Donaldson's single-point second-order model [13] is used to close the Reynolds stress transport equations in cylindrical coordinates. A reduced set of equations are then solved for the decay of axisymmetric vortices and jets. A self-similar solution to the axisymmetric vortices is obtained numerically. The characteristics of the mean flow variables as well as the Reynolds stresses in this solution are discussed. Comparisons of the current results with Donaldson[13J and Donaldson and Sullivan[16] are also presented. The results show that the vortex core is free from turbulent shear stresses. The turbulent kinetic energy is also found to be relatively weak within the core region. The overshoot of the circulation is found to be 5% of the circulation at infinity over a wide range of Reynolds numbers. The effects of Reynolds number on the decay of the vortices are computed and discussed. Some of the quantities, such as mean flow circulation and turbulent kinetic energy, are found to be sensitive to the Reynolds number. However, the overshoot is found to be insensitive to the Reynolds number but its location does. A set of suitable model constants for the axisymmetric jets is also found and a self similar solution for the jet case is obtained. Comparisons of the computed results with some recent experimental data are presented. / Master of Science

The primary purpose of this thesis is to quantify the effects of RANS turbulence modeling on the resolution of free shear vortical flows. The simulation of aerodynamic wing-tip vortices is used as a test bed. The primary configuration is flow over an isolated finite wing with aspect ratio, , and Reynolds number, . Tip-vortex velocity profiles, vortex core and wake turbulence levels, and Reynolds stresses are compared with wind tunnel measurements. Three turbulence models for RANS closure are tested: the Lumley, Reece, and Rodi full Reynolds stress transport model and the Sparlart-Allmaras model with and without a proposed modification. The main finding is that simulations with the full Reynolds stress transport model show remarkable mean flow agreement in the vortex and wake due to the proper prediction of a laminar vortex core. Simulations with the Spalart-Allmaras model did not indicate a laminar core and predicted over-diffusion of the tip-vortex. Secondary investigations in this work include the study of wall boundary layer treatment and simulating the wake-age of an isolated rotorcraft in hover using a steady-state RANS solver. By comparing skin friction plots over the NACA 0012 airfoil, it is shown that wall functions are most effective in the trailing edge half of the airfoil, while high velocity gradient and curvature of the leading edge make them more vulnerable to discrepancies. The rotorcraft simulation uses the modified Spalart-Allmaras turbulence model and shows proper, qualitative, resolution of the interaction between the vortex sheet and the tip vortex. / Master of Science

This research is intended to determine the role of riparian vegetation in stream morphology. This experiment examined the effects of riparian vegetation on boundary shear stress (BSS) by completing the following objectives: (1) evaluating the effects of streambank vegetation on near-bank velocity and turbulence; (2) determining a method for measuring BSS; and, (3) examining the effects of streambank vegetation on BSS using an existing model. A second order prototype stream, with individual reaches dominated by the three vegetation types (trees, shrubs, and grass) was modeled using a fixed-bed Froude-scale modeling technique. One model streambank of the prototype stream was constructed for each vegetation type in addition to one bank with only grain roughness. Velocity profiles were measured using an acoustic Doppler velocimeter (ADV) and a miniature propeller (MP). A flush-mounted Dantec MiniCTA system was used to measure shear stress at the streambank wall. The addition of vegetation on a sloping streambank increased the streamwise free stream velocity and decreased the near-bank streamwise velocity. The turbulence caused by the upright shrub treatment increased turbulent kinetic energy and Reynolds stresses near the streambank toe, an area susceptible to fluvial erosion. The presence of dense, semi-rigid vegetation may encourage the formation of a wider channel with a vertical streambank. The small range of CTA shear stress measurements (0.02—2.14 Pa) suggested that one estimate can describe a streambank. The law of the wall technique is not appropriate because the velocity profiles did not follow the necessary logarithmic shape. Vegetative roughness present in channels created secondary flow; turbulence characteristics more appropriately estimated BSS. The BSS model predicted velocity fields in similar distribution to that measured by the ADV and MP. BSS calculated using the ray-isovel method for both velocity measurement devices were different than the measured BSS values, likely due to distortions in the measured velocity field. In general, the predicted BSS distribution increased with water depth and decreased with increasing vegetation density. The predicted BSS at the shrub toe indicated a spike in shear stress consistent with TKE estimates. / Ph. D.

