This work evaluates the capabilities of the RANS and LES techniques for the simulation of high speed reacting flows. These methods are used to gain further insight into the physics encountered and regimes present in supersonic combustion. The target application of this research is the scramjet engine, a propulsion system of great promise for efficient hypersonic flight. In order to conduct this work a new highly parallelised code, PULSAR, is developed. PULSAR is capable of simulating complex chemistry combustion in highly compressible flows, based on a second order upwind method to provide a monotonic solution in the presence of high gradient physics. Through the simulation of a non-reacting supersonic coaxial helium jet the RANS method is shown to be sensitive to constants involved in the modelling process. The LES technique is more computationally demanding but is shown to be much less sensitive to these model parameters. Nevertheless, LES results are shown to be sensitive to the nature of turbulence at the inflow; however this information can be experimentally obtained. The SCHOLAR test case is used to validate the reacting aspects of PULSAR. Comparing RANS results from laminar chemistry and assumed PDF combustion model simulations, the influence of turbulence-chemistry interactions in supersonic combustion is shown to be small. In the presence of reactions, the RANS results are sensitive to inflow turbulence, due to its influence on mixing. From complex chemistry simulations the combustion behaviour is evaluated to sit between the flamelet and distributed reaction regimes. LES results allow an evaluation of the physics involved, with a pair of coherent vortices identified as the dominant influence on mixing for the oblique wall fuel injection method. It is shown that inflow turbulence has a significant impact on the behaviour of these vortices and hence it is vital for turbulence intensities and length scales to be measured by experimentalists, in order for accurate simulations to be possible.

Le travail de cette thèse est consacré à la simulation aux grandes échelles (LES) et à la modélisationde la combustion supersonique, dont l’application est rencontrée dans les moteurs detype scramjet. Dans ce contexte, une étude LES appliquée au cas d’une flamme supersoniquehydrogène-air (flamme de Cheng) a été effectuée sur trois niveaux de raffinements de maillage.Les résultats en termes de profils moyens et fluctuations de composition et de température sontconfrontés aux mesures expérimentales, et l’impact du raffinement de maillage est établi. Parailleurs, à partir des données issues de cette étude LES, une modélisation de la combustionturbulente dans un milieu fortement compressible est proposée sur la base d’une approche tabuléede la chimie. Une analyse temporelle des interactions choc/flamme a ensuite été menée,permettant de mettre en évidence la présence de structures transitoires ayant une influence surles processus de stabilisation de la flamme. / This PhD study is focused on the large eddy simulation (LES) and on the modelisation of supersonic combustion as encountered in scramjet types engines. In this context, a LES study was performed for an hydrogen-air supersonic flame (Cheng’s flame) with three mesh refinement levels. The results obtained for mean and fluctuations of composition and temperature are compared to experimental measurements, and the impact of the grid resolution is established. Moreover, a modelisation of turbulent combustion in highly compressible flows is proposed based of tabulated chemistry approach. An analysis of the dynamics of shock/flame interaction was then conducted, and the presence of transient structures, which impact the flame stabilisation processes, was emphasized.

L’allumage est un point essentiel dans le dimensionnement des moteurs-fusées, et il nécessite de prendre en compte plusieurs phénomènes physiques très distincts qui sont autant de challenges numériques. Le premier point abordé pendant cette thèse est la modélisation et la simulation par Simulation aux Grandes Échelles d’un allumeur de type VINCI. Des gaz chauds, riches en oxygène, sont délivrés de façon supersonique dans une chambre remplie d’hydrogène faisant apparaître un jet fortement sous-détendu et de multiples interactions choc/choc ou choc/flamme. Les premiers instants du processus d’allumage sont ici détaillés. Le second point abordé est la modélisation et la simulation numérique de la combustion H2/O2 à haute pression. En particulier, les effets d’une diffusion non-idéale sont étudiés dans le cas de flammes de prémélange 1D et sur la configuration 2D de type ‘splitter plate’. Un impact de la modélisation sur les espèces produites et le champ de température est ici mis en lumière. / Ignition is a key point in the design of liquid rocket engine (LRE), and it requires to take into account several distinct physical phenomena that constitute numerical challenges. The first point addressed during this thesis is the modeling and simulation using Large Eddy Simulation of a LRE igniter in a configuration close to VINCI rocket engine. The hot gases from the igniter, rich in oxygen, are delivered at supersonic speeds in a chamber filled with hydrogen. Such configuration creates under-expanded jets with multiple shock/shock or shock/flame interactions. A focus is done on the ignition process. The second point addressed is the modeling and simulation of high pressure H2/O2 combustion which occurs. In particular, the effects of non-ideal diffusion are studied through a 1D premixed flames and a 2D splitter plate configuration. An impact of modeling on the species produced and the temperature field is highlighted.

