A gas-diffusion tracer experiment was conducted at the ChemNuclear, Inc., nuclear waste burial site near Barnwell, South Carolina, on June 1-10; 1981, testing a new methodology to measure the in situ gaseous diffusion characteristics of unsaturated porous media for the purpose of estimating the diffusive flux of volatile contaminants from the burial ground. The tracers used were CClBrF₂ and SF₆. They were released in the subsurface from permeation devices that closely approximate an ideal point-diffusion source. The permeation devices contain the tracer in liquid form and allow the tracer to escape at a constant rate by diffusion through a Teflon membrane. The release rates for CClBrF₂ and SF6 during the test were 105 and 3.3 nanograms/second, respectively. These compounds were selected on the basis of their compatabi1ity with the permeation-release device, their absence in the subsurface, and detectability in the part-per-tri11ion range in soil gas. Analyses were made in the field on a Varian 3700 series gas chromatograph equipped with an electron-capture detector. The instrument was modified to introduce soil gas through sampling valves and a Nafion tube desiccant. The diffusion sources were placed in the unsaturated soil at depths of 2 meters and 13 meters below land surface. Diffusive movements of tracer were monitored for a period of 7 days and tracer breakthrough was observed at points up to 3.5 meters away. Diffusion was modeled using a three-dimensional, continuous point source, transient-state, analytical model which allowed estimation of the effective diffusion coefficient of the porous media, and an independent assessment of the media's sorptive effects on the tracer gas. The model was calibrated using least squares and curve matching techniques, the latter of which enables a field technician to quickly interpret observed field data. Field values obtained for effective diffusion coefficient ranged from 0.026 to 0.037 cm²/sec. The average tortuosity factor observed for test site was 0.705.

Advances in mathematical modelling and the availability of high speed computers with considerable memory size is making it possible to study the hydraulics of border irrigation in a greater depth than every before. A zero inertia mathematical model was found to be reliable and inexpensive among the models available in border irrigation hydraulics and was used for this study to simulate free outflow flowing border irrigation. Special emphasis was given to the runoff produced from such a system. This study dealt particularly with, the identification of pertinent open channel variables affecting runoff in border irrigation, presentation of predictive graphical and mathematical solution to quantify runoff, and with utilization of these solutions in developing reuse system design criteria. Inflow rate, surface resistance, border slope, soil infiltration characteristics, application time (time of cutoff and length of run of the border) were among other variables studied. As one might expect, runoff was found to increase with slope, flow rate, application time and decrease with increase in infiltration rate, length of run and bed and vegetation drag. Considering the number of variables affecting runoff characteristics from a given irrigation, it was obvious to see a thorough examination of each variable in dimensional terms was practically impossible. Also, presentation of the results would have required too many graphs. Dimensional anslysis was used to solve this problem and in developing dimensionless runoff curves. The ability to quantify runoff made it possible to develop reuse system design formula for proper sizing of reuse systems under several operational requirements. Shape function for the ultimate infiltrated depth profile was used to get times of runoff and also calculate various efficiencies which are useful for evaluating the system. The study shows, through the use of reuse system, the potential application efficiency can be changed from present values of 60 percent to 90 percent in Arizona. It also can be used to demonstrate the saving in energy that can be realized through such system. Step by step procedures for the design of reuse system using graphical and mathematical solutions are presented with a sample problem worked out. It is expected that the result of this study can be used by designers as well as operators of border irrigation systems without any difficulty with the aid of a simple pocket calculator. Other uses of the study include getting optimal design for the system itself by evaluating various possible designs and classroom instruction on the application of dimensional analysis to open channel hydraulics problems and design of reuse systems.

Hot-wire measurements taken in the turbulent wake of a flat plate are presented. Symmetrical and antisymmetrical perturbations at various amplitudes and frequencies were introduced into the wake by small flap oscillations. As predicted by linear stability theory, the sinuous (antisymmetric) mode was observed to be more significant than the varicose (symmetric) mode. When the amplitude of the perturbation was low, the spatial development of the introduced coherent perturbation was predicted well by linear stability theory. At high forcing levels, the wake spreading showed dramatic deviations from the well known square-root behavior of the unforced case. Measured coherent Reynolds stresses changed sign in the neighborhood of the neutral point of the perturbation, as predicted by the linear theory. However, the linear theory failed to predict the disturbance amplitude and transverse shapes close to the neutral point. Some nonlinear aspects of the evolution of instabilities in the wake are discussed. Theoretical predictions of the mean flow distortion and the generation of the first harmonic are compared to experimental measurements. Given the unforced flow and the amplitude of the fundamental wave, the mean flow distortion and the amplitude of the first harmonic are predicted remarkably well.

This dissertation investigates spanwise periodic shear flow past two-dimensional bodies. The flow is assumed to be inviscid and incompressible. Using singular perturbation techniques, the solution is developed for ε = L/ℓ ≪ 1, where L represents body cross-sectional size, and ℓ the period of the oncoming flow U(z). The singular perturbation analysis involves three regions: the inner, wake and outer regions. The leading order solutions are developed in all regions, and in the inner region higher order terms are obtained. In the inner region near the body, the primary flow (U₀, V₀, P₀) corresponds to potential flow past the body with a local free stream value of U(z). The spanwise variation in U(z) produces a weak O(ε) secondary flow W₁ in the spanwise direction. As the vortex lines of the upstream flow are convected downstream, they wrap around the body, producing significant streamwise vorticity in a wake region of thickness O(L) directly behind the body. This streamwise vorticity induces a net volume flux into the wake. In the outer region far from the body, a nonlifting body appears as a distribution of three-dimensional dipoles, and the wake appears as a sheet of mass sinks. Both singularity structures must be included in describing the leading outer flow. For lifting bodies, the body appears as a lifting line, and the wake appears as a sheet of shed vorticity. The trailing vorticity is found to be equal to the spanwise derivative of the product of the circulation and the oncoming flow. For lifting bodies the first higher order correction to the inner flow is the response of the body to the downwash produced by the trailing vorticity. At large distances from the body, the flow takes on remarkably simple form.

