Globale Krisen, Rohstoffengpässe oder Preisschwankungen stellen die globalisierten Lieferkettensysteme der westlichen Produzenten vor große Herausforderungen. Das Konzept der Kreislaufwirtschaft ist eine Möglichkeit, sich angesichts dieser Herausforderungen robuster zu positionieren, um weniger abhängig von äußeren Einflüssen zu sein. Die größte Hürde bei dem Aufbau von Netzwerken für Kreislaufwirtschaftsprozesse ist die Identifikation von potentiellen Partnern auf Basis von Stoffstrommodellen. Ein erfolgreiches Mapping ist von vielen Faktoren abhängig. Aktuell existiert kein Ansatz, um die Stoffströme so zu modellieren, dass die Darstellung und Berechnung für eine Partnersuche in der Kreislaufwirtschaft geeignet ist. Um der Komplexität, sowohl der Stoffstrommodellierung, als auch der Partnersuche gerecht zu werden, wird hier ein MBSE-Ansatz gewählt - ein überlegener Modellierungsansatz im Detaillierungsgrad und der Adaptionsfähigkeit. Das Modell verknüpft die 3 Hauptelemente der Wertstromanalyse (Produktionsprozess, Materialfluss und Geschäftsprozess) und ermöglicht dadurch neuartige Kennzahlen zu ermitteln. Diese Kennzahlen und die detaillierte Modellierung schaffen eine verbesserte Informationslage, auf Basis derer die Effektivität der Partnersuche in der Kreislaufwirtschaft signifikant gesteigert wird. Nach einer theoretischen Herleitung der Modellierungslogik und der Erweiterung des bestehenden Ansatzes der nachhaltigen Wertstromanalyse (engl. Sustainable Value Stream Mapping – Sus-VSM) wird anhand eines Beispiels das MBSE-Modell implementiert und validiert. Dieser MBSE-Ansatz besitzt das Potential, die Beschreibung industrieller Produktions- und Herstellungsprozesse erheblich zu verfeinern und dadurch Analysen und Berechnungen zu optimieren, was zu einer besseren Vernetzung der Industrie führt. Die dadurch identifizierten industriellen Symbiosen fördern die Kreislaufwirtschaft maßgeblich und helfen Ressourcen nachhaltiger zu nutzen.

The aim of this thesis is to study the issue of eniveromental scanning electron microscopy and pumping gas to create vacuum in the newly designed scintillation detector. Further, creating a model of recently proposed scintillation detector and simulating and analyzing pumping gas in differentially pumped chamber of detector. The theoretical part deals with electron microscopy, electron sources, electron optics and secondary electrons detectors. It is also presented which signals are generated by the electron beam on the surface of a solid. Further fluid flow issues and equations describing the flow in the solved chamber are dismantled. Furthermore, the impact of gaseous environment on the trajectory of primary electrons, because there are collisions of primary beam with atoms and molecules of gas. The following section discusses creating, quality and importance of the network in mathematical modelling. A method of a final volume used to calculate the differential equations describing the flow of gas at the premises of the detector is described . The practical part consists in creating a model of scintillation detector and analyzing the gas flow in drawing a vacuum in the newly designed scintillation detector. At the end the simulation results of gas flow are compared for different variants of apertures and various pressures on the neck of a scintillation detector designed for optimum performance of the detector. The outcome of this thesis is model of newly designed scintillation detector with optimized shapes of apertures according to functional requirements.

The aim of this thesis is to study the issue of eniveromental scanning electron microscopy and pumping gas to create a vacuum in the newly designed scintillation detector. Further, creating a model of recently proposed scintillation detector and simulating and analyzing pumping gas in differentially pumped chamber of detector and the results compare with the previous model. The theoretical part deals with electron microscopy, electron sources, electron optics and secondary electrons detectors. It is also presented which signals are generated by the electron beam on the surface of a solid. Further fluid flow issues and equations describing the flow in the solved chamber are dismantled. Furthermore, the impact of gaseous environment on the trajectory of primary electrons, because there are collisions of primary beam with atoms and molecules of gas. The following section discusses creating, quality and importance of the network in mathematical modelling. A method of a final volume used to calculate the differential equations describing the flow of gas at the premises of the microscope is described . The practical part consists in creating a model of scintillation detector and analyzing the gas flow in drawing a vacuum in the newly designed scintillation detector. Furthermore, the simulation results are compared with the results of simulations on the older type of scintillation detector. The output of this thesis is model of recently proposed scintillation detector with visualized simulation results.