During a rocket launch, the point at which the most thrust is needed is at lift-off where the rocket is the heaviest since it is full of propellant. Unfortunately, this is also the point at which rocket engines perform the most poorly due to the relatively high atmospheric pressure at sea level. The Thrust Augmenting Nozzle (TAN) investigated in this paper provides a solution to this dilemma. By injecting extra propellant into the nozzle but downstream of the throat, the internal nozzle pressure is raised and the thrust is increased, and the nozzle efficiency, or specific impulse is potentially improved as well. Using this concept, the payload capacity of a launch vehicle can be increased and provides an excellent option for single stage to orbit vehicles.

For flights beyond Mach 6 ramjets are inefficient engines due to huge total pressure loss in the normal shock systems, combustion conditions that lose a large fraction of the available chemical energy due to dissociation and high structural loads. However if the flow remains supersonic inside the combustion chamber, the above problems could be alleviated and here the concept of SCRAMJET(supersonic combustion ramjet) comes into existence. The scramjets could reduce launching cost of satellites by carrying only fuel and ingesting oxygen from atmospheric air. Further applications could involve defense and transcontinental hypersonic transport. In the current study an effort is made to achieve supersonic combustion in a ground based short duration test facility(combustion driven shock-tunnel), which in addition to flight Mach number can simulate flight Reynolds number as well. In this study a simple method of injection i.e. wall injection of the fuel into the combustion chamber is used. The work starts with threedimensional numerical simulation of a non-reacting gas(air) injection into a hypersonic cross-flow of air to determine the conditions in which air penetrates reasonably well into the cross-flow. Care is taken so that the process does not induce huge pressure loss due to the bow shock which appears in front of the jet column. The code is developed in-house and parallelized using OpenMp model. This is followed by experiments on air injection into a hypersonic cross-flow of air in a conventional shock-tunnel HST2 existing in IISc. The most tricky part is synchronization of injection with start of test-flow in such a short duration(test time 1 millisecond) facility. Next part focuses on numerical simulations to determine the free-stream conditions, mainly the temperature and pressure of air, so that combustion takes place when hydrogen is injected into a supersonic cross-flow of air. The simulations are two-dimensional and includes species conservation equations and source terms due to chemical reactions in addition to the Navier-Stokes equations. This code is also built in-house and parallelized because of more number of operations with the inclusion of species conservation equations and chemical non-equilibrium. However, the predicted conditions were not achievable by HST2 due to low stagnation conditions of HST2. Therefore, a new shock-tunnel which could produce the required conditions is built. The new tunnel is a combustion driven shock-tunnel in which the driver gas is at higher temperature than conventional shock-tunnel. The driver gas is basically a mixture of hydrogen, oxygen and helium at a mole ratio of 2:1:10 initially. The mixture is ignited by spark plugs and the hydrogen and oxygen reacts releasing heat. The heat released raises the temperature of the mixture which is now predominantly helium and small fractions of water vapour and some radicals. The composition of the driver gas and initial pressure are determined through numerical simulations. Experiments follow in the new tunnel on hydrogen injection into a region of supersonic cross-flow between two parallel plates with a wedge attached to the bottom plate. The wedge reduces the hypersonic free-stream to Mach 2. A high-speed camera monitors the flow domain around injection point and sharp rise in luminosity is observed. To ascertain whether the luminosity is due to combustion or not, two more driven gases namely nitrogen and oxygen-rich air are used and the luminosity is compared. In the first case, the free-stream contains no oxygen and luminosity is not observed whereas in the second case higher luminosity than air driver case is visible. Additionally heat-transfer rates are measured at the downstream end of the model and at a height midway between the plates. Similar trend is observed in the relative heat-transfer rates. Wall static pressure at a location downstream of injection port is also measured and compared with numerical simulations. Results of numerical simulations which are carried out at the same conditions as of experiments confirm combustion at supersonic speed. Experiments and numerical simulations show presence of supersonic combustion in the setup. However, further study is necessary to optimize the parameters so that thrust force could be generated efficiently.

