Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: near field; starting flow; buoyant flow; unsteady flow. Includes bibliographical references (p. 81-82).

The impact of buoyancy on the development of starting flows in the near field was experimentally investigated using the Digital Particle Image Velocimetry and Planar Laser Induced Flourescence techniques. The experiments were conducted by releasing cylindri-cal columns of fluid into a glass water tank. Two diameters (0.95 and 1.9 cm) and four aspect ratios, ranging from 2 to 8, were examined. The fluid was released by bursting the thin latex membrane that held it in the tube. The buoyant fluid had a density difference of 4.7%. The flow was imaged at 60 Hz up to 7 diameters downstream. For the aspect ratio of 2, the flow developed into a single buoyant vortex ring (BVR), and was compared to a purely momentum driven vortex ring (MVR) generated with the same setup. For the aspect ratios of 4, 6, and 8, the flow was similar to a starting plume, with a vortical cap, followed by a columnar tail. The BVR's diameter grew linearly in space, with a full spreading angle of 18 degrees, while the MVR's diameter remained constant. The BVR started out as an axis touching ring, and transitioned to non-axis touching, opposite of the behavior of the MVR. The total circulation for the BVR was more than twice the amount predicted by the slug flow model, and the impulse grew linearly in time. The impulse of the MVR decayed slightly after the intial growth. The flows began to transition to thermal behavior at down-stream distance proportional to the cube root of the initial fluid volume. For all aspect ratios the impulse grew linearly in time. The growth rate was roportional to the initial buoyant force. The circulation generated by the addition of buoyancy was proportional to the square root of the initial buoyant force. Also the addition of buoyancy suppressed the separation of a starting vortex.

Buoyant flows are characterized with unsteady large-scale structures and thus time-dependent large eddy simulation (LES) is generally favored. In this dissertation, to further explore LES for buoyant flow, an LES code based on a collocated grid system is first developed. A multigrid solver using a control strategy is developed for the pressure Poisson equations. The control strategy significantly accelerated the convergence rate. A temperature solver using a fourth-order Runge-Kutta approach is also developed. The LES code is extensively tested before it is applied. Although the collocated grid system will introduce conservation errors, in tests of a steady lid-driven cavity flow and transient start-up flow, the effect of the non-conservation of the collocated grid system was not significant. <p>In LES, the effect of SGS scales is represented by SGS models. A novel dynamic nonlinear model (DNM) for SGS stress is tested using isothermal channel flow at Reynolds number 395. The kinetic energy dissipation and geometrical characteristics of the resolved scale and SGS scale with respect to the DNM are investigated. In general, the DNM is reliable and has relatively realistic geometrical properties in comparison with the conventional dynamic model in the present study. In contrast to a pure advecting velocity field, a scalar (temperature) field displays very different characteristics. The modelling of SGS heat flux has not been as extensively studied as that of SGS stress partly due to the complexity of the scalar transport. In this dissertation, LES for a turbulent combined forced and natural convection is studied. The DNM model and a nonlinear dynamic tensor diffusivity model (DTDM-HF) are applied for the SGS stress and heat flux, respectively. The combined effect of the nonlinear models is compared to that of linear models. Notable differences between the nonlinear and linear SGS models are observed at the subgrid-scale level. At the resolved scale, the difference is smaller but relatively more distinguishable in terms of quantities related to the temperature field. <p>Finally, the geometrical properties of the resolved velocity and temperature fields of the thermal flow are investigated based on the LES prediction. Some universal geometrical patterns have been reproduced, e.g. the positively skewed resolved enstrophy generation and the alignment between the vorticity and vortex stretching vectors. The present research demonstrates that LES is an effective tool for the study of the geometrical properties of a turbulent flow at the resolved-scales. The wall imposed anisotropy on the flow structures and orientation of the SGS heat flux vector are also specifically examined. In contrast to the dynamic eddy diffusivity model, the DTDM-HF successfully predicts the near-wall physics and demonstrates a non-alignment pattern between the SGS heat flux and temperature gradient vector.