Mass changes of polar ice sheets have an important societal impact, because they affect global sea level. Estimating the current mass budget of ice sheets is equivalent to determining the balance between the surface mass gain through precipitation and the outflow across the grounding line. In Antarctica, the latter is mainly governed by oceanic processes and outlet glacier dynamics.<p>In this thesis, we assess the mass balance of a part of eastern DronningMaud Land via an input/output method. Input is given by recent surface accumulation estimations of the whole drainage basin. The outflow at the grounding line is determined from the radar data of a recent airborne survey and satellite-based velocities using a flow model of combined plug flow and simple shear. We estimate the regional mass balance in this area to be between 1.88±8.50 and 3.78±3.32 Gt a−1 depending on the surface mass balance (SMB) dataset used. This study also reveals that the plug flow assumption is acceptable at the grounding line of ice streams.<p>The mass balance of drainage basins is governed by the dynamics of their outlet glaciers and more specifically the flow conditions at the grounding line. Thanks to an airborne radar survey we define the bed properties close to the grounding line of the West Ragnhild Glacier (WRG) in the Sør Rondane Mountains. Geometry and reflectivity analyses reveal that the bed of the last 65 km upstream of the grounding line is sediment covered and saturated with water. This setting promotes the dominance of basal motion leading to a change in the flow regime: in the interior flow is governed by internal deformation while its relative importance decreases to become driven by basal sliding.<p>Subsequently we present the results of the reconstruction of the SMB across an ice rise through radar data and inverse modelling. The analysis demonstrates that atmospheric circulation was stable during the last millennium. Ice rises induce an orographic uplift of the atmospheric flow and therefore influence the pattern of the SMB across them, resulting in an asymmetric SMB distribution. Since the geometry of the internal reflection horizons observed in radar data depends on the SMB pattern, the asymmetry observed in radar layers reveals the trajectories of air masses at the time of deposit. We present an original and robust method to quantify this SMB distribution. Combining shallow and deep radar layers, SMB across Derwael Ice Rise is reconstructed. Two methods are employed as a function of the depth of the layers: i.e. the shallow layer approximation for the surface radar layers and an optimization technique based on an ice flow model for the deeper ones. Both methods produce similar results. We identify a difference in SMB magnitude of 2.5 between the flanks and the ice rise divide, as well as a shift of ≈4 km between the SMB maximum and the crest. Across the ice rise, SMB exhibits a very large variability, ranging from 0.3 to 0.9 mw.e. a−1. This anomaly is robust in time.<p>Finally we draw a comprehensive description of the Sør Rondane Mountains sector. The glacial system is close to the equilibrium and seems stable but evidences suggest that it is a fragile equilibrium. The proximity of the open ocean certainly favours the interaction between warm water and the ice shelf cavity conducting to potential important melting. The thinning associated with this melting can detach the ice shelf from pinning points. This will reduce the buttressing from the ice shelf, outlet glaciers will accelerate and mass transfer toward the ocean will increase. Therefore, the future of Antarctic Ice Sheet directly depends on the changes affecting its boundaries and assessing the sensitivity of the ice sheets is essential to quantify and anticipate the future variation of mass balance. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The Aw-Rascle-Zhang (ARZ) model has become a favorable ``second order" macroscopic traffic model, which corrects several shortcomings of the Payne-Whitham (PW) model. The ARZ model possesses a family of flow rate versus density (FD) curves, rather than a single one as in the ``first order" Lighthill-Whitham-Richards (LWR) model. This is more realistic especially during congested traffic state, where the historic fundamental diagram data points are observed to be set-valued. However, the ARZ model also possesses some obvious shortcomings, e.g., it assumes multiple maximum traffic densities which should be a ``property" of road. Instead, we propose a Generalized ARZ (GARZ) model under the generic framework of ``second order" macroscopic models to overcome the drawbacks of the ARZ model. A systematic approach is presented to design generic ``second order" models from historic data, e.g., we