One of the major technological innovations that are necessary for faster and cheaper access-to-space will be the commercial realization of supersonic combustion jet engines (SCRAMJET). The establishment of the flow through the inlet is one the prime requirement for the success of a SCRAMJET engine. The flow through a SCRAMJET inlet is dominated by inviscid /viscous coupling, transition, shock-shock interaction, shock boundary layer interaction, blunt leading edge effects and flow profile effects. Although the literature is exhaustive on various aspects of flow features associated with SCRAMJET engines, very little is known on the fundamental gasdynamic features dictating the flow establishment in the SCRAMJET inlet. On one hand we need the reduction of flight Mach number to manageable supersonic values inside the SCRAMJET combustor, but on the other hand we have to achieve this with minimum total pressure loss. Hence the dynamics of ramp/cowl shock interaction process ahead of the inlet has a direct bearing on the quality and type of flow inside the SCRAMJET engine. There is virtually no data base in the open literature focusing specifically on the cowl/ramp shock interactions at hypersonic Mach numbers. Hence in this backdrop, the main aim of the present investigation is to systematically understand the ramp/cowl shock interaction processes in front of a generic inlet model. Since we are primarily concerned with the shock interaction process ahead of the cowl all the investigations are carried out without any fuel injection. Variable geometry is necessary if we want to operate the inlet for a wide range of Mach numbers in actual flight. The investigation mainly comprises of three variable geometry configurations; namely, variation of contraction ratios at 00 cowl (CR 8.4, 5.0 and 4.3), variation of cowl length for a given chamber height (four lengths of cowls at 10 mm chamber height) and variation of cowl angle (three angles cowl each for two chamber heights). The change in cowl configuration results in different ramp/cowl shock interaction processes affecting the performance of the inlet. Experiments are performed in IISc hypersonic shock tunnel HST 2 (test time ~ 1 ms) at two nominal Mach numbers 8.0 and 5.74 for design and off-design testing conditions. Exhaustive numerical simulations are also performed to compliment the experiments. Further the effect of concentrated energy deposition on forebody /cowl shock interactions has also been investigated. A 2D, planar, single ramp scramjet inlet model has been designed and fabricated along with various cowl geometries and tested in a hypersonic shock tunnel to characterize the forebody/cowl shock interaction process for different inlet configurations. Further a DC plasma power unit and a plasma torch have been designed, developed and fabricated to serve as energy source for conducting flow-alteration experiments in the inlet model. The V-I characteristics of the plasma torch is studied and an estimation of plasma temperature is also performed as a part of characterizing the plasma flame. Initial standardization experiments of blunt body flow field alteration using the plasma torch and hence its drag reduction, are performed to check the torch’s suitability to be used as a flow-altering device in a shock tunnel. The plasma torch is integrated successfully with the inlet model in a shock tunnel to perform experiments with plasma jet as the energy source. The above experiments are first of its kind to be conducted in a shock tunnel. They are performed at various pressure ratios and supply currents. Time resolved schlieren flow visualization using Phantom 7.1 (Ms Vision Research USA) high speed camera, surface static pressure measurements inside a generic inlet using miniature kulite transducer and surface convective heat transfer rate measurements inside a generic inlet using platinum thin film sensors deposited on Macor substrate are some of the shock tunnel flow diagnostics that have been used in this study. Some of the important conclusions from the study are: • Experiments performed at different contraction ratios