Table of contents

The probability density function (pdf) of a streamwise velocity component is studied in zero-pressure gradient boundary layers. From analyzing the data up to R_θ≃13,000, it is found that pdfs have self-similar profiles ranging from y⁺≃180 to 0.049Δ⁺, where Δ is Rotta–Clauser boundary layer thickness. Pdf profiles asymptote to the universal shape very close to the Gaussian, but are positively skewed at the core region, indicating smaller values in the tail parts. Based on this experimental fact, the mean velocity profile is reconsidered from the standpoint of pdf equation. The log-law profile is expected as the mean velocity distribution. The Kármán constant is evaluated to be 0.38, and the log-region starts at y_s⁺ = 180 and ends at y_r⁺ = 0.021Δ⁺+96.5 for R_θ > 4000. The end point locates in 0.15δ⁺ ≤ y_r⁺ ≤ 0.2δ⁺. The relation to the new scaling law derived from Lie-group theory is also discussed.

Combined analytical and experimental investigation of sinusoidal mass flow-controlled, pulsating, laminar and fully developed pipe flow was carried out. The experimental investigation employed a mass flow control unit built at LSTM-Erlangen for the present investigation. For the analytical investigation, the equations describing such flows were normalized to allow for a general solution, depending only on the normalized amplitude m_A^* of the mass flow pulsation and the normalized frequency F. The analytical and experimental results are presented in this normalized way and it is shown that good agreement between the results of the authors is obtained. A diagram is presented for the condition of flow reversal in terms of the dimensionless frequency F and the mass flow rate amplitude m_A^*.

An analysis is made of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a surface which is stretched with a velocity proportional to the distance from a fixed point. It is found that for very small shear in the free stream, the flow has a boundary layer structure and the thickness of the boundary layer decreases with increase in straining motion near the stagnation region. It is also observed that the flow has an inverted boundary layer structure when the stretching velocity of the surface exceeds the stagnation velocity of the free stream. In this case, the surface shear stress decreases with increase in free stream stagnation velocity.

A theory of an unsteady incompressible inviscid flow past an accelerated lamina, moving across the fluid, is extended to address a bent (rather than flat) lamina and finite size (rather than point) vortices in its wake. It is shown that when the velocity of the lamina varies with time t as t^m, the distance of the vortices from the lamina and the size of their cores grow, initially, as t^(2m+2)/3 and t^(2m+2)/3exp(-Ct^-(8m+2)/3), respectively, where C is a strictly positive constant. The growth rate of the core dimensions with time seems to provide a plausible energy argument for the experimentally observed wake asymmetry that culminates the initial symmetric vortex arrangement.

The flow of an incompressible, viscous, electrically conducting fluid past a sphere in an aligned magnetic field is investigated using the finite difference method for Re 100 and 200 and interaction parameter N in the range 0 ≤ N ≤ 10 (or 0 ≤ M ≤ 100), where M is the Hartmann number defined by M = (2N Re)^1/2. The length of the recirculation bubble in the flow reduces monotonically with increasing magnetic field up to N = 1 and starts growing when N ≥ 2. A non-monotonic behavior of the boundary layer separation angle is found when N < 1, where the backward movement of the separation angle is observed. For higher values of N, a linear dependence with √N of the pressure drag coefficient, the total drag coefficient and the rear pressure is found. With increasing values of N, a general increase in upstream base pressure and a decrease in downstream base pressure is noted. The features found in this work are in agreement with those of experimental findings.