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High Rayleigh number(Ra) turbulent free convection has many unresolved issues related to the phenomenology behind the flux scaling, the presence of a mean wind and its effects, exponential probability distribution functions, the Prandtl number dependence and the nature of near wall structures. Few studies have been conducted in the high Prandtl number regime and the understanding of near wall coherent structures is inadequate for $Ra > 10^9$. The present thesis deals with the results of investigations conducted on high Rayleigh number turbulent free convection in the high Schmidt number(Sc) regime, focusing on the role of near wall coherent structures. We use a new method of driving the convection using concentration difference of NaCl across a horizontal membrane between two tanks to achieve high Ra utilising the low molecular diffusivity of NaCl. The near wall structures are visualised by planar laser induced fluorescence. Flux is estimated from transient measurement of concentration in the top tank by a conductivity probe. Experiments are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR = 0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of 0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine membrane (and for the coarse membrane at low driving potentials), the transport across the partition becomes diffusion dominated, while the transport above and below the partition becomes similar to unsteady non penetrative turbulent free convection above flat horizontal surfaces (Figure~\ref{fig:schem}(A)). In this type of convection, the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is the near wall concentration difference, similar to that in Rayleigh - B\'nard convection . Hence, we are able to study turbulent free convection over horizontal surfaces in the Rayleigh Number range of $\sim 10^- 10 ^$ at Schmidt number of 602, focusing on the nature and role of near wall coherent structures. To our knowledge, this is the first study showing clear images of near wall structures in high Rayleigh Number - high Schmidt number turbulent free convection. We observe a weak flow across the membrane in the case of the coarser membrane at higher driving potentials (Figure \ref(B)). The effect of this through flow on the flux and the near wall structures is also investigated. In both the types of convection the near wall structure shows patterns formed by sheet plumes, the common properties of these patterns are also investigated. The major outcomes in the above three areas of the thesis can be summarised as follows \subsection* \label \subsubsection* \label The non-dimensional flux was similar to that reported by Goldstein\cite at Sc of 2750. Visualisations show that the near wall coherent structures are line plumes. Depending on the Rayleigh number and the Aspect ratio, different types of large scale flow cells which are driven by plume columns are observed. Multiple large scale flow cells are observed for AR = 0.65 and a single large scale flow for AR= 0.435. The large scale flow create a near wall mean shear, which is seen to vary across the cross section. The orientation of the large scale flow is seen to change at a time scale much larger than the time scale of one large scale circulation The near wall structures show interaction of the large scale flow with the line plumes. The plumes are initiated as points and then gets elongated along the mean shear direction in areas of larger mean shear. In areas of low mean shear, the plumes are initiated as points but gets elongated in directions decided by the flow induced by the adjacent plumes. The effect of near wall mean shear is to align the plumes and reduce their lateral movement and merging. The time scale for the merger of the near wall line plumes is an order smaller than the time scale of the one large scale circulation. With increase in Rayleigh number, plumes become more closely and regularly spaced. We propose that the near wall boundary layers in high Rayleigh number turbulent free convection are laminar natural convection boundary layers. The above proposition is verified by a near wall model, similar to the one proposed by \cite{tjfm}, based on the similarity solutions of laminar natural convection boundary layer equations as Pr$\rightarrow\infty$. The model prediction of the non dimensional mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$ - where $Ra_\lambda$ is the Rayleigh number based on the plume spacing $\lambda$, and $Z_w$ is a near wall length scale for turbulent free convection - matches the experimental measurements. Therefore, higher driving potentials, resulting in higher flux, give rise to lower mean plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is a constant for a given fluid. We also show that the laminar boundary layer assumption is consistent with the flux scaling obtained from integral relations. Integral equations for the Nusselt