vuurpylmotor ontwerp en die spektrale uitset modelleer. Twee datastelle was beskikbaar vir analise: Emissie spektra van vaste dryfmiddel vuurpyle en ook van vaste dryfmiddel fakkels. Die invoer tot die neurale netwerk van die vuurpyle het bestaan uit die chemiese samestelling van die dryfmiddel en 4 vuurpylmotor eienskappe. Die uitvoer van die netwerk het weer bestaan uit 146 spektrale irradiansie waardes in die golflengte band van 2-5μm. Die 4 vuurpylmotor eienskappe is afgelei uit massavloei teorie vir vuurpyl motors, aangesien die uitvloei van die produkgasse ‘n invloed op die pluim van die motor sal hê. Die massavloei het weer ‘n effek op die spektrale handtekening van die pluim. Die eienskappe van die massavloei deur die mondstuk van die vuurpylmotor bepaal die termodinamiese eienskappe van die verbrandingsproses. Die invloed op die verbrandingsproses bepaal weer watter tipe produkte gevorm word en by watter temperatuur hulle energie uitstraal. Die gevolg is dat ‘n funksie gedefinieer kan word wat die pluim beskryf.Pluim handtekening = f{, temperatuur, mondstuk keël grootte, vernouings verhouding van mondstuk, dryfmiddelsamestelling} Deur net 18 invoer nodes te gebruik kon die netwerk die irradiansie suksesvol voorspel met ‘n variansie in al die invoer waardes. Deur byvoorbeeld die Kalium inhoud van die dryfmiddel samestelling te verminder het die model die vermindering van ‘n vlam onderdrukker suksesvol nageboots deurdat die irradiansie ‘n hoër uitset gehad het. Die sensitiwiteit van die model is verder getoets deur die temperatuur in die verbrandingskamer te verlaag, met ‘n korrekte laer irradiansie uitset, as gevolg van die feit dat die temperatuur die molekulêre vibrasie en translasie beweging beheer. Dieselfde benadering is gebruik om die model te bou vir die voorspelling van die fakkels se infrarooi irradiansie. Anders as die vuurpylmotors vind die verbranding in die geval van die fakkels in die atmosfeer plaas. Dit was dus ook nodig om na die termodinamiese eienskappe van die fakkel verbranding te kyk. Verskeie parameters is bereken, maar 4 parameters, naamlik die brandstof-suurstof verhouding, temperatuur, molêre massa en die maksimum verbrandingstemperatuur, tesame met die dryfmiddel samestelling kon die irradiansie van die fakkels suskesvol voorspel. Die bestaande netwerk struktuur vir die vuurpylmotors is verbeter en geoptimiseer vir ‘n minimum hoeveelheid veranderlikes in die stelsel. Die geoptimiseerde netwerk het ‘n klein verbetering in die voorspellings getoon, maar die oplei het drasties afgeneem. Dieselfde benadering is gebruik om die optimale netwerk vir die fakkels te bepaal. Optimisering van die netwerk struktuur is bereik deur met die eenvoudigste struktuur te begin en die hoeveelheid veranderlikes te vermeerder totdat ‘n bevredigende oplossing gevind is. Na die struktuur van die netwerk bevestig is, kon die oordragfunksies op die nodes verder geoptimiseer word om die model verder te verbeter. Dit het verder geblyk dat dit moonlik is om die netwerk vir die vuurpylmotors om te draai sodat die irradiansie gebruik word om die dryfmiddel samestelling en motor eienskappe te voorspel. Die netwerk is eenvoudig omgedraai en die insette het die uitsette geword.Die resultate van die omgekeerde netwerk het bevestig dat dit wel moontlik is om die dryfmiddel samestelling en motor eienskappe te voorspel vanaf die irradiansie. Die voorspelde spektra van beide die vuurpylmotors en die fakkels het nie altyd goed gekorreleer met die gemete data nie. Van die spektra kom voor in ‘n lae digtheidsdeel van die veranderlike ruimte. Dit het tot gevolg gehad dat daar nie genoeg data vir opleiding van die netwerk in die omgewing van die toetsdata was nie. Hierdie data is eintlik uitlopers en moet verwyder word van die opleidingsdata, maar daar is alreeds nie genoeg data beskikbaar om die uitlopers te verwyder nie. Dit is nodig om te bepaal hoe goed die voorspelde data vergelyk met die gemete data. Twee parameters is gebruik om te bepaal hoe goed die data korreleer. Die eerste is die “Pearson product moment of coefficient of correlation”, wat ‘n goeie aanduiding gee van hoe goed die voorspelde waardes die gemete waardes se profiel volg. Die tweede parameter meet die relatiewe afstand tussen die teiken en die voorspelde waardes. Vir beide die vuurpylmotors en die fakkels het die toetsstelle ‘n korrelasiewaarde van baie na aan 1 gegee, wat ‘n goeie korrelasie is. Die waardes van die twee parameters vir een van die fakkel toetstelle was onderskeidelik 0.998 en 0.992. Die model is geverifieer deur te bepaal of die model ‘n beter oplossing bied as die gemiddeld van die veranderlike ruimte. Drie statistiese toetse is gedoen: “Mean-squarederror” toets, T-toets en ‘n “Wilcoxon ranksum” toets. In al drie gevalle word die gemiddelde van die veranderlike ruimte (statiese model) en die voorspelde waardes (Neurale netwerk model) teen die gemete waardes getoets. Vir beide die T-toets en die “Wilcoxon ranksum” toets word die nul hipotese verwerp indien t < ta = 1.645 en dan word die alternatiewe hipotese aanvaar, wat bepaal dat die fout van die neurale netwerk model kleiner is as die van die statiese model. Die “mean-squared-error” van die statiese model was 0.102, in vergelyking met 0.0167 van die neurale netwerk model vir ‘n vuurpylmotor toetsstel. ‘n T-toets is gedoen vir dieselfde toetsstel, met ‘n resultaat van-2.71, wat kleiner is as –1.645 en aandui dat die neurale netwerk model weereens beter presteer as die statiese model. Die Z waarde uit die “Wilcoxon ranksum” toets is Z=- 11.9886, wat baie kleiner is as –1.645. Die resultate van die statitiese toetse toon dat die neurale netwerk ‘n geldige model is en die oplossings van die model ook uniek is.