An experimental investigation was performed to measure Reynolds stresses in the turbulent flow downstream of a large-scale linear turbine cascade. A rotatable X-wire hot-wire probe that allows redundant data to be taken with solution for mean velocities and turbulence quantities by least-squares fitting procedures was developed. This measurement technique was verified in a fully-developed turbulent pipe flow; the results show the accuracy of the probe when used in an end-flow orientation at various incidence angles and with a multiple number of angular settings. Traverses with a single hot-wire at mid-span near the blade row exit show very high levels of turbulence locally in the blade wake near the trailing edge which quickly lessen in magnitude downstream. The rotatable X-wire was used to obtain the Reynolds stresses on a measurement plane located 10% of an axial chord downstream of the trailing edge. Here the turbulence kinetic energy exhibits a distribution resembling the contours of total pressure loss obtained previously, but is highest in the blade wake where losses are relatively low. The turbulent shear stresses obtained are consistent in sign and magnitude with the gradients of mean velocity. The mass-averaged turbulence kinetic energy accounts for 21% of the total pressure loss at this measurement plane. / Master of Science

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

The premise of the work presented here is to use a common analytical tool, Computational Fluid dynamics (CFD), along with a difference turbulence models. Eddy viscosity models as well as state-of-the-art Large Eddy Simulation (LES) were used to study the flow past bluff bodies. A suitable CFD code (CFX5.6b) was selected and implemented. Simulation of turbulent transport for the gas through the gaps of the randomly distributed spherical fuel elements (pebbles) was performed. Although there are a number of numerical studies () on flows around spherical bodies, none of them use the necessary turbulence models that are required to simulate flow where strong separation exists. With the development of high performance computers built for applications that require high CPU time and memory; numerical simulation becomes one of the more effective approaches for such investigations and LES type of turbulence models can be used more effectively. Since there are objects that are touching each other in the present study, a special approach was applied at the stage of building computational domain. This is supposed to be a considerable improvement for CFD applications. Zero thickness was achieved between the pebbles in which fission reaction takes place. Since there is a strong pressure gradient as a result of high Reynolds Number on the computational domain, which strongly affects the boundary layer behavior, heat transfer in both laminar and turbulent flows varies noticeably. Therefore, noncircular curved flows as in the pebble-bed situatio n, in detailed local sense, is interesting to be investigated. Since a compromise is needed between accuracy of results and time/cost of effort in acquiring the results numerically, selection of turbulence model should be done carefully. Resolving all the scales of a turbulent flow is too costly, while employing highly empirical turbulence models to complex problems could give inaccurate simulation results. The Large Eddy Simulation (LES) method would achieve the requirements to obtain a reasonable result. In LES, the large scales in the flow are solved and the small scales are modeled. Eddy viscosity and Reynolds stress models were also be used to investigate the applicability of these models for this kind of flow past bluff bodies at high Re numbers.