show different shock patterns. At CR 8.4, the SOL condition is satisfied, but the flow gets choked due to over contraction and flow through inlet is not established. For CR 5.0, formation of a small Mach stem before the chamber is observed with the reflection point on the cowl and the weak reflected shock entering inside the chamber. The Mach stem grows with time. For CR 4.3, the forebody/cowl shock interference created an Edney’s Type II shock interaction pattern. However, at off-design conditions, for CR 5 the shock reflection is regular and at CR 4.3, the Edney’s Type II pattern lasts for a short time. • For all lengths of cowl tested, 131mm and 141mm showed Edney’s Type II shock interference where as 151mm showed Edney’s Type I pattern at design condition. In all cases the flow is choked for high contraction ratio. At off-design condition these shock patterns do not last for the entire test time but rather it becomes a lambda pattern with the normal shock before the inlet. • For inlet configurations with cowl angle other than 00, the flow is found to be established for all cases at designed condition and except for 100 cowl at off-design condition. • For CR 8.4 the peak value of pressure (~1.7x104 Pa) occurs at a location of 151mm, where as for CR 5.0 and 4.3 they occur at 188mm and 206mm having values ~1.6x104 Pa and ~1.4x104 Pa respectively. These locations indicate the likely locations of shock impingements inside the chamber. • For cowl angle of 00 for a 10 mm chamber the maximum pressure value recorded is ~1.7x104 Pa whereas for 100 and 200 cowl it is ~1.1x104 Pa and 1.2 x104 Pa respectively. This is because in the first case the inlet is choked because of over contraction whereas in the other two cases the CR is less and flow is established inside the inlet. • The average heat transfer rates of last four heat transfer gauges (180 mm, 190 mm, 200 mm and 210 mm from the forebody tip) for all lengths of cowls tested are found to be almost same (~ 20 W/cm2). This is because the flow is choked in all these cases. The numerical simulation also shows uniform distribution here, consistent with the experimental findings. • The locations of heat transfer peaks for 100 cowl at design condition can be observed to be occurring at 170 mm and 200 mm from the forebody tip having values ~44 W/cm2 and ~39 W/cm2 respectively. For a 200 cowl they seem to be occurring at 170 mm and 180 mm from the forebody tip having values ~50 W/cm2 and ~30 W/cm2. These locations indicate the likely locations of shock impingements inside the chamber. With the evolution of concept of upstream fuel injection in recent times these may the most appropriate locations for fuel injection. • At higher jet pressure ratios the plasma jet/ramp shock interaction results in a lambda shock pattern with the triple point forming vertically above the cowl level. This means the normal shock stands in front of the inlet making a part of the flow entering the inlet subsonic. The reflected shock from the triple point also separates the ramp boundary layer. • At lower jet pressure ratios the triple point is formed below the cowl level and the flow entering inside the inlet is supersonic. The reflected shock interacts with the cowl shock and a weak separation shock is seen. • Experiments are performed with concentrated DC electric discharge as energy source. Even though the amount of energy dumped here is less than 0.25% of the total energy it creates a perceptible disturbance in the flow. • Experiments are also performed to see the effect of electric discharge as energy source on height of Mach stem for a given inlet configuration. Deposition of energy in the present location does not seem to alter the Mach stem height. However more experiments need to be performed by varying the energy location to see its effect. Non-intrusive energy sources like microwave and lasers can be thought of as options for depositing energy to study its effect on Mach stem height. Since they provide more flexibility on varying the location of energy the optimum location of energy can be found out for highest reduction of Mach stem height.