A dual-frequency microwave bum rate measurement system for solid rocket motors has been developed and is described. The system operates in the X-band (8.2-12.4 Ghz) and uses two independent frequencies operating simultaneously to measure the instantaneous bum rate in a solid rocket motor. Modeling of the two frequency system was performed to determine its effectiveness in limiting errors caused by secondary reflections and errors in the estimates of certain material properties, particularly the microwave wavelength in the propellant. Computer simulations based upon the modeling were performed and are presented. Limited laboratory testing of the system was also conducted to determine its ability perform as modeled.

Simulations showed that the frequency ratio and the initial motor geometry (propellant thickness and combustion chamber diameter) determined the effectiveness of the system in reducing secondary reflections. Results presented show that higher frequency ratios provided better error reduction. Overall, the simulations showed that a dual frequency system can provide up to a 75% reduction in burn rate error over that returned by a single frequency system. The hardware and software for dual frequency measurements was developed and tested, however, further instrumentation work is required to increase the rate at which data is acquired using the methods presented here. The system presents some advantages over the single frequency method but further work needs to be done to realize its full potential.

Master of Science

Controlling unsteady combustion induced gas flow fluctuations and the resultant motor vibrations is a very significant step in rocket motor design. It occurs when the unsteady heat release due to combustion happens to feed the acoustic oscillations of the closed duct forming a feed-back system. The resultant vibrations concerned may even lead to total failure of the rocket system unless analysed and tested thoroughly. This thesis aims developing a linear numerical analysis method for the growth rate of instabilities and possible mode shape of a liquid-propelled chamber geometry. In particular, A 3-D Helmholtz code, utilizing Culicks spatial averaging linear iterative method, is developed to find the form of deformed mode shapes iteratively to obtain possible effects of heat source and impedance boundary conditions. The natural mode shape phase is solved through finite volume discretization and the open-source eigenvalue extractor, ARPACK, and its parallel implementation PARPACK. The iterative method is particularly used for analyzing the geometries with complex shapes and essentially for disturbances of small magnitudes to natural mode shapes. The developed tools are tested via two simple cases, a duct with inactive flame and a Rijke tube, used as validation cases for the code particularly with only boundary contribution and heat contribution respectively. A sample 2-D and 3-D liquid-propelled combustion chamber is also analysed with heat sources. After comparing with the expected values, it is eventually proved that the method should be only used for determining the modes instability analysis, as to whether it keeps vibrating or decays. The methodology described can be used as a preliminary design tool for the design of liquid-propellant rocket engine combustors, rapidly revealing only the onset of instabilities.

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.

This chapter briefly introduces hybrid rocket propulsion for general audience. Advantageous of hybrid rockets over solids and liquids are presented. This chapter also explains how to design a test setup for hybrid motor firings. Hybrid propulsion provides sustainable, safe and low cost systems for space missions. Therefore, this chapter proposes hybrid propulsion system for Mars Ascent Vehicles. Paraffin wax is the fuel of the rocket. Propulsion system uses CO2/N2O mixture as the oxidizer. The goal is to understand the ignition capability of the CO2 as an in-situ oxidizer on Mars. CO2 is known as major combustion product in the nature. However, it can only burn with metallic powders. Thus, metallic additives are added in the fuel grain. Results show that CO2 increase slows down the chemical kinetics thus reduces the adiabatic flame temperature. Maximum flammability limit is achieved at 75% CO2 by mass in the oxidizer mixture. Flame temperature is 1700 K at 75% CO2. Ignition quenches below the 1700 K.