construct a family of flow rate curves by fitting with data. Based on the GARZ model, we then propose a phase-transition-like model that allows the flow rate curves to coincide in the free flow regime. The resulting model is called Collapsed GARZ (CGARZ) model. The CGARZ model keeps the flavor of phase transition models in the sense that it assume a single FD function in the free-flow phase. However, one should note that there is no real phase transition in the CGARZ model. To investigate to which extent the new generic ``second order" models (GARZ, CGARZ) improve the prediction accuracy of macroscopic models, we perform a comparison of the proposed models with two types of LWR models and their ``second order" generalizations, given by the ARZ model, via a three-detector problem test. In this test framework, the initial and boundary conditions are derived from real traffic data. In terms of using historic traffic data, a statistical technique, the so-called kernel density estimation, is applied to obtain density and velocity distributions from trajectory data, and a cubic interpolation is employed to formulate boundary condition from single-loop sensor data. Moreover, a relaxation term is added to the momentum equation of selected ``second order" models to address further unrealistic aspects of homogeneous models. Using these inhomogeneous ``second order" models, we study which choices of the relaxation term &tau are realistic. / Mathematics

This thesis presents a finite element methodology for simulating fluid–solid interactions in the left ventricle (LV) under LVAD support. The developed model was utilised to study the passive and active characteristics of ventricular function in anatomically accurate LV geometries constructed from normal and patient image data. A non–conforming ALE Navier–Stokes/finite–elasticity fluid–solid coupling system formed the core of the numerical scheme, onto which several novel numerical additions were made. These included a fictitious domain (FD) Lagrange multiplier method to capture the interactions between immersed rigid bodies and encasing elastic solids (required for the LVAD cannula), as well as modifications to the Newton–Raphson/line search algorithm (which provided a 2 to 10 fold reduction in simulation time). Additional developments involved methods for extending the model to ventricular simulations. This required the creation of coupling methods, for both fluid and solid problems, to enable the integration of a lumped parameter representation of the systemic and pulmonary circulatory networks; the implementation and tuning of models of passive and active myocardial behaviour; as well as the testing of appropriate element types for coupling non–conforming fluid– solid finite element models under high interface tractions (finding that curvilinear spatial interpolations of the fluid geometry perform best). The behaviour of the resulting numerical scheme was investigated in a series of canonical test problems and found to be convergent and stable. The FD convergence studies also found that discontinuous pressure elements were better at capturing pressure gradients across FD boundaries. The ventricular simulations focused firstly on studying the passive diastolic behaviour of the LV both with and without LVAD support. Substantially different vortical flow features were observed when LVAD outflow was included. Additionally, a study of LVAD cannula lengths, using a particle tracking algorithm to determine recirculation rates of blood within the LV, found that shorter cannulas improved the recirculation of blood from the LV apex. Incorporating myocardial contraction, the model was extended to simulate the full cardiac cycle, converging on a repeating pressure–volume loop over 2 heart beats. Studies on the normal LV geometry found that LVAD implementation restricts the recirculation of early diastolic inflow, and that fluid–solid coupled models introduce greater heterogeneity of myocardial work than was observed in equivalent solid only models. A patient study was undertaken using a myocardial geometry constructed using image data from an LVAD implant recipient. A series of different LVAD flow regimes were tested. It was found that the opening of the aortic valve had a homogenising effect on the spatial variation of work, indicating that the synchronisation of LVAD outflow with the cardiac cycle is more important if the valve remains shut. Additionally, increasing LVAD outflow during systole and decreasing it during diastole led to improved mixing of blood in the ventricular cavity – compared with either the inverse, or holding outflow constant. Validation of these findings has the potential to impact the treatment protocols of LVAD patients.

