Jim Brown

Transient, turbulent, smooth pipe friction

Two of the most promising analytical models of unsteady friction in turbulent pipe flows are based on sharply contrasting hypotheses. One uses the history of the flow; the other uses instantaneous conditions. The purposes of this paper are to present an analysis using the former approach and to indicate how to determine which of the two methods is appropriate. A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that ...

An overview of wave propagation in tunnels

The propagation of pressure waves along railway tunnels is reviewed with special emphasis on isolated compressive waves such as those generated during the early stages of train entry to a tunnel. Particular attention is paid to the evolution of pressure gradients in the leading regions of the waves — because the gradients just before the tunnel exit determine the strengths of micro-pressure waves that are the focus of attention in TRANSAERO Work Package 4.1. The physical phenomena considered herein are (i) inertia, (ii) skin friction, both quasi-steady and unsteady, and (iii) the compliance of air trapped between aggregate elements in ballast track tunnels. It is shown that the first of these tends to cause steepening of wavefronts and that the others tend to cause flattening. Skin friction is found to have a strong influence on pressure amplitudes as well as on pressure gradients.

Influence of radial seepage on temperature distribution around a cylindrical cavity in a porous medium

Abstract Temperature distributions are obtained around a long cylindrical cavity in a permeable medium in the presence of steady radial seepage. Constant temperature and constant heat flux conditions are considered at the cavity surface. Transient solutions are derived as quadratures, yielding closed form solutions for particular seepage rates. Steady states are derived as limiting cases. Small and large time approximations are derived for the cavity temperature and flux. With inward seepage, the thermal radius of influence is restricted and steady state attained more rapidly. For outward seepage, the radius of influence becomes infinite and the steady temperatures uniform.

Evaluation of Unsteady Wall Shear Stress by Zielke’s Method

The method used in the classical paper by Zielke to estimate the unsteady component of shear stress in unsteady pipe flows is revisited. It is found that the method is undesirably sensitive to the size of the integration time step. The sensitivity is shown to be caused dominantly by the first term in the integration when inadequate allowance is made for the infinite value of the weighting function. A simple method of avoiding the error without requiring the use of small grid sizes is presented.

Influence of time-dependent viscosity on wall shear stresses in unsteady pipe flows

The behaviour of wall shear stresses in unsteady flows in pipes is investigated for flows in which the effective kinematic viscosity varies in time. Such variations can arise through the effects of temperature, pressure, shear or chemical change. The theoretical approach is founded on an analytical method of solution using finite Hankel transforms. It is well suited to studying trends arising in flows with viscosity that is uniform spatially, but varies in time. The method is applied to a range of flows driven by pulsed pressure gradients. The overall wall shear stress is found to follow trends similar to those followed by the mean velocity, but the unsteady component of the wall shear stress is much more strongly influenced by the acceleration. The kinematic behaviour tends to be influenced more strongly by the instantaneous viscosity (or, strictly, by its local temporal average) than by the local rate of change of viscosity.

Reduction of Micro-Pressure Wave by Active Control of Propagating Compression Wave in High Speed Train Tunnel

For the improvement of the sound environment around a portal of a high speed train tunnel, model experiments for the reduction of MPW (Micro-Pressure Wave) have been studied. In order to reduce the level of MPW, a control wave, that is a positive pressure, is generated at a side-branch in a model tunnel and is superposed on the incident wave front of a compression wave propagating through the tunnel. The method of active reduction of MPW and experimental equipment are shown. Characteristics of the wave forms of the compression wave and the control wave with suitably designed servo actuators were examined. The experimental results of the reduced level of MPW agreed well with numerical calculation results.

Applicability of Frozen-Viscosity Models of Unsteady Wall Shear Stress

AbstractThe validity of assumed frozen-viscosity conditions underpinning an important class of theoretical models of unsteady wall shear stress in transient flows in pipes and channels is assessed using detailed computational fluid dynamics (CFD) simulations. The need for approximate one-dimensional (1D){x,t} models of the wall stress is unavoidable in analyses of transient flows in extensive pipe networks because it would be economically impracticable to use higher order methods of analysis. However, the bases of the various models have never been established rigorously. It is shown herein that a commonly used approach developed by the first authors is flawed in the case of smooth-wall flows although it is more plausible for rough-wall flows. The assessment process is undertaken for a particular, but important, unsteady flow case, namely, a uniform acceleration from an initially steady turbulent flow. First, detailed predictions from a validated CFD method are used to derive baseline solutions with which...

Creeping motion of a cylinder through incompressible fluid bounded by a coaxial closed cylinder

Abstract The finite element method based on the Galerkin process is used to study the translation of a cylinder through fluid occupying the space between it and a co-axial cylindrical container under incompressible creeping flow conditions. The resistance force on the inner cylinder is calculated for the case of cylinders with diameters equal to their lengths, at the instant when their centroids are coincident. These resistance forces are compared with those for concentric spheres having equal radii or surface areas or volumes to the cylinders. The resistance force is also determined for the more general case when the inner cylinder approaches the end of the container for a range of aspect ratios (both cylinders having the same aspect ratio). The ratio of the pressure drag to the wall friction is also studied.