number(Nu) from the scalar variance equations for unsteady non penetrative convection are derived. Estimating the boundary layer dissipation using laminar natural convection boundary layers and using the mean plume spacing relation, we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation is only considered. The contribution of bulk dissipation is found to be a small perturbation on the dominant 1/3 scaling, the effect of which is to reduce the effective scaling exponent. In the appendix to the thesis, continuing the above line of reasoning, we conduct an exploratory re-analysis (for $Pr\sim 1$) of the Grossman and Lohse's\cite scaling theory for turbulent Rayleigh - B\'enard convection. We replace the Blasius boundary layer assumption of the theory with a pair of externally forced laminar natural convection boundary layers per plume. Integral equations of the externally forced laminar natural convection boundary layer show that the mixed convection boundary layer thickness is decided by a $5^{th}$ order algebraic equation, which asymptotes to the laminar natural convection boundary layer for zero mean wind and to Blasius boundary layer at large mean winds. \subsubsection*{Effect of wall normal flow on flux and near wall structures} \label{sec:effect-wall-normal} For experiments with the coarser($35\mu$) membrane, we observe three regimes viz. the strong through flow regime (Figure~\ref{fig:schem}(b)), the diffusion regime (Figure \ref{fig:schem}(a)), and a transition regime between the above two regimes that we term as the weak through flow regime. At higher driving potentials, only half the area above the coarser membrane is covered by plumes, with the other half having plumes below the membrane. A wall normal through flow driven by impingement of the large scale flow is inferred to be the cause of this (Figure \ref{fig:schem}(b)). In this strong through flow regime, only a single large scale flow circulation cell oriented along the diagonal or parallel to the walls is detected. The plume structure is more dendritic than the no through flow case. The flux scales as $\Delta C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed with the fine membrane. The phenomenology of a flow across the membrane driven by the impingement of the large scale flow of strength $W_*$, the Deardorff velocity scale, explains the cubic scaling. We find the surprising result that the non-dimensional flux is smaller than that in the no through flow case for similar parameters. The mean plume spacings in the strong through flow regime are larger and show a different Rayleigh number dependence vis-a-vis the no through flow case. Using integral analysis, an expression for the boundary layer thickness is derived for high Schmidt number laminar natural convection boundary layer with a normal velocity at the wall. (Also, solutions to the integral equations are obtained for the $Sc\sim 1$ case, which are given as an Appendix.) Assuming the gravitational stability condition to hold true, we show that the plume spacing in the high Schmidt number strong through flow regime is proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length scale from the through flow velocity. This inference is fairly supported by the plume spacing measurements At lower driving potentials corresponding to the transition regime, the whole membrane surface is seen to be covered by plumes and the flux scaled as $\Delta C_w^{4/3}$. The non-dimensional flux is about the same as in turbulent free convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to occur on one side of the membrane. This is expected to occur in the area averaged sense with different parts of the membrane having predominance of diffusion or through flow dominant transport. At very low driving potentials corresponding to the diffusion regime, the diffusion corrected non dimensional flux match the turbulent free convection values, implying a similar phenomena as in the fine membrane. \subsubsection*{Universal probability distribution of near wall structures} \label{sec:univ-prob-distr} We discover that the probability distribution function of the plume spacings show a standard log normal distribution, invariant of the presence or the absence of wall normal through flow and at all the Rayleigh numbers and aspect ratios investigated. These plume structures showed the same underlying multifractal spectrum of singularities in all these cases. As the multifractal curve indirectly represents the processes by which these structures are formed, we conclude that the plume structures are created by a common generating mechanism involving nucleation at points, growth along lines and then merging, influenced by the external mean shear. Inferring from the thermodynamic analogy of multifractal analysis, we hypothesise that the near wall plume structure in turbulent free convection might be formed so that the entropy of the structure is maximised within the given constraints.