Rapid mixing and spreading of supersonic jets are two important characteristics in supersonic ejectors, noise reduction in jets and fuel mixing in supersonic combustion. It helps in changing the acoustic and thermal signature in supersonic exhaust. The supersonic nozzles in most cases result in compressible mixing layers. The subsonic nozzles form incompressible mixing layers but at high Mach numbers even they form compressible mixing layers. Compressible mixing layers have been found to have much lower mixing and spreading rates than incompressible mixing layer Birch & Eggers (1972). In order to enhance the spreading and mixing of mixing layers from supersonic nozzles various active and passive methods have been deviced. Active methods include fluid injection, fluid lobes and plasma actuation. Passive methods are mostly based on modifying the nozzle geometry such that the fluid expansion is ideal or the shock cell is broken. Many nozzles with exotic shapes have been developed to obtain mixing enhancements in supersonic jets Gutmark et al. (1995). To achieve enhanced mixing an innovative nozzle named as the Elliptic Sharp Tipped Shallow (ESTS) lobed nozzle has been developed in L.H.S.R., I.I.Sc., India Rao & Jagadeesh (2014). This nozzle has a unique geometry involving elliptical lobes and sharp tips. These lobes are generated using a simple manufacturing process from the throat to the exit. This lobed and sharp tipped structure introduces stream wise vortices and azimuthal velocity components which must help in enhanced mixing and spreading. The ESTS lobed nozzle has shown mixing enhancement with 4 lobes. The spreading rate was found to be double of the reference conical nozzle. This thesis is motivated by the need to investigate the flow physics involved in the ESTS lobed nozzle. The effect of varying the number of lobes and the design Mach number of the nozzle on the mixing and spreading characteristics will be further discussed. Visualisation studies have been performed. The schlieren and planar LASER Mie scattering techniques have been used to probe the flow. Instantaneous images were taken at axial planes with the reference conical and ESTS nozzles with three, four, five and six lobes. The nozzles are for design Mach number 2.0 and 2.5. The stagnation chamber pressure was maintained to obtain over expanded, ideally expanded and under expanded flows. LASER scattering was obtained by seeding the flow with water to observe the behaviour of the primary flow. The condensation of moisture due to the cold primary flow mixing with the ambient air was exploited to scatter laser and observe the flow structures in the mixing layer. A comparison of the images of the reference conical nozzle and the ESTS lobed nozzles shows changes in the mixing layers due to the ESTS lobed nozzles. The image of the reference conical nozzle shows a distinct potential core and mixing layers all along the length of the image. For the ESTS lobed nozzles this distinction becomes unclear shortly after the nozzle exit. Thus mixing of the primary flow and ambient air is seen to be enhanced in the case of all the ESTS lobed nozzles. The flow in the case of the ESTS lobed nozzles if found to be highly non axis symmetric. The starting process of the nozzles has been visualised using time resolved schlieren. Image processing was performed on the nozzles to quantify the spread rate. The shock structure of the nozzles has been studied and found to be modified due to the lobed geometry. The level of convolution of the mixing layer due to the lobed structure has been studied using fractal analysis. The four lobed nozzle was found to have the highest spread rate and th most convoluted shear layer. Hence this nozzle was further studied using background oriented schlieren and particle image velocimetry to quantify the flow field. These experimental results have been compared with CFD simulations using the commercial software CFX5. The computations and experiments don’t match accurately but the trends match. This allows for simulations to be used as a good first approximation. The acoustic properties of a jet are dependent on the flow structure behaviour. The ESTS lobes have been found to change the flow structure. Hence the ESTS lobed nozzle was predicted to change the acoustic signature of the flow. The acoustic measurements of the flow were carried out at National Aerospace Laboratories, Bengaluru. The screech of the overexpanded flow was seen to be eliminated and the overall sound levels were found to have been reduced in all cases. Thus the lobed nozzle was found to have acoustic benefits over the reference conical nozzle. Thus the ESTS lobed nozzle has been studied and compared with the conical nozzle using several methods. The changes due to the lobed structure have been studied quantitatively. Future studies would focus on the change in thrust due to the lobed structure. Also new geometries have been proposed inspired by the current design but with possible thrust benefits or manufacturing benefits.

The probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of turbulent reacting flows. In this approach, the joint-PDF of all reacting scalars is estimated by solving a PDF transport equation, thus providing detailed information about small-scale correlations between these quantities. The objective of this work is to further develop the LES/PDF approach for studying flame stabilization in supersonic combustors, and for soot modeling in turbulent flames. Supersonic combustors are characterized by strong shock-turbulence interactions which preclude the application of conventional Lagrangian stochastic methods for solving the PDF transport equation. A viable alternative is provided by quadrature based methods which are deterministic and Eulerian. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a new approach called semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach. For soot modeling in turbulent flows, an LES/PDF approach is integrated with detailed models for soot formation and growth. The PDF approach directly evolves the joint statistics of the gas-phase scalars and a set of moments of the soot number density function. This LES/PDF approach is then used to simulate a turbulent natural gas flame. A Lagrangian method formulated in cylindrical coordinates solves the high dimensional PDF transport equation and is coupled to an Eulerian LES solver. The LES/PDF simulations show that soot formation is highly intermittent and is always restricted to the fuel-rich region of the flow. The PDF of soot moments has a wide spread leading to a large subfilter variance. Further, the conditional statistics of soot moments conditioned on mixture fraction and reaction progress variable show strong correlation between the gas phase composition and soot moments. / text