Table of contents

Effects of flexible walls or flow disturbance are studied experimentally using thin-walled rubber tubes of different lengths of conveying steady inflow of water. Experiments are performed for the tubes surrounded by air, water and glycerin. Fluctuations of the flow velocity and displacements of the outer tube wall caused by the fluctuating flow around the laminar-turbulent transition are measured with a hot-film anemometer and a gap sensor. Results show that when tube lengths are varied in different surrounding media, the critical Reynolds number for rubber tubes is higher than that for rigid tubes in each case and suggest that the wall flexibility suppress the occurrence of turbulence. Spectral analyses of fluctuated velocity and vibration of tube wall reveal that the two frequency ranges are negatively correlated. Thus it can be inferred that will vibration plays an important role in governing the occurrence and growth of disturbance flow.

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step towards application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable has been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Numerical studies are made of flows of a gas in a rapidly rotating cylindrical container. The reference Ekman number is small, and the peripheral Mach number is O(1). The internal flows are generated by applying a small temperature gradient on the boundaries of the cylinder. Analyses are made of comprehensive and systematically organized numerical results, which have been acquired by solving the complete, compressible Navier-Stokes equations. The results are examined to recall the effects of the Ekman number and of the cylinder aspect ratio. The existence of the short-bowl flow regime is verified by cross-checking the numerical data with the previous analytical predictions. The characteristic details of this flow regime are described. The diagnostic studies by using the numerical results exhibit the predominant dynamic balance in the flow field. The changeover in the character of the flow is scrutinized by varying the aspect ratio λ. For large values of λ, the long-bowl approach solution is shown to be consistent with the numerical results. The demarcation between these two regimes is assessed by reviewing the numerical data.

A mathematical model which describes three-dimensional fully developed flow in mildly curved open channel is developed. The side-wall boundary layers are included in the analysis, and the normal component of the secondary current is constrained to be zero at the side walls. It is found that the advective transport of fluid momentum due to the secondary current induces accumulation of primary-flow (streamwise) fluid momentum near the outer bank. The analysis makes it possible to analyze the curvature-induced excess of shear stress at the outer bank. The model is well supported by available laboratory data.

The buoyancy induced convection arising from a point heat source in a fluid saturated Darcy porous medium bounded by an adiabatic conical surface, of apex angle 2θ_ω, has been studied. The point heat source is located at the apex and the axis of the conical surface coincides with the direction of bouyant force vector. The self-similar equations are obtained for 0 < θ_ω < π and Rayleigh number Ra from zero to infinity. The numerical solutions of self-similar equations have been obtained for θ_ω (free plume), 3π/4, π/2 (plume bounded by horizontal surface), and π/4. It is shown that for a given Ra, the centre line velocity and temperature increases as π_ω (the bounding space) decreases. A perturbation solution for Ra → 0 also been studied to present closed form solution.

The governing equations describing the propagation of a moderate planar normal shock wave into a homogeneous dust-gas suspension were formulated and solved numerically using the flux-corrected transport (FCT) technique. The numerically predicted attenuation of the shock wave was compared with the experimental results of Sommerfeld. Good agreement was obtained. It was found that the attenuation of moderate normal planar shock waves propagating into dusty gases with relatively high loading ratios of solid particles can be described by a general attenuation law.

The statistically stable posture of a triangular or a square cylinder is experimentally studied when it is free to rotate about its central axis fixed perpendicular to a uniform flow. Both cylinders come to rest in a stable posture with a side perpendicular to the uniform flow.