The objective of this research is to assess the performance of two popularReynolds-averaged Navier-Stokes (RANS) models, standard k-E and k-w, andto suggest modifications to improve model predictions for high-speed flows. Numerical simulations of turbulent ow past a at plate are performed at M1 = 2:25; 7:2.The results from these two Mach number cases are compared with Direct NumericalSimulation (DNS) results from Pirozzoli et al. (2004) and experimental results fromHorstman & Owen (1975). The effect of the Boussinesq coefficient (Cu) and turbulenttransport coefficients (sigmak; sigmaE; sigma; sigma*) on the boundary layer ow is examined. Further,the performance of a new model with realizability-based correction to Cu and corresponding modifications to sigma; sigma* is examined. The modification to Cu is based oncontrolling the ratio of production to dissipation of kinetic energy (P/E=1). The firstchoice of P/E = 1 ensures that there is no accumulation of kinetic energy in stagnation or free-stream regions of the ow. The second choice of P/E= 1:6 holds underthe assumption of a homogeneous shear ow. It is observed that the new model'sperformance is similar to that of the existing RANS models, which is expected for asimple ow over a at plate. Finally, the role of turbulent Prandtl number (Prt) intemperature and density predictions is established. The results indicate that the k-wmodel's performance is better compared to that of the standard k-E model for highMach number flows. A modification to Cu must be accompanied with correspondingchanges to sigmak; sigmaE; sigma; sigma* for an accurate log-layer prediction. The results also indicate that a Prt variation is required across the boundary layer for improved temperatureand density predictions in high-speed flows.

The objective of this research is to assess the performance of two popularReynolds-averaged Navier-Stokes (RANS) models, standard k-E and k-w, andto suggest modifications to improve model predictions for high-speed flows. Numerical simulations of turbulent ow past a at plate are performed at M1 = 2:25; 7:2.The results from these two Mach number cases are compared with Direct NumericalSimulation (DNS) results from Pirozzoli et al. (2004) and experimental results fromHorstman & Owen (1975). The effect of the Boussinesq coefficient (Cu) and turbulenttransport coefficients (sigmak; sigmaE; sigma; sigma*) on the boundary layer ow is examined. Further,the performance of a new model with realizability-based correction to Cu and corresponding modifications to sigma; sigma* is examined. The modification to Cu is based oncontrolling the ratio of production to dissipation of kinetic energy (P/E=1). The firstchoice of P/E = 1 ensures that there is no accumulation of kinetic energy in stagnation or free-stream regions of the ow. The second choice of P/E= 1:6 holds underthe assumption of a homogeneous shear ow. It is observed that the new model'sperformance is similar to that of the existing RANS models, which is expected for asimple ow over a at plate. Finally, the role of turbulent Prandtl number (Prt) intemperature and density predictions is established. The results indicate that the k-wmodel's performance is better compared to that of the standard k-E model for highMach number flows. A modification to Cu must be accompanied with correspondingchanges to sigmak; sigmaE; sigma; sigma* for an accurate log-layer prediction. The results also indicate that a Prt variation is required across the boundary layer for improved temperatureand density predictions in high-speed flows.

A numerical study is performed to model the 2-D axisymmetric turbulent flow of supercritical water flowing upward in vertical pipes with constant wall heat fluxes, using ANSYS CFX v14.5. This study was aimed to use CFD in analyzing supercritical flow instability and heat transfer. Two types of flow instabilities are analyzed and results are compared with 1-D non-linear code solutions. Also, conditions for approximating the thresholds of instabilities based on steady-state results are assessed. It is determined that the results of instability thresholds obtained using the k-ɛ and the SST models are similar. Also the results of CFD and 1-D codes are different mainly due to the difference in the pressure drop predictions. Moreover, approximating the flow instability threshold by the conditions proposed holds true for a CFD solution. Results also indicate that Prt does not have a noticeable effect on the instability threshold for the cases examined.