The heat transfer phenomena in the near-wall region of a randomly packed pebble bed are important in the design of a Pebble Bed Reactor (PBR), especially when considering the safety case during accident conditions. At higher temperatures the contribution of the radiation heat transfer component to the overall heat transfer in a PBR increases significantly. The wall effect present in the near-wall region of a packed pebble bed affects the heat transfer in this region. Various correlations exist to predict the effective thermal conductivity through a packed pebble bed, but not all of the correlations consider the contribution of radiation and some are only applicable to the bulk region. Experimental research has been done on the heat transfer through a packed pebble bed. However, most of the results are case specific and cannot necessarily be used to validate models or simulations to predict the effective thermal conductivity of a pebble bed. The objective of this study is to develop a methodology that uses experimental work together with Computational Fluid Dynamics (CFD) simulations to predict the effective thermal conductivity in the near-wall region of a randomly packed pebble bed, and to separate the conduction and radiation components of the effective thermal conductivity. The proposed methodology inter alia includes experimental tests and the calibration of a CFD model to obtain numerical results that correlate well with the experimental results. To illustrate the proposed methodology the newly constructed Near-wall Effect Thermal Conductivity Test Facility (NWETCTF) was used to gather experimental results for the temperature and heat transfer distribution through a randomly packed pebble bed. Two identical but separate experimental tests were performed and the results of the two tests were in good agreement. From the experimental results the effective thermal conductivity was derived. The effect of the near-wall region on the heat transfer and the significance of radiation at higher temperatures are evident from the results. Recommendations were made for future experimental work with the NWETCTF from the findings of the investigation. A numerically packed pebble bed that is representative of the experimental pebble bed was generated using the Discrete Element Method (DEM) and a CFD model was set up for the heat transfer through the pebble bed using STAR-CCM+.. The CFD results showed trends similar to that of the experimental results. However, some discrepancies were identified that must be addressed in future studies by calibrating the CFD model. The effective thermal conductivity for the numerical simulation was determined using the CFD results and the conduction and radiation components were separated. / MSc (Mechanical Engineering), North-West University, Potchefstroom Campus, 2015

The heat transfer phenomena in the near-wall region of a randomly packed pebble bed are important in the design of a Pebble Bed Reactor (PBR), especially when considering the safety case during accident conditions. At higher temperatures the contribution of the radiation heat transfer component to the overall heat transfer in a PBR increases significantly. The wall effect present in the near-wall region of a packed pebble bed affects the heat transfer in this region. Various correlations exist to predict the effective thermal conductivity through a packed pebble bed, but not all of the correlations consider the contribution of radiation and some are only applicable to the bulk region. Experimental research has been done on the heat transfer through a packed pebble bed. However, most of the results are case specific and cannot necessarily be used to validate models or simulations to predict the effective thermal conductivity of a pebble bed. The objective of this study is to develop a methodology that uses experimental work together with Computational Fluid Dynamics (CFD) simulations to predict the effective thermal conductivity in the near-wall region of a randomly packed pebble bed, and to separate the conduction and radiation components of the effective thermal conductivity. The proposed methodology inter alia includes experimental tests and the calibration of a CFD model to obtain numerical results that correlate well with the experimental results. To illustrate the proposed methodology the newly constructed Near-wall Effect Thermal Conductivity Test Facility (NWETCTF) was used to gather experimental results for the temperature and heat transfer distribution through a randomly packed pebble bed. Two identical but separate experimental tests were performed and the results of the two tests were in good agreement. From the experimental results the effective thermal conductivity was derived. The effect of the near-wall region on the heat transfer and the significance of radiation at higher temperatures are evident from the results. Recommendations were made for future experimental work with the NWETCTF from the findings of the investigation. A numerically packed pebble bed that is representative of the experimental pebble bed was generated using the Discrete Element Method (DEM) and a CFD model was set up for the heat transfer through the pebble bed using STAR-CCM+.. The CFD results showed trends similar to that of the experimental results. However, some discrepancies were identified that must be addressed in future studies by calibrating the CFD model. The effective thermal conductivity for the numerical simulation was determined using the CFD results and the conduction and radiation components were separated. / MSc (Mechanical Engineering), North-West University, Potchefstroom Campus, 2015

