Table of contents

Unsteady flow fields past a projectile either in parabolic motion or in accelerated motion are investigated numerically, with special attention to shock wave focusing phenomena induced by the motions. The two-dimensional Euler equations are solved by a moving-cell, MUSCL TVD finite-volume method with Steger-Warming flux-vector splitting. The pattern of shock wave focusing induced by the projectile is found to be similar to that of shock waves reflected from a concave wall observed in a laboratory experiment using a shock tube. Effects of projectile shapes and trajectories on focusing are also examined.

Fluid flow in a rotating cylindrical container of radius R_w and height H with a co-axially rotating disk of radius R_d at the fluid surface is numerically investigated. The container and the disk rotate with angular velocities Ω_w and Ω_d, respectively. We solve the axisymmetric Navier-Stokes equations using a finite-volume method. The effects of the relative directions and magnitudes of the disk and container rotations are studied. The calculations are carried out with various ratios of Ω_w and Ω_d for H/R_w = 2 and R_d/R_w = 0.7. Streamlines and velocity vectors in the meridional plane and azimuthal velocities are obtained. The flow fields in the meridional plane are discussed with relation to azimuthal velocities in the interior of the container. The numerical results are also compared with experimental data.

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[ = ({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh ( = (x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g ( = N_o²/(∂u∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.

The problem of the capillary-gravity waves which may arise at an interface between two stratified fluids of different densities is investigated. Particular attention is paid to the case when two different wave modes move at the same speed and to the wave train produced by the ensuing interaction. In contrast to most previous studies, the wave steepness and the wave bandwidth are not taken to be of the same order of magnitude, but the latter is of one order smaller. This leads to a system of nonlinear evolution equations which can be used to predict the subsequent progression of the wave field. These equations may be compared with the more usual nonlinear Schrödinger set which are valid under the equal bandwidth assumption and also a recently derived set which describe broader bandwidth waves. A large class of solutions to the equations is found and the corresponding wave profiles are presented.

Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. for example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity ω and the eigenvectors of the rate of strain tensor λ_i (especially — but not only — between ω and λ₂) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field — even with the weakest measurable enstrophy — is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector W_i ≡ ω_jS_ij. It is shown that the quasi-two-dimensional regions corresponding to large cos(ω, λ₂) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field.

Theoretical study of double-layered porous Rayleigh-step bearings with second-order fluid as lubricant is presented. An approximate method for the solutions of the governing fluid film equations for a porous region is proposed. The expressions for the pressure distribution, load capacity and frictional coefficient are obtained in compact form. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the double porous layer yields an increase in the load capacity and ensures decrease in frictional force at the porous lining as compared with the conventional porous Rayleigh-step bearings. The maximum dimensionless load-carrying capacity is found to occur at a slightly larger step ratio as compared with the conventional porous Rayleigh-step bearings.