After nearly 50 years of development, Computational Fluid Dynamics (CFD) has become an indispensable component of research, forecasting, design, prototyping and testing for a very broad spectrum of fields including geophysics, and most engineering fields (mechanical, aerospace, biomedical, chemical and civil engineering). The fastest and most affordable CFD approach, called Reynolds-Average-Navier-Stokes (RANS) can predict the drag around a car in just a few minutes of simulation. This feat is possible thanks to simplifying assumptions, semi-empirical models and empirical models that render the flow governing equations solvable at low computational costs. The fidelity of RANS model is good to excellent for the prediction of flow rate in pipes or ducts, drag, and lift of solid objects in Newtonian flows (e.g. air, water). RANS solutions for the prediction of scalar (e.g. temperature, pollutants, combustable chemical species) transport do not generally achieve the same level of fidelity. The main culprit is an assumption, called Reynolds analogy, which assumes analogy between the transport of momentum and scalar. This assumption is found to be somewhat valid in simple flows but fails for flows in complex geometries and/or in complex fluids. This research explores optimization methods to improve upon existing RANS models for scalar transport. Using high fidelity direct numerical simulations (numerical solutions in time and space of the exact transport equations), the most common RANS model is a-priori tested and investigated for the transport of temperature (as a passive scalar) in a turbulent channel flow. This one constant model is then modified to improve the prediction of the temperature distribution profile and the wall heat flux. The resulting modifications provide insights in the model’s missing physics and opens new areas of investigation for the improvement of the modeling of turbulent scalar transport.

This thesis is concerned with the study of parallel mixing of two dissimilar gases under compressible conditions in the confined environment. A number of numerical studies are reported in the literature for the compressible mixing of two streams of gases where (1) both the streams are of similar gases at the same temperatures, (2) both the streams are at different temperatures with similar gases, and (3) dissimilar gases are with nearly equal temperatures. The combination of dissimilar gases at large temperature difference, mixing under compressible conditions, as in the case of scramjet propulsion, has not been adequately addressed numerically. Also many of the earlier studies have used two dimensional numerical simulation and showed good match with the experimental results on mixing layers that are inherently three dimensional in nature. In the present study, both two-dimensional (2-d) and three dimensional (3-d) studies are reported and in particular the effect of side wall on the three dimensionality of the flow field is analyzed, and the reasons of the good match of two dimensional simulations with experimental results have been discussed. Both two dimensional and three dimensional model free simulations have been conducted for a flow configuration on which experimental results are available. In this flow configuration, the mixing duct has a rectangular cross section with height to width ratio of 0.5. In the upper part of the duct hydrogen gas at a temperature of 103 K is injected through a single manifold of two Ludweig tubes and in the lower part of the duct nitrogen gas at a temperature of 2436 K is supplied through an expansion tube, both the gases are at Mach numbers of 3.1 and 4.0 respectively. Measurements in the experiment are limited to wall pressures and heat flux. The choice of this experimental condition gives an opportunity to study the effect of large temperature difference on the mixing of two dissimilar gases with large molecular weights under compressible conditions. Both two dimensional and three dimensional model free simulations are carried out using higher order numerical scheme (4th order spatial and 2nd order temporal) to understand the structure and evolution of supersonic confined mixing layer of similar and dissimilar gases. Two dimensional simulations are carried out by both SPARK (finite difference method) and OpenFOAM (finite volume method based open source software that was specially picked out and put together), while 3D model free simulations are carried out by OpenFOAM. A fine grid structure with higher grid resolution near the walls and shear layer is chosen. The effect of forcing of fluctuations on the inlet velocity shows no appreciable change in the fully developed turbulent region of the flow. The flow variables are averaged after the attainment of statistical steady state established through monitoring the concentration of inert species introduced in the initial guess. The effect of side wall on the flow structure on the mixing layer is studied by comparing the simulation results with and without side wall. Two dimensional simulations show a good match for the growth rate of shear layer and experimental wall pressures. Three dimensional simulations without side wall shows 14% higher growth rate of shear layer than that of two dimensional simulations. The wall pressures predicted by these three dimensional simulations are also lower than that predicted using two dimensional simulations (6%) and experimental (9%) results in the downstream direction of the mixing duct. Three dimensionality of the flow is thought of as a cause for these differences. Simulations with the presence of side wall show that there is no remarkable difference of three dimensionality of the flow in terms of the variables and turbulence statistics compared to the case without side walls. However, the growth rate of shear layer and wall surface pressures matches well with that