Thesis: Ph. D., Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2019 / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 137-153). / Each year, surface ocean ecosystems export sinking particles containing gigatons of carbon into the ocean's interior. This particle flux connects the entire ocean microbiome and constitutes a fundamental aspect of marine microbial ecology and biogeochemical cycles. Particle flux is also variable and intricately complex, impeding its mechanistic or quantitative description. In this thesis we pair compilations of available data with novel mathematical models to explore the relationships between particle flux and other key variables - temperature, net primary production, and depth. Particular use is made of (probability) distributional descriptions of quantities that are known to vary appreciably. First, using established thermodynamic dependencies for primary production and respiration, a simple mechanistic model is developed relating export efficiency (i.e. the fraction of primary production that is exported out of the surface ocean via particle flux) to temperature. / The model accounts for the observed variability in export efficiency due to temperature without idealizing out the remaining variability that evinces particle flux's complexity. This model is then used to estimate the metabolically-driven change in average export efficiency over the era of long-term global sea surface temperature records, and it is shown that the underlying mechanism may help explain glacial-interglacial atmospheric carbon dioxide drawdown. The relationship between particle flux and net primary production is then explored. Given that these are inextricable but highly variable and measured on different effective scales, it is hypothesized that a quantitative relationship emerges between collections of the two measurements - i.e. that they can be related not measurement-by-measurement but rather via their probability distributions. / It is shown that on large spatial or temporal scales both are consistent with lognormal distributions, as expected if each is considered as the collective result of many subprocesses. A relationship is then derived between the log-moments of their distributions and agreement is found between independent estimates of this relationship, suggesting that upper ocean particle flux is predictable from net primary production on large spatiotemporal scales. Finally, the attenuation of particle flux with depth is explored. It is shown that while several particle flux-versus-depth models capture observations equivalently, these carry very different implications mechanistically and for magnitudes of export out of the surface ocean. A model is then proposed for this relationship that accounts for measurements of both the flux profile and of the settling velocity distribution of particulate matter, and is thus more consistent with and constrained by empirical knowledge. / Possible future applications of these models are discussed, as well as how they could be tested and/or constrained observationally. / by Brendan Barry. / Ph. D. / Ph.D. Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution)

Yes / When using point measurement for environmental or sediment laden flows, there is well-recognised risk for not having aligned measurements that causes misinterpretation of the measured velocity data. In reality, these kinds of mismeasurement mainly happen due to the misinterpretation of bed orientation caused by the complexity of its determination in natural flows, especially in bedload laden or rough bed flows. This study proposes a novel bed realignment method to improve the measured data benchmarking by three-dimensional (3D) bed profile orientation and implemented it into different sets of experimental data. More specifically, the effects of realignment on velocity profile and streamwise turbulence structure measurements were investigated. The proposed technique was tested against experimental data collected over a water-worked and an experimentally arranged well-packed beds. Different from the well-packed rough bed, the water-worked bed has been generated after long sediment transport and settling and hence can be used to verify the proposed bed-alignment technique thoroughly. During the flow analysis, the corrected velocity, turbulence intensity and Reynolds stress profiles were compared to the theoretical logarithmic law, exponential law and linear gravity (universal Reynolds stress distribution) profiles, respectively. It has been observed that the proposed method has improved the agreement of the measured velocity and turbulence structure data with their actual theoretical profiles, particularly in the near-bed region (where the ratio of the flow measurement vertical distance to the total water depth, z/h, is limited to ≤0.4).

Yes / This study uses an improved k –ε coupled shallow water equations (SWE) model that equipped with the numerical computation of the velocity fluctuation terms to investigate the turbulence structures of the open channel flows. We adapted the Kolmogorov K41 scaling model into the k –ε equations to calculate the turbulence intensities and Reynolds stresses of the SWE model. The presented model was also numerically improved by a recently proposed surface gradient upwind method (SGUM) to allow better accuracy in simulating the combined source terms from both the SWE and k –ε equations as proven in the recent studies. The proposed model was first tested using the flows induced by multiple obstructions to investigate the utilised k –ε and SGUM approaches in the model. The laboratory experiments were also conducted under the non-uniform flow conditions, where the simulated velocities, total kinetic energies (TKE) and turbulence intensities by the proposed model were used to compare with the measurements under different flow non-uniformity conditions. Lastly, the proposed numerical simulation was compared with a standard Boussinesq model to investigate its capability to simulate the measured Reynolds stress. The comparison outcomes showed that the proposed Kolmogorov k –ε SWE model can capture the flow turbulence characteristics reasonably well in all the investigated flows. / The Major State Basic Research Development Program (973 program) of China (No. 2013CB036402)