Buoyant flows are characterized with unsteady large-scale structures and thus time-dependent large eddy simulation (LES) is generally favored. In this dissertation, to further explore LES for buoyant flow, an LES code based on a collocated grid system is first developed. A multigrid solver using a control strategy is developed for the pressure Poisson equations. The control strategy significantly accelerated the convergence rate. A temperature solver using a fourth-order Runge-Kutta approach is also developed. The LES code is extensively tested before it is applied. Although the collocated grid system will introduce conservation errors, in tests of a steady lid-driven cavity flow and transient start-up flow, the effect of the non-conservation of the collocated grid system was not significant. <p>In LES, the effect of SGS scales is represented by SGS models. A novel dynamic nonlinear model (DNM) for SGS stress is tested using isothermal channel flow at Reynolds number 395. The kinetic energy dissipation and geometrical characteristics of the resolved scale and SGS scale with respect to the DNM are investigated. In general, the DNM is reliable and has relatively realistic geometrical properties in comparison with the conventional dynamic model in the present study. In contrast to a pure advecting velocity field, a scalar (temperature) field displays very different characteristics. The modelling of SGS heat flux has not been as extensively studied as that of SGS stress partly due to the complexity of the scalar transport. In this dissertation, LES for a turbulent combined forced and natural convection is studied. The DNM model and a nonlinear dynamic tensor diffusivity model (DTDM-HF) are applied for the SGS stress and heat flux, respectively. The combined effect of the nonlinear models is compared to that of linear models. Notable differences between the nonlinear and linear SGS models are observed at the subgrid-scale level. At the resolved scale, the difference is smaller but relatively more distinguishable in terms of quantities related to the temperature field. <p>Finally, the geometrical properties of the resolved velocity and temperature fields of the thermal flow are investigated based on the LES prediction. Some universal geometrical patterns have been reproduced, e.g. the positively skewed resolved enstrophy generation and the alignment between the vorticity and vortex stretching vectors. The present research demonstrates that LES is an effective tool for the study of the geometrical properties of a turbulent flow at the resolved-scales. The wall imposed anisotropy on the flow structures and orientation of the SGS heat flux vector are also specifically examined. In contrast to the dynamic eddy diffusivity model, the DTDM-HF successfully predicts the near-wall physics and demonstrates a non-alignment pattern between the SGS heat flux and temperature gradient vector.

Buoyant flows are present in nature and also in many engineering applications,from domestic heating to the cooling of nuclear power plants. This experimental study focuses on the effects of angle of inclination on buoyancy-driven flows inside tall, rectangular, differentially-heated cavities. The objective is to produce detailed local flow and thermal data, which will advance our understanding of the flow physics and also provide CFD validation data. It considers a 2.18m × 0.52m × 0.0762m cavity, resulting in an aspect ratio of 28.6, with its two opposing long walls maintained at constant but different temperatures, while all the remaining walls are thermally insulated. The Rayleigh number, based on the temperature difference and spacing of the long sides, is 0.86 x 106 for most cases and the working fluid is air (Prandtl number0.71). Experimental data for the flow and the thermal fields, using laser Doppler anemometry and Chromel-Alumel thermocouple traverses respectively, are presented for the cavity inclined at 60° and 15° to the horizontal, for both stable (the hot surface being the upper surface) and unstable (the hot surface the lower one) orientations. The 15° stable case is investigated at a higher Rayleigh number of 1.54 x106 and some additional data for the 15° unstable case are also presented at this high value of Rayleigh number. Comparisons with the measurements of Betts and Bokhari [1], for the same cavity at the vertical position, are also included. For moderate angles of inclination, the flow is two-dimensional and the effects of inclination are primarily confined to the fluctuating fields. For large angles of inclination, the flow becomes three-dimensional. In the unstable 15° angle of inclination case, a set of four longitudinal vortices are formed over the entire length of the cavity, with four counter-rotating re-circulation cells within the cross-section parallel to the thermally active walls. The enhanced mixing at 15° unstable inclination leads to uniform temperature in the cavity core and thus only minor deviations from two dimensionality in the thermal field. A modest rise in Rayleigh number, in the 15° unstable case, does not affect the mean motion, but causes an increase in the normalised turbulence intensities, which in turn leads to a more uniform temperature within the cavity core and a practically two-dimensional thermal field. The stable 15° angle of inclination case, surprisingly, leads to the formation of two longitudinal vortices and two re-circulation cells. The lack of mixing, in the 15° stable case, leads to more noticeable three-dimensional thermal field. The thesis includes a full set of flow and thermal predictions and also spectral analysis of thermal fluctuations, which show a significant effect of the angle of inclination on both the power density level and the ranges of frequencies involved.