On étudie dans ce travail des systèmes de lois de conservation hyperboliques. La première partie étudie le temps d'existence des solutions régulières et régulières par morceaux de la dynamique des fluides compressibles. Après avoir présenté l'état de l'art en matière de solutions régulières, on montre une extension d'un théorème de Grassin à des gaz de Van der Waals. On étudie ensuite les solutions ondes de chocs : on poursuit l'approche de T. T. Li pour estimer leur temps d'existence dans le cas isentropique à symétrie sphérique, et l'approche de Whitham afin d'obtenir une équation approchée vérifiée par la surface de discontinuité. Dans une deuxième partie, motivée par la modélisation d'un rond-point en trafic routier, on étudie une extension multi-classe du modèle macroscopique de Lighthill-Whitham-Richards sur une route infinie avec des jonctions. On différencie les véhicules selon leur origine et leur destination et on introduit des conditions aux bords adaptées au niveau des jonctions. On obtient existence et unicité d'une solution au problème de Riemann pour ce modèle. Des simulations numériques attestent que les solutions obtenues existent en temps long. On aborde enfin le problème de Cauchy par la méthode de front tracking. La dernière partie concerne les lois de conservation scalaires. La première question abordée est le contrôle de la variation totale de la solution et la stabilité des solutions faibles entropiques par rapport au flux et à la source. Ce résultat nous permet d'étudier des équations avec flux non-local. Une fois établi leur caractère bien posé, on montre la Gâteaux-différentiabilité du semi-groupe obtenu par rapport aux conditions initiales. / In this work, we study hyperbolic systems of balance laws. The first part is devoted to compressible fluid dynamics, and particularly to the lifespan of smooth or piecewise smooth solutions. After presenting the state of art, we show an extension to more general gases of a theorem by Grassin.We also study shock waves solutions: first, we extend T. T. Li's approach to estimate the time of existence in the isentropic spherical case; second, we develop Whitham's ideas to obtain an approximated equation satisfied by the discontinuity surface. In the second part, we set up a new model for a roundabout. This leads us to study a multi-class extension of the macroscopic Lighthill-Whitham-Richards' model. We study the traffic on an infinite road, with some points of junction. We distinguish vehicles according to their origin and destination and add some boundary conditions at the junctions. We obtain existence and uniqueness of a weak entropy solution for the Riemann problem. As a complement, we provide numerical simulations that exhibit solutions with a long time of existence. Finally, the Cauchy problem is tackled by the front tracking method. In the last part, we are interested in scalar hyperbolic balance laws. The first question addressed is the control of the total variation and the stability of entropy solutions with respect to flow and source. With this result, we can study equations with non-local flow, which do not fit into the framework of classical theorems. We show here that these kinds of equations are well posed and we show the Gâteaux-differentiability with respect to initial conditions, which is important to characterize maxima or minima of a given cost functional.

Gas, liquid and powder flow in the lower part of a blast furnace is complex phenomena. In order to understand the aerodynamics of the blast furnace properly, these phenomena must be included in their advanced form. Previous studies have shown that the conditions of blast furnace resemble the cold model experiments which have been done in decreasing gas velocities. Also, the recent studies have shown that liquid flow in a blast furnace can be represented more realistically considering it discrete in nature. In the current study, both the phenomena have been considered along with the injection of powder through a nozzle while studying the fluid flow behaviour in a packed bed. The situation resembles the lower part of an ironmaking blast furnace. In this study, gas flow has been modelled using k-ε turbulent model and has been coupled with previously developed stress model to calculate the raceway size. Coal powder is treated as continuum and has been modelled in the similar way as gas flow. After this gas and powder flow model were coupled with previously developed discrete liquid flow model. Liquid flow model has been considered for structured bed only. The governing equations for gas phase were discretized. Finite Volume method was used for the solution. Co-located grid is used for the simulation. Blending of upwind difference scheme and central difference scheme (deferred correction approach) is used to achieve the stability of upwind scheme and accuracy of central difference scheme. Similar treatment was employed for powder phase. For the solution of volume fraction of powder, powder phase continuity equation was used along with pseudo time step scheme. Results obtained from gas and powder models have been validated against published experimental data. Similarly, gas-liquid flow results have been validated against published experimental data on gas-powder flow. Results obtained by gas-powder-liquid model could not be validated against any experimental or theoretical data as they are not available in the literature. The effect of various parameters on the fluid flow (gas/liquid/powder) behaviour have been studied like the effect of increasing and decreasing gas velocities, flow rates of liquid, gas and powder, size of powder and packing etc. It is found that the above mentioned phenomena have significant effect on the fluid flow behaviour in a packed bed.

