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.

<p> An experimental study of free convection heat transfer from a heated horizontal plate facing downwards in air is reported in this thesis. The results of this study are in good agreement with the results obtained by Fishenden and Saunders. This study also investigates the effects of restraining the development of the thermal boundary layer with 1/2" and 1" edge strips around the edges of the test plate. This study led to the conclusion that edge restrains tended to decrease the heat transfer from the plate. </p> <p> The range of Grashof Prandtl Number product investigated is between 4 x 10⁸ and 8 x 10⁹ resulting in the heat flux range of 0.7 Btu/hrft² to 102 Btu/hrft². Correlations are presented relating heat flux and temperature difference between plate surface temperature and ambient temperature. </p> / Thesis / Master of Engineering (ME)

No description available.

Scalar (heat or mass) transfer plays an important role in many industrial and engineering applications. Difficulties in experimental measurements means that there is limited detailed information available, especially in the near-wall region. Prediction in simple flows is well documented and the basis for development of many Computational Fluid Dynamics (CFD) models. This is, however, not the case for scalar transfer, especially when the Prandtl (Pr) or Schmidt number (Sc) is much greater than unity. In complex flows that involve separation and reattachment, the scalar transfer coefficient is significantly different to that of fully developed turbulent flow. The purpose of this Thesis is to investigate high Prandtl number (Pr ≥ 10) scalar transfer in fully developed (pipe) and disturbed (sudden pipe expansion) turbulent flow using CFD. Direct Numerical Simulation (DNS) is the most straight-forward approach to the solution of turbulent flows with scalar transfer. However, this technique is computationally intensive because all turbulent scales need to be resolved by the simulation. Large eddy simulation (LES) is a compromise compared to DNS. Instead of resolving all spatial scales, LES resolves only the large-scales with the small-scales being accounted for by a subgrid-scale model. Chapter 2 details the mathematical, numerical and computational details of LES with scalar transfer. From this, an optimized and highly scalable parallel LES solver was developed based on state-of-the-art LES subgrid-scale models and numerical techniques. Chapter 3 provides a verification of the LES solver for fully developed turbulent pipe flow. Reynolds numbers between Re = 180 and 1050 were simulated with a single Prandtl number of Pr = 0.71. Detailed turbulent statistics are provided for Re = 180, 395 and 590 with varying grid resolution for each Reynolds number. The results from these simulations were compared to established experimental and numerical databases of fully developed turbulent pipe and channel flows. The LES solver was shown to be in good agreement with the prior work with most discrepancies being accounted for by only reporting the resolved (large-scale) component directly reported from the LES results. For a Prandtl number close to unity, the mechanisms of turbulent transport and scalar transfer are similar. The near-wall region was shown to be dominated by large-scale sweeping structures that bring high momentum and scalar concentrations to the near-wall region. These are convected parallel to the wall as diffusion mechanisms act to transfer this to the wall where dissipation takes effect. An ejection structure then acts to transport the resultant low momentum, scalar depleted fluid back to the bulk to be replenished and continue the cycle. As the Prandtl number increases, molecular diffusivity decreases relative to viscosity, and the mechanisms of scalar transfer differ to those at Pr = 0.71. This is investigated in Chapter 4 using simulations at Re = 180, 395 and 590, with detailed statistics at Re = 395 for Pr = 0.71, 5, 10, 100 and 200. Where possible the results are compared to other numerical work and the LES solver was shown to accurately resolve the higher Prandtl number flows. There are marked variations in the scalar transfer with increasing Prandtl number as the turbulent scalar transfer becomes concentrated closer to the wall and dominated by large-scale turbulent structures. Sweeping structures are still responsible for bringing the high scalar concentrations towards the wall, however, high Prandtl number scalars are unable to completely diffuse to the wall in the time that the structure is convected parallel to the wall adjacent to the diffusive sublayer. Therefore, most of the high Prandtl number scalar is returned to the bulk via the ejection structure rather than being dissipated at the wall. Chapter 5 uses the sudden pipe expansion (SPE) to investigate disturbed turbulent flow for an inlet Reynolds numbers of Reb = 15600 and a diameter ratio of E = 1.6. These simulation parameters were chosen to match the experimental LDA measurements of Stieglmeier et al. (1989). The LES results for a range of grid resolutions were shown to be in very good agreement with the experimental work. From the LES results it was determined that the fluctuations in the wall shear stress are important in the near-wall turbulent transport. These are the result of eddies originating from the free shear layer down-washing and impinging upon the wall. This is a more effective sweeping mechanism than that observed for the fully developed turbulent pipe flow. Despite the down-wash structures impinging upon the wall, a viscous sublayer still exists in the reattachment region, albeit much thinner than the fully developed turbulent pipe flow further downstream. Using the same Reynolds number and diameter ratio, scalar transfer simulations were also undertaken in the SPE with Prandtl numbers of Pr = 0.71, 5, 10, 100 and 200. An applied scalar flux was used to heat the expanded pipe wall. The LES results are in agreement with experimental Nusselt numbers from Baughn et al. (1984) for Pr = 0.71. The disturbed turbulent flow enhances the scalar transfer and this is the result of down wash events transporting low (cold) scalar from the inlet pipe to the near-wall of the expanded pipe. This cools the heated wall and enhances localized scalar transfer downstream of the expansion. A diffusive sublayer still exists in the reattachment region within the viscous sublayer for Prandtl numbers greater than unity. As the Prandtl number increases the diffusivity decreases relative to viscosity and near-wall scalar transfer enhancement decreases as the diffusion time-scales increase.

No description available.

Fast breeder nuclear reactors use liquid metals such as Sodium (Na), Sodium-Potassium (Na-K), and Lead (Pb) as coolants since these liquids have high thermal conductivity, high thermal diffusivity, and lower heat capacity compared to water and air, thus involving low Prandtl numbers (Pr). However, liquid metals solidify at room temperature which poses challenges for experimental studies, making computational fluid dynamics (CFD) is considered a valuable analysis and design tool. Furthermore, the accurate modeling of turbulent heat transfer in low Pr flows remains one of the main challenges due to the gap between momentum and turbulent thermal diffusion. The study aims to address this challenge by enhancing the understanding of liquid metal coolant behavior and improving the accuracy of turbulence models in these types of fluids under different convective conditions. This research consists of two main parts, where the first one encompasses generating a DNS dataset for Reτ = 640, Pr = 0.004, 0.025, and 0.71, and Gr = 0 and 17.4×106 to supplement existing DNS databases, providing a more comprehensive foundation for turbulence models validation, and the second one envelop assessing the predictive capabilities of linear eddy viscosity-based Reynolds average Navier Stokes (RANS), Partially-average Navier stokes (PANS), and large eddy simulation (LES). The assessment covers four test cases ranging from canonical turbulent flow to more complex flow regimes involving separating and reattaching flows under different convective conditions for Reynolds numbers (Re) ranging from 640 to 40,341 and Pr varying from 0.004 up to 0.71. DNS results improve the understanding of Re, Pr, and buoyancy effects on both mean turbulent flows. Analysis reveals that buoyancy enhances heat transfer more significantly for lower Re and Pr. Furthermore, buoyancy alters flow and thermal structures by enhancing and reducing turbulence on both aiding and opposing sides, affecting heat transport. In addition, the assessment of different turbulence models demonstrates the superiority of LES compared to other models where the average of the prediction errors is 6% over all the cases aligning with findings from the excessive literature review.

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.