A study of laminar free convection about horizontal plates of finite width with one side heated isothermally and the other insulated is presented in this thesis. This investigation forms part of a continuing program, and its technological origin and significance are discussed in the introduction. The governing partial differential equations comprising the continuity, momentum and energy equations are solved numerically through a finite difference method using a successive-over relaxation technique for a Rayleigh number range from 0.22 to 500, at three values of Prandtl number (0.72, 5.0 and 10.0). The variation of the flow, vorticity and temperature fields with the change of both Grashof and Prandtl numbers is discussed on the basis of the streamline, iso-vorticity and isothermal plots obtained . The effect of Prandtl number alone on the momentum field, energy distribution and heat transfer rate is discussed, by a comparison of the isotherms, streamlines and correlation curves obtained for the three different Prandtl numbers. The theoretical analysis places emphasis on the singular nature of the boundary conditions specified and on the influence of the finite size of the domain of the finite difference scheme. Some results for an upward facing horizontal isothermally heated plate of finite width were also obtained, and were compared to data for the downward facing case. A semi-focussing Schlieren colour system was used order to investigate experimentally the flow behaviour on a horizontal plate with the heated surface facing-downward The experimental results sought were evidence of the non-boundary layer nature of the flow. The evidence of non-boundary layer flow was obtained conclusively. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Flat plate turbulent boundary layers disturbed by periodic moving wakes have been observed in an experimental rig mounted in a low speed wind tunnel. The wakes are produced periodically by cylinders traversing in front of the leading edge of a flat plate on which the boundary layers are measured. This is to simulate the unsteady flow pattern generated by upstream blades on the downstream blade boundary layer in an axial flow turbomachine. Both the time-averaged and ensemble-averaged data are taken from the free stream and boundary layer at different flow conditions. Free stream steady and unsteady wakes are compared and found to be similar to each other. The wake disturbance in the free stream is a function of time and distance from the cylinder. The periodic disturbance in the inner half of the boundary layer lags behind that in the free stream. This phase lag is due to the lower convection velocity near the solid surface. Similar to a steady wake, the velocity defect of an unsteady wake is higher in boundary layer than in free stream. This results in the maximum velocity defect amplitude in the inner half of the boundary layer. Phase lag and amplitude ratio profiles of the boundary layers are plotted and found to be similar to data obtained from axial flow turbomachines. Phase-averaged velocity and turbulence intensity profiles at different phase angles between two successive wakes are shown in a series of transparencies. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The velocity profile shape and boundary layer thickness of an equilibrium boundary layer grown over a long fetch of roughness are closely matched with those of a boundary layer artificially thickened using spires (by adjusting the shape and height of the spires). Other turbulent characteristics of these two wind tunnel simula tions of the atmospheric wind are then compared. At the same time, more information on rough wall boundary layers is obtained to allow for a rational choice of the shape and spacing of roughness elements required to produce a particular simulation of the full scale boundary layer. A technique for calculating the shape of boundary layers in exact equilibrium with the roughness beneath, using a data correlation for the wall stress associated with very rough boundaries and a semi-empirical calculation method, is examined experimentally. Wall shear stress, measured directly from a drag plate, i combined with boundary layer integral properties to show that the shear stress formula is reasonably accurate and that the boundary layer grown over a long fetch of roughness is close to equilibrium after passing over a streamwise distance equal to about 350 times the roughness element height. The boundary layer quickly generated using spires proved to be a fair approximation to that grown over a long fetch of roughness, but did not accurately represent the longitudinal turbulence intensity of the full scale atmospheric wind or the naturally grown boundary layer. The boundary layer produced here by spires showed little change in gross characteristics after travelling about eight spire heights downstream of the spires. A distance of six or seven such heights has been advised by other workers in the past. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Turbulent flows are encountered in nearly every case where fluid motion is involved. Turbulent flow in pipes is of great practical interest, and the problem of flow in the entry region is of special importance since the great majority of applications are in the realm of developing flow.

When entering into the subject of turbulent flow, it is essential to understand that the kind of flow with which we deal belongs to a particular class known as shear flow. These types of flow comprise flow fields in which relative velocities have been induced by shear stresses rather than by the action of pressure forces. In pipe flow, when the fluid enters through the well-rounded bell from a reservoir or from the calm open air, a uniform velocity distribution occurs at the pipe entrance. Immediately down stream from the entrance of the pipe, the flow is structured with a boundary layer near the wall, and is of uniform velocity profile in the central part. Due to the action of wall friction, the boundary layer grows thicker and thicker downstream. As the mass flux is constant throughout the pipe,’ the central stream must accelerate to compensate for this retardation of the flow near the wall. Finally, the boundary layer thickness reaches the value of pipe radius. The free stream, therefore, disappears from the central part of the pipe. Furthermore, Barbin and Jones (1)* pointed out that following the disappearance of the free stream, further changes in the velocity profile and turbulence structure occur before a fully developed condition is reached* The flow in the inlet region of a pipe is, therefore, a transition from a boundary layer type flow at the entrance to a fully developed flow downstream. The change of the free stream velocity in the entry region causes a greater reduction of the static pressure than that in the fully developed region.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1968. / Vita. / Bibliography: leaves 109-117. / by Rory Thompson. / Ph.D.

The research on transition in supersonic and hypersonic boundary layers has been reinvigorated in the last decades because of the increased interest in high-speed flight. The receptivity to environmental disturbances of high-speed boundary layers developing over flat plates or curved surfaces is a very important problem because the transition process is directly impacted by it. The main objective of the research is to determine the effect of small steps on laminar high-speed boundary-layers that are excited by freestream disturbances in the form of vorticity and acoustic waves. Both supesonic and hypersonic regimes are analyzed using a high-order compressible Navier-Stokes numerical algorithm. It is found that both the backward and the forward steps are capable of stabilizing the disturbances that propagate inside the boundary layer. This will potentially delay the formation of three-dimensional disturbances that are precursors to transition into turbulence.

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