[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Since the damping functions employed by most of the low-Reynolds-number models are related to the non-dimensional distance y+[ special character ??? near-wall non-dimensional distance in y direction], which is based on local wall shear stress, these models become invalid for separated flows, because the wall shear stress is zero at the reattachment point. In addition, the pressure-velocity correlation term is neglected in most of these models, although this term is shown in this thesis to be important in the near-wall region for simple flows and large pressure gradient flows. In this thesis, two main efforts are made to improve the k ??? [special character - dissipation rate] model. First, based on Myong and Kasagi???s (1990) low-Reynolds-number model (hereafter referred to as MK model), a more general damping function [special character - turbulent viscosity damping function in LRN turbulent model] is postulated which only depends on the Reynolds numbers [formula ??? near-wall turbulence Reynolds number]. Second, a form for the pressure-velocity correlation term is postulated based on the Poisson equation for pressure fluctuations. This modified model predicts the turbulent flow over a flat plate very well. It is found that the inclusion of the pressure-velocity correlation term leads to significant improvement of the prediction of near-wall turbulence kinetic energy. When the model is applied to turbulent flow over a backward-facing step, it produces better predictions than the traditional k ??? [special character - dissipation rate] model, FLUENT???s two-layer model and the MK model. Again, the pressure-velocity correlation term improves the turbulence kinetic energy prediction in the separated region over that of other models investigated here. The studies of numerical methods concerning computational domain size and grid spacing reveal that a very large domain size is required for accurate flat plate flow computation. They also show that a fine grid distribution in the near-wall region upstream of the step is necessary for acceptable flow prediction accuracy in the downstream separated region.

Turbulent gas-solid flows are readily encountered in many industrial and environmental processes. The development of a generic modeling technique for gas-solid turbulent flows remains a significant challenge in the field of mechanical engineering. Eulerian models are typically used to model large systems of particles. In this dissertation, a numerical analysis was carried out to assess a current state-of-the-art Eulerian two-fluid model for fully-developed turbulent gas-solid upward flow in a vertical pipe. The two-fluid formulation of Bolio et al. (1995) was adopted for the current study and the drag force was considered as the dominant interfacial force between the solids and fluid phase. In the first part of the thesis, a two-equation low Reynolds number k-ε model was used to predict the fluctuating velocities of the gas-phase which uses an eddy viscosity model. The stresses developed in the solids-phase were modeled using kinetic theory and the concept of granular temperature was used for the prediction of the solids velocity fluctuation. The fluctuating drag, i.e., turbulence modulation term in the transport equation of the turbulence kinetic energy and granular temperature was used to capture the effect of the presence of the dispersed solid particles on the gas-phase turbulence. The current study documents the performance of two popular turbulence modulation models of Crowe (2000) and Rao et al. (2011). Both models were capable of predicting the mean velocities of both the phases which were generally in good agreement with the experimental data. However, the phenomena that small particles cause turbulence suppression and large particles cause turbulence enhancement was better captured by the model of Rao et al. (2011); conversely, the model of Crowe (2000) produced turbulence enhancement in all cases. Rao et al. (2011) used a modified wake model originally proposed by Lun (2000) which is activated when the particle Reynolds number reaches 150. This enables the overall model to produce turbulence suppression and augmentation that follows the experimental trend. The granular temperature predictions of both models show good agreement with the limited experimental data of Jones (2001). The model of Rao et al. (2011) was also able to capture the effect of gas-phase turbulence on the solids velocity fluctuation for three-way coupled systems. However, the prediction of the solids volume fraction which depends on the value of the granular temperature shows noticeable deviations with the experimental data of Sheen et al. (1993) in the near-wall region. Both turbulence modulation models predict a flat profile for the solids volume fraction whereas the measurements of Sheen et al. (1993) show a significant decrease near the wall and even a particle-free region for flows with large particles. The two-fluid model typically uses a low Reynolds number k-ε model to capture the near-wall behavior of a turbulent gas-solid flow. An alternative near-wall turbulence model, i.e., the two-layer model of Durbin et al. (2001) was also implemented and its performance was assessed. The two-layer model is especially attractive because of its ability to include the effect of surface roughness. The current study compares the predictions of the two-layer model for both clear gas and gas-solid flows to the results of a conventional low Reynolds number model. The effects of surface roughness on the turbulence kinetic energy and granular temperature were also documented for gas-particle flows in both smooth and rough pipes.