predicted using two dimensional simulations. It has been argued that this good match in shear layer growth rate occurs due to formation of oblique disturbances in presence of side walls that are considered responsible for the decrease in growth rate in 3-d mixing layers. The wall pressure match is argued to be good because of hindrance from side wall in the distribution of momentum in third direction results in higher wall pressure. The effect of dissimilar gases at large temperature difference on the growth rate reduction in compressible conditions is studied. Taking experimental conditions as baseline case, simulations are carried out for a range of convective Mach numbers. Simulations are also carried out for the same range of convective Mach numbers considering the mixing of similar gases at the same temperature. The normalized growth rates with incompressible counterpart for both the cases show that the dissimilar gas combination with large temperature difference shows higher growth rate. This result confirms earlier stability analysis that predicts increased growth rate for such cases. The growth rate reduction of a compressible mixing layer is argued to occur due to reduced pressure strain term in the Reynolds stress equation. This reduction also requires the pressure and density fluctuation correlation to be very near to unity. This holds good for a mixing layer formed between two similar gases at same temperature. For dissimilar gases at different temperatures this assumption does not hold well, and pressure-density correlation coefficient shows departure from unity. Further analysis of temperature density correlation factor, and temperature fluctuations shows that the changes in density occur predominantly due to temperature effects, than due to pressure effects. The mechanism of density variations is found to be different for similar and dissimilar gases, while for similar gases the density variations are due to pressure variations. For dissimilar gases density variation is also affected by temperature variations in addition to pressure variations. It has been observed that the traditional k-ε turbulence model within the RANS (Reynolds Averaged Navier Stokes) framework fails to capture the growth rate reduction for compressible shear layers. The performance of k-ε turbulence model is tested for the mixing of dissimilar gases at large temperature difference. For the experimental test case the shear layer growth rate and wall pressures show good match with other model free simulations. Simulations are further carried out for a range of convective Mach numbers keeping the mixing gases and their temperatures same. It has been observed that a drop in the growth rate is well predicted by RANS simulations. Further, the compressibility option has been removed and it has been observed that for the density and temperature difference, even for incompressible case, the drop in growth rate exists. This behaviour shows that the decrease in growth rate is mainly due to the interaction of temperature and species mass fraction on density. Also it can be inferred that RANS with k-ε turbulence model is able to capture the compressible shear layer growth rate for dissimilar gases at high temperature difference. The mixing of heat and species is governed by the values of turbulent Prandtl and Schmidt numbers respectively. These numbers have been observed to vary for different flow conditions, while affecting the flow field considerable in the form of temperature and species distribution. Model free simulations are carried out on an incompressible convective Mach number mixing layer, and the results are compared with that of a compressible mixing layer to study the effect of compressibility on the values of turbulent Prandtl / Schmidt numbers. It has been observed that both turbulent Prandtl and Schmidt numbers show an almost constant value in the mixing layer region for incompressible case. While, for a compressible case, both turbulent Prandtl and Schmidt numbers show a continuous variation within the mixing layer. However, the turbulent Lewis number is observed to be near unity for both incompressible and compressible cases. The thesis is composed of 8 chapters. An introduction of the subject with critical and relevant literature survey is presented in chapter 1. Chapter 2 describes the mathematical formulation and assumptions along with solution methodology needed for the simulations. Chapter 3 deals with the two and three dimensional model free simulations of the non reacting mixing layer. The effect of the presence of side wall is studied in chapter 4. Chapter 5 deals with the effect of compressibility on the mixing of two dissimilar gases at largely different temperatures. The performance of k-ε turbulence model is checked for dissimilar gases in Chapter 6. Chapter 7 is concerned with the effect of compressibility on turbulent Prandtl and Schmidt numbers. Finally concluding remarks are presented in chapter 8. The main aim of this thesis is the exploration of parallel mixing of dissimilar gases under compressible conditions for both two and three dimensional cases. The outcome of the thesis is (a) a finding that the presence of sidewall in a mixing duct does not make flow field two dimensional, instead it causes the formation of oblique disturbances and the shear layer growth rate is reduced, (b) that it has been shown that the growth rates of dissimilar gases are affected far more by large temperature difference than by compressibility as in case of similar gases, (c) that the growth rates of compressible shear layers formed between dissimilar gases are better predicted using k-εturbulence model and (d) that for compressible mixing conditions the turbulent Prandtl and Schmidt numbers vary continuously in the mixing layer region necessitating the use of some kind of model instead of assuming constant values.