Fluid damping arising from squeeze film flow of air or some inert gas trapped between an oscillating micro mechanical structure, such as a beam or a plate, and a fixed substrate often dominates the other energy dissipation mechanisms in silicon based MEM devices. As a consequence, it has maximum effect on the resonant response or dynamic response of the device. Unfortunately, modelling of the squeeze film flow in most MEMS devices is quite complex because of several factors unique to MEMS structures. In this thesis, we set out to study the effect of these factors on squeeze film flow. First we list these factors and study each of them in the context of a particular application, using experimental measurements, extensive numerical simulations, and analytical modelling for all chosen factors. We consider five important factors. The most important factor perhaps is the effect of rarefaction that is dominant when a device is vacuum packed with low to moderate vacuum, typical for MEMS packaging. The second problem is to investigate and model the effect of perforations which are usually provided for efficient etching of the sacrificial layer during fabrication of the suspended structures. The third problem is to consider the effect of non-uniform deflection of the structure such as those in MEMS cantilever beams and model its effect on the squeeze film. The fourth effect studied is the influence of different boundary conditions such as simple, fully open and partially closed boundaries around the vibrating structure on the characteristics of the squeeze film flow. The fifth problem undertaken is to analyze the effect of high operating frequencies on the squeeze film damping. In the first problem, the rarefaction effect is studied by performing experiments under varying pressures. Depending on the ambient pressure or the size of the gap between the vibrating and the fixed structure, the fluid flow may fall in any of the flow regimes, ranging from continuum flow to molecular flow, and giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number, which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. Here, we study the effect of fluid pressure on the squeeze film damping by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 torr to 0.001 torr. The variation of this pressure over six orders of magnitude ensures the required rarefaction to range over all flow conditions. Finally, we get the variation of the quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q P-r, with different values of the exponent r in different flow regimes. To numerically model the effect of rarefaction, we propose the use of effective viscosity in Navier-Stokes equation. This concept is validated with analytical results for a simple case. It is then compared with the experimental results presented in this thesis. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h0/L < 0.01). However, as this ratio increases, the range of validity decreases. Next, a semianalytical approach is presented to model the rarefaction effect in double-gimballed MEMS torsion mirror. In this device, the air gap thickness is 80 µm which is comparable to the lateral dimension 400 µm of the oscillating plate and thus giving the air-gap to length ratio of 0.2. As the ratio 0.2 is much greater than 0.01, the conventional Reynolds equation cannot be used to compute the squeeze film damping. Consequently, we find the effective length of an equivalent simple mirror corresponding to the motion about the two axes of the mirror such that the Reynolds equation still holds. After finding the effective length, we model the rarefaction effect by incorporating effective viscosity which is based on different models including the one proposed in this paper. Then we compare the analytical solution with the experimental result and find that the proposed model not only captures the rarefaction effect in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime. For the second problem, several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon previously reported models by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cells differently as proposed by Mohite et al. The proposed model is governed by a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green’s function. The solution thus obtained adds an additional term Γ to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting Γ = 0, one recovers Blech’s formulas. We benchmark all the models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. The approximate limit of maximum frequencies under which the formulas give reasonable results is also discussed. In the third problem, we study the effect of elastic modeshape during vibration on the squeeze film flow. We present an analytical model that gives the values of squeeze film damping and spring coefficients for MEMS cantilever resonators taking into account the effect of flexural modes of the resonator. We use the exact modeshapes of a 2D cantilever plate to solve for pressure in the squeeze film and then derive the equivalent damping and spring coefficient relations from the back force calculations. The relations thus obtained can be used for any flexural mode of vibration of the resonators. We validate the analytical formulas by comparing the results with numerical simulations carried out using coupled finite element analysis in ANSYS, as well as experimentally measured values from MEMS cantilever resonators of various sizes and