A theory is presented which accounts for a particular aspect of nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities. Quasilinear expressions for the time-dependent nonlocal dispersivity and spatial covariance tensors of ensemble mean concentration are derived, as a function of time, variance σᵧ² of log hydraulic conductivity, degree of anisotropy, and flow direction. One important difference between existing linear theories and the new quasilinear theory is that in the former transverse nonlocal dispersivities tend asymptotically to zero whereas in the latter they tend to nonzero Fickian asymptotes. Another important difference is that while all existing theories are nominally limited to situations where σᵧ² is less than 1, the quasilinear theory is expected to be less prone to error when this restriction is violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.

Many environmental studies of water transport through the vadose zone require a field determination of saturated hydraulic conductivity. The purpose of this dissertation is to analyze the reliability of existing methods to determine saturated hydraulic conductivity, K(s), in the vadose zone from constant head borehole infiltration test data. In methods developed by the U. S. Bureau of Reclamation [USBRI, and in lesser known ones, K(s) is computed knowing the height of water in the borehole, length open to the formation, borehole radius, distance above the water table, and steady flow rate. The mathematical formulas on which these methods rest are derived on the basis of numerous simplifying assumptions. The free surface approach is used as the conceptual model of flow from a borehole. Results of numerical simulations are used to compare with the analytical solutions. Simulations with a steady-state finite element computer program, FREESURF, show that the Nasberg-Terletskata solution most closely approximates flow from a borehole with the free surface approach. The influence of capillarity is simulated for saturated-unsaturated porous media in four soils using a finite element computer program, FLUMP, and an integrated finite difference program, TRUST. Contrary to what one finds with the free surface approach, only a small portion of the flow field near the borehole is saturated at steady-state and the cross sectional area normal to the flow path increases with depth below the borehole. For deep water table conditions in fine textured soils, values of K(s) computed using the USBR open-hole equations may be more than 160% greater than the true values; and in coarse sands the USBR solutions may under-estimate the actual value by more than 35%. Mostly because of the influence of unsaturated soil properties there is no unique relationship between K(s), borehole conditions, and steady flow rate, as implied in the analytical solutions. Steady-state simulations demonstrate that existing solutions for borehole infiltration tests in anisotropic or nonuniform soils may also lead to significant errors. Time dependent simulations show that the time to reach a steady flow rate may be more than several days in very dry, low-permeable soils. The time to reach a steady flow rate can be significantly reduced by decreasing the open area between the borehole and formation while increasing the height of water in the borehole. Two methods are proposed to minimize the time, water volume requirements, and cost of conducting constant head borehole infiltration tests. Simulations show that a plot of the inverse of flow rate versus logarithm of time departs from a straight line after about 80% of the steady rate is achieved for various soil and borehole conditions; the steady rate is approximately 0.8 times the rate at the break in slope. In the second method flow rate is plotted versus the inverse of the square root of time and the steady rate is estimated within about 10% by linear extrapolation of early time measurements. USBR field data generally support this linear relationship. Two empirical equations are proposed to compute K(s). The first is applicable for a range of borehole conditions and approximately accounts for capillary effects with a single parameter. The second applies if the height of water in the borehole is I meter, and is based on the time to reach 80% of the steady rate and saturation deficit of the field soil.

The flow field behavior of axial flow turbines is of great importance, especially in modern designs that may operate at a low Reynolds number. At these low Reynolds numbers, the efficiency loss is significantly augmented compared to higher Reynolds number flows. A detailed incompressible numerical study of a single stage axial-flow turbine at a low Reynolds number is investigated with the use of multiple eddy-viscosity turbulence models. The study includes epistemic uncertainty quantification as a form of numerical error estimation. The numerical results show good qualitative and quantitative agreement with experimental data. It was found that the shear stress transport (SST) k - ω turbulence model with rotation/curvature correction and inclusion of transition modeling is most capable at predicting the mean velocity distribution, which is further enhanced when the URANS formulation is employed. However, all the cases indicate a large variation in the prediction of the root-mean-squared of the turbulent velocity fluctuations. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Thesis. 1979. Ph.D.--Massachusetts Institute of Technology. Alfred P. Sloan School of Management. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY. / Bibliography: leaves 141-150. / Ph.D.

In this thesis, we focus on the problem of interactions between solids and fluids. / The main part is the study of the motion of a rigid body immersed in an incompressible fluid. First, for the case of 2D ideal flow, a global weak solution is derived. Second, for the case of viscous flow in 3D, the problem is investigated in the Lp--framework. We get a decomposition of Lp-space associated with the problem. Then We prove that the corresponding semigroup is analytic in L65 R3∩L pR3 (p ≥ 2). Our result yields a local in time existence and uniqueness of strong solutions taking initial data in L65 R3∩L pR3 (p ≥ 3). / The other part is some research about micro-macro models of polymeric fluids. We provide a new proof for the global well-posedness of the coupling systems in 2D. / Wang, Yun. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 112-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Hu Bingbing. / "July 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 69-73). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.