Nous présentons dans cette étude le développement de la convection à partir de différentes perturbations de l'état conductif d'une couche fluide confinée dans une cavité cylindrique, chauffée par le bas et avec une surface supérieure libre. La discrétisation spatiale du domaine repose sur la méthode des éléments spectraux et les itérations temporelles sont assurées par une méthode splitting.Au déclenchement de la convection, les structures convectives correspondent à des modes de Fourier, et les seuils critiques dépendent du rapport de forme de la cavité, et des nombres de Biotet de Marangoni qui caractérisent la surface libre. Les transitions d'écoulements au-delà du seuil primaire sont caractérisées quantitativement en fonction du nombre de Rayleigh pour différentes valeurs du nombre de Biot et Ma = 0. Les résultats présentés sont obtenus en résolvant l'ensemble des équations non-linéaires de conservation à travers une méthode de continuation. Lorsque la convection se déclenche sous la forme d'un mode axisymétrique m = 0, l'évolution non-linéaire montre la coexistence de différentes structures convectives, des structures axisymétriques avec écoulement montant ou descendant au centre de la cavité et des structures correspondant à des combinaisons de modes qui apparaissent sur des branches secondaires sous-critiques.L'action d'un champ magnétique constant est ensuite étudiée pour des fluides conducteurs dans une même configuration comprenant une surface supérieure libre. Nous montrons l'effet stabilisateur du champ magnétique sur les seuils primaires ainsi que son action sélective sur les différents modes de convection. Nous analysons l'évolution des structures convectives au delà de ces seuils et montrons comment le champ magnétique modifie les transitions entre ces structures.En soumettant le bain fondu à un champ magnétique tournant, le mouvement de rotation du fluide se superpose aux mouvements de convection thermique et on observe une diminution des fluctuations de température et un retard du déclenchement de l'instabilité de Rayleigh-Bénard(lorsque les deux parois haut/bas du bain sont rigides). La rotation influe sur ce déclenchement qui de stationnaire devient oscillatoire, à l'exception du mode m = 0 de Fourier, pour qui la transition reste stationnaire jusqu'à une certaine valeur critique du nombre de Taylor magnétique.La dynamique de l'écoulement axisymétrique de part et d'autre de cette valeur critique sera étudiée en détail. / The growth of thermal convection out of different perturbations of the conductive base state is investigated using a spectral element time-stepping code. The fluid is subject to a vertical heat transfer in a cylindrical cavity with an upper free surface corresponding to the so-called Rayleigh-Bénard-Marangoni situation and the heat exchange through the free surface is evaluated via the Biot number. The results of the stability diagrams show that the evolution of the primary thresholds are largely influenced by the Biot number, the Marangoni number, and the aspect ratio of the cavity. Flow transitions are elucidated in quantitative detail as a function of the Rayleigh number for different Biot numbers in the tension free limit Ma = 0. The results shown are obtained by solving the full nonlinear field equations numerically among a continuation method. When an axisymmetric m = 0 Fourier mode is obtained at onset, the non-linear evolution shows the coexistence of different convective structures, the axisymmetric structures with up-ow or down-ow at the center and mixed-mode structures which appear on secondary subcritical branches. The action of a constant magnetic field is then considered for melts in the same type of configuration with an upper free surface. We show the global stabilizing effect of the magnetic field on the primary bifurcation thresholds and the selective effect on the different instability modes. We also analyze the evolution of the convective structures above the thresholds and show how the magnetic field modifies the transitions between these structures. When applying a magnetic body forcing in the azimuthal direction (RMF), one can damp the unavoidable thermal fluctuations inside the melt and delay the transition to the Rayleigh-Bénard instability (for rigid-rigid circular plates at top and bottom). The rotation effect also changes the transitions from steady to oscillatory, except for the m = 0 Fourier mode where the transitionis first steady until a critical Taylor number and then becomes oscillatory. The dynamics of the transitions to the axisymmetric flow, below and above this value of critical magnetic Taylor number, is particularly interesting and will be described.