vibrating in different modes. The analytically predicted values of damping are, in the worst case, within less than 10% of the values obtained experimentally or numerically. We also compare the results with previously reported analytical formulas based on approximate flexural modeshapes and show that the proposed model gives much better estimates of the squeeze film damping. From the analytical model presented here, we find that the squeeze film damping drops by 84% from the first mode to the second mode in a cantilever resonator, thus improving the quality factor by a factor of six to seven. This result has significant implications in using cantilever resonators for mass detection where a significant increase in quality factor is obtained only by using vacuum. In the fourth and fifth problem, the effects of partially blocked boundary condition and high operating frequencies on squeeze films are studied in a MEMS torsion mirror with different boundary conditions. For the structures with narrow air-gap, Reynolds equation is used for calculating squeeze film damping, generally with zero pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: (a) for an air-gap thickness comparable to the lateral dimensions of the micro structure, and (b) for non-trivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures, such as torsional MEMS structures, that have non-trivial boundary conditions arising from partially blocked boundaries. The most common example is the double-gimballed MEMS torsion mirror of rectangular, circular, or hexagonal shape. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air-gap and partially blocked boundaries due to static frames. Next we model the same structure in ANSYS and carry out CFD (computational fluid dynamics) analysis to evaluate the stiffness constant K, the damping constant C, as well as the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors. Subsequently, we use the CFD calculations to study the effect of two important boundary parameters, the side clearance c, and the flow length s, that specify the partial blocking. We show the sensitivity of K and C on these boundary design parameters. The results clearly show that the effect of these parameters on K and C is substantial, especially when the frequency of excitation becomes close to resonant frequency of the oscillating fluid and high enough for inertial and compressibility effects to be significant. Later, we present a compact model to capture the effect of side boundaries on the squeeze film damping in a simple rectangular torsional structure with two sides open and two sides closed. The analytical model matches well with the numerical results. However, the proposed analytical model is limited to low operating frequencies such that the inertial effect is negligible. The emphasis of this work has been towards developing a comprehensive understanding of different significant factors on the squeeze film damping in MEMS devices. We have proposed various ways of modelling these effects, both numerically as well as analytically, and shown the efficacy of these models by comparing their predictive results with experimental results. In particular, we think that the proposed analytical models can help MEMS device designers by providing quick estimates of damping while incorporating complex effects in the squeeze film flow. The contents of the thesis may also be of interest to researchers working in the area of microfluidics and nanofluidics.

In the present work, two phase reacting flow in a single cavity Trapped Vortex Combustor (TVC) is studied at atmospheric conditions. KIVA-3V, numerical program for simulating three dimensional compressible reacting flows with sprays using Lagrangian-Drop Eulerian-fluid procedure is used. The stochastic discrete droplet model is used for simulating the liquid spray. In each computational cell, it is assumed that the volume occupied by the liquid phase is very small. But this assumption of very low liquid volume fraction in a computational cell is violated in the region close to the injection nozzle. This introduces grid dependence in predictions of liquid phase in the region close to the nozzle in droplet collision algorithm, and in momentum coupling between the liquid and the gas phase. Improvements are identified to reduce grid dependence of these algorithms and corresponding changes are made in the standard KIVA-3V models. Pressure swirl injector which produces hollow cone spray is used in the current study along with kerosene as the liquid fuel. Modifications needed for modelling pressure swirl atomiser are implemented. The Taylor Analogy Breakup (TAB) model, the standard model for predicting secondary breakup is improved with modifications required for low pressure injectors. The pressure swirl injector model along with the improvements is validated using experimental data for kerosene spray from the literature. Simulations of two phase reacting flow in a single cavity TVC are performed and the temperature distribution within the combustor is studied. In order to identify an optimum configuration with liquid fuel combustion, the following parameters related to fuel and air such as cavity fuel injection location, cavity air injection location, Sauter Mean Diameter (SMD) of injected fuel droplets, velocity of the fuel injected are studied in detail in order to understand the effect of these parameters on combustion characteristics of a single cavity TVC.