No description available.

No description available.

A three-dimensional linear stability analysis is presented for two-dimensional boundary layer flows. The method of multiple scales is used to derive the amplitude and the wave number modulation equations, which take into account the nonparallelism of the basic flow. The zeroth-order eigenvalue problem is numerically integrated to calculate the quasi-parallel growth rates which are then integrated together with the nonparallel growth rates along the characteristics of the wave number modulation equations to evaluate the n-factors. The n-factors are used to determine the most dangerous frequency. The most critical frequency is defined to be the one that yields the n-factor corresponding to transition in the shortest possible distance. This definition is used to evaluate the critical frequency for the Blasius boundary layer, a wedge flow and an axisymmetric boundary layer. The effect of three-dimensional disturbances is evaluated and found to be less critical than two-dimensional disturbances regardless of the pressure gradient, the temperature distribution of the wall and the wall geometry. The effect of heating the boundary layer is evaluated for the Blasius, Falkner-Skan and axisymmetric boundary layers. In all the cases considered, heating substantially reduces the n-factors. Results are compared with those of Strazisar & Reshotko (1978) and Nayfeh & El-Hady (1980). / Ph. D.

As the aviation industry expands, consuming oil reserves, generating carbon dioxide gas and adding to environmental concerns, there is an increasing need for drag reduction technology. The ability to maintain a laminar flow promises significant reductions in drag, with economic and environmental benefits. Whilst development of flow control technology has gained interest, few studies investigate the impacts that uncertainty, in flow properties, can have on flow stability. Inclusion of uncertainty, inherent in all physical systems, facilitates a more realistic analysis, and is therefore central to this research. To this end, we study the stability of stochastic shear flows, and adopt a framework based upon the Wiener Chaos expansion for efficient numerical computations. We explore the stability of stochastic Poiseuille, Couette and Blasius boundary layer type base flows, presenting stochastic results for both the modal and non modal problem, contrasting with the deterministic case and identifying the responsible flow characteristics. From a numerical perspective we show that the Wiener Chaos expansion offers a highly efficient framework for the study of relatively low dimensional stochastic flow problems, whilst Monte Carlo methods remain superior in higher dimensions. Further, we demonstrate that a Gaussian auto-covariance provides a suitable model for the stochasticity present in typical wind tunnel tests, at least in the case of a Blasius boundary layer. From a physical perspective we demonstrate that it is neither the number of inflection points in a defect, nor the input variance attributed to a defect, that influences the variance in stability characteristics for Poiseuille flow, but the shape/symmetry of the defect. Conversely, we show the symmetry of defects to be less important in the case of the Blasius boundary layer, where we find that defects which increase curvature in the vicinity of the critical point generally reduce stability. In addition, we show that defects which enhance gradients in the outer regions of a boundary layer can excite centre modes with the potential to significantly impact neutral curves. Such effects can lead to the development of an additional lobe at lower wave-numbers, can be related to jet flows, and can significantly reduce the critical Reynolds number.

No description available.

No description available.

A good understanding of flow in a number of hydraulic structures, such as energy dissipators, among others, is needed to effectively control upstream and downstream flow conditions, for instance, high water depth and velocity to ensure, scouring, flow stability and control scouring, which is thus crucial to ensuring safe acceptable operation. Although some previous research exists on minimizing scouring and flow fluctuations after hydraulic structures, none of this research can fully resolve all issues of concern. In this research, three types of structures were studied, as follows: a) a vertical gate; b) a vertical gate with an expansion; and c) a vertical gate with a contraction. A Stability Concept was introduced and defined to characterize the conditions downstream of gated structures. When established criteria for stability are met, erosion is prevented. This research then investigated and evaluated two methods to classify the flow downstream of a gated vii structure to easily determine stability. The two classification methods are: the Flow Stability Factor and the Flow Stability Number. The Flow Stability Factor, which is developed based on the Fuzzy Concept, is defined in the range of 0 to 1; the maximum value is one and indicates that the flow is completely stable; and the minimum value is zero and indicates that the flow is completely unstable. The Flow Stability Number is defined as the ratio of total energy at two channel sections with a maximum value of one, and it allows flow conditions to be classified for various hydraulic structures; the number is dimensionless and quantitatively defines the flow stability downstream of a hydraulic structure under critical and subcritical flow conditions herein studied, also allowing for an estimate of the downstream stable condition for operation of a hydraulic structure. This research also implemented an Artificial Neural Network to determine the optimal gate opening that ensures a downstream stable condition. A post-processing method (regression-based) was also introduced to reduce the differences in the amount of the gate openings between experimental results and artificial intelligence estimates. The results indicate that the differences were reduced approximately 2% when the post-processing method was implemented on the Artificial Neural Network estimates. This method provides reasonable results when few data values are available and the Artificial Neural Network cannot be well trained. Experiments were conducted in two laboratories, for two different scales, to investigate any possible scale effect. Results indicate, for instance, that the case of the vertical gate with an expansion performs better in producing a downstream stable condition than the other two studied structures. Moreover, it was found that smaller changes caused by expansions and contractions on the channel width show better performance in ensuring a viii downstream stable condition in the cases of a vertical gate with an expansion and a vertical gate with a contraction over a wide range of structures. Moreover, upstream flow depths in the gate with expansion are higher than in the cases of a gate and a gate with a contraction, suggesting that it may be more appropriate for agriculture applications. This research also applied Game Theory and the Nash Equilibrium Concept in selecting the best choice among various structures, under different flow expectations. In addition, the accuracy of the Flow Stability Factor and the Flow Stability number were compared. This showed that the Flow Stability Factor and the Flow Stability number had good agreement in stable conditions. Hence, the Flow Stability Factor can then be used instead of the Flow Stability number to define stable conditions, as a visual method that does not need any measurement. Importantly, a Fuzzy-based Efficiency Index, a method based on an image processing technique, was also innovatively tested to estimate the hydraulic efficiency of the hydraulic structures. The method was tested and validated using laboratory data with an average agreement of 96.45%, and then demonstrated for prototype case situations in Florida and California. These cases yielded overall efficiencies of 96% and 97.87% in Spillway Park, FL and Oroville Dam, CA, respectively. Statistical assessment was also done on the image, determining an Efficiency Index. Specifically, an image histogram was extracted from the grayscale image, then the mean and standard deviation of the histogram was used to calculate the Index. The method uses the darkness and whiteness of the image to estimate the Efficiency Index; it is easy to use, quick, low cost, and trustworthy.

One approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations. / text

Turbulent swirling flows are important in many applications including gas turbines, furnaces and cyclone dust separators among others. Although the mean flow fields have been relatively well studied, a complete understanding of the flow field including its dynamics has not been achieved. The work contained in this dissertation attempts to shed further light on the behavior of turbulent swirling flows, especially focused on the dynamic behavior of a turbulent swirling flow encountering a sudden expansion. Experiments were performed in a new isothermal turbulent swirling flow test facility. Two geometrical nozzle configurations were studied. The \cb\ nozzle configuration exhibits a cylindrical \cb\ in the center of the nozzle. The free vortex nozzle configuration is obtained when the cylindrical \cb\ is removed. Detailed laser velocimeter measurements were performed to map out the flow field near the sudden expansion of the 2.9" (ID) nozzle leading to the 7.4" (ID) downstream section. In addition to presenting detailed flow profiles for both nozzle and downstream flow fields, representative frequency spectra of the flow dynamics are presented. Along with the flow time histories and histograms, the wide variety of dynamic behavior was thus described in great detail. The dynamics observed in the experiment can be classified into three main categories: coherent and large scale motion, intermittent motion and coherent periodic motion. Free vortex geometry flows, in the parameter space of the experiments (Swirl number = 0 - 0.21), exhibited mostly coherent and large scale motion. The spectra in these cases were broadband with very light concentration of spectral energy observed in some specific cases. Center--body geometry flows exhibited all three categories of flows as swirl strength was increased from zero. Flows with little or no swirl exhibited broad--band spectra similar to those for the free vortex geometry. Intermediate swirl levels resulted in a large amount of low frequency energy which, with the aid of the time histories, was identified as a large scale intermittence associated with radial movement of the annular jet as it enters the sudden expansion. Large swirl levels resulted in high magnitude coherent oscillations concentrated largely just downstream of the sudden expansion. Linear stability analysis was used to help in the interpretation of the observed dynamics. Although, as implemented here (using the parallel flow assumption), the analysis was not successful in quantitatively matching the experimentally observed dynamics, significant insight into the physical mechanisms of the observed dynamics was obtained from the analysis. Specifically, the coherent oscillations observed for larger swirl levels were able to be described in terms of the interaction between the inner and outer shear layers of the flow field. / Ph. D.

The flow in a layer of volatile fluid driven by a horizontal temperature gradient is a fundamental transport model for numerous evaporative passive cooling applications. When a thin film of a volatile liquid is subject to a horizontal temperature gradient, changes in the surface tension at the free surface lead to Marangoni stresses that drive the flow. In a thicker liquid layer, the flow is also affected by buoyancy. This thesis describes experimental studies of convection driven by a combined action of Marangoni stresses and buoyancy in simple and binary volatile liquid layers confined in a sealed rectangular cavity heated at one end and cooled at the other. Experiments with varying concentrations of noncondensables (i.e., air) ca were performed to investigate their effect on the phase change and heat and mass transport. In the simple liquid, thermocapillary stresses drive the liquid near the free surface away from the heated end. Varying ca is shown to strongly affect the stability of this buoyancy-thermocapillary flow for Marangoni numbers Ma = 290 - 3600 and dynamic Bond numbers BoD = 0.56 - 0.82: removing air suppresses transition to multicellular and unsteady flow. The results are compared with numerical simulations and linear stability analysis. In the binary liquid considered here, a methanol-water (MeOH-H2O) mixture, solutocapillary stresses drive the flow near the free surface towards the heated end. Four distinct flow regimes are identified for this complex flow driven by thermocapillarity, solutocapillarity, and buoyancy, and are summarized in a flow regime map as a function of ca and the liquid composition (MeOH concentration). At low ca, solutocapillary effects are strong enough to drive the liquid near the free surface towards the heated end over the entire liquid layer, suggesting that binary-fluid coolants could significantly reduce film dryout.