[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Since the damping functions employed by most of the low-Reynolds-number models are related to the non-dimensional distance y+[ special character ??? near-wall non-dimensional distance in y direction], which is based on local wall shear stress, these models become invalid for separated flows, because the wall shear stress is zero at the reattachment point. In addition, the pressure-velocity correlation term is neglected in most of these models, although this term is shown in this thesis to be important in the near-wall region for simple flows and large pressure gradient flows. In this thesis, two main efforts are made to improve the k ??? [special character - dissipation rate] model. First, based on Myong and Kasagi???s (1990) low-Reynolds-number model (hereafter referred to as MK model), a more general damping function [special character - turbulent viscosity damping function in LRN turbulent model] is postulated which only depends on the Reynolds numbers [formula ??? near-wall turbulence Reynolds number]. Second, a form for the pressure-velocity correlation term is postulated based on the Poisson equation for pressure fluctuations. This modified model predicts the turbulent flow over a flat plate very well. It is found that the inclusion of the pressure-velocity correlation term leads to significant improvement of the prediction of near-wall turbulence kinetic energy. When the model is applied to turbulent flow over a backward-facing step, it produces better predictions than the traditional k ??? [special character - dissipation rate] model, FLUENT???s two-layer model and the MK model. Again, the pressure-velocity correlation term improves the turbulence kinetic energy prediction in the separated region over that of other models investigated here. The studies of numerical methods concerning computational domain size and grid spacing reveal that a very large domain size is required for accurate flat plate flow computation. They also show that a fine grid distribution in the near-wall region upstream of the step is necessary for acceptable flow prediction accuracy in the downstream separated region.

This thesis is a study of the effects of distributed roughness elements on a two-dimensional turbulent boundary layer. Measurements were taken on a total of ten rough wall configurations: four involving Gaussian spikes, and six with circular cylindrical posts. Rough wall flows are particularly suited to study with Laser Doppler Velocimetry (LDV) due to the fact that measurements are required near a solid surface, as well has in highly turbulent fluid. The LDV system used in this study is a fine resolution (~50 micron), three-component, fiber optic system. All mean velocities, Reynolds stresses, and triple products are measured. This study is unique in the range and variety of roughness cases for which data was taken. The data show that the flow over a rough wall is characterized by high levels of turbulence near the roughness element peaks at the interface between low-speed, near-wall fluid and the higher speed fluid above. Behind an element, high-momentum fluid sweeps toward the wall, and there is a small region of ejection of low-momentum fluid. Cylindrical elements typically have larger magnitudes of turbulent stresses at their peaks compared to Gaussian elements. Trends in mean velocity profile parameters such as displacement height, roughness effect, and wake parameter are examined with respect to roughness element geometry and spacing. / Master of Science

Advanced cooling techniques are required to increase the Brayton cycle temperature ratio necessary for the increase of the overall cycle's efficiency. Current turbine components are cooled with an array of internal cooling channels in the midchord section of the blade, pin fin arrays at the trailing edge and impingement channels in the leading edge. Impingement channels provide the designer with high convective coefficients on the target surface. Increasing the heat transfer coefficient of these channels has been a subject of research for the past 20 years. In the current study, a triple row impingement channel is studied with a jet to target spacing of 6, 8 and 10. The effects of sidewalls are also analyzed. Temperature sensitive paint alongside thin foil heaters are used to obtain heat transfer distributions throughout the target and side walls of the three different channels. Thermal performances were also calculated for the two largest channels. It was found that the side walls provide a significant amount of cooling especially when the channels are mounted side by side so that their sidewalls behave as fins. Similar to literature it was found that an increase in Z/D decreases heat transfer coefficient and provides a more uniform profile. It was also found that the Z/D = 6 and 8 target wall heat transfer profiles are very similar, hinting to the fact that successful potential core impingement may have occurred at height of eight diameters. A Computational Fluid Dynamics, or CFD, study was also performed to provide better insight into the flow field that creates such characteristic heat transfer profiles. The Realizable k-µ solution with enhanced wall functions gave surface heat transfer coefficients 30% off from the experimental data.