Alan Vardy

A characteristics model of transient friction in pipes

A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielkes (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.

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 ...

Transient turbulent friction in fully rough pipe flows

A weighting-function model of unsteady skin friction in fully rough-walled flows in one-dimensional ducts is derived using an idealized radial viscosity distribution. The model complements previous work by the authors for smooth-walled flows. It is assumed that, for sufficiently short-lived transients, the viscosity distribution in the cross-section may be regarded as constant and equal to that in a pre-existing steady flow. The eddy viscosity in an outer annulus is assumed to vary linearly from a minimum at the wall to a maximum at the edge of a central core of uniform viscosity. The resulting weighting-function model for short-lived transients is used to develop a simple formula predicting values of unsteady skin friction coefficients suitable for an instantaneous-acceleration model of unsteady skin friction in fully rough pipe flows.

A weighting function model of transient turbulent pipe friction

A weighting function model of transient turbulent pipe friction at moderate Reynolds Numbers is developed in a similar manner to Zielkes equivalent expression for laminar flow (1968). It is shown that a family of weighting function curves exists and that Zielkes curve is an upper bound asymptote that is valid for low Reynolds numbers, not only for laminar flow. The new weighting function model is based on an approximate representation of a turbulent pipe flow as a laminar annulus surrounding a uniform core. The acceptability of this representation is demonstrated by comparing wall shear-stress histories predicted using this model with equivalent histories predicted using a five-region eddy viscosity model. It is shown that the new weighting function curves can be represented with sufficient accuracy by exponential relationships similar to those proposed by Trikha for transient laminar flows (1975).

Wall friction and turbulence dynamics in decelerating pipe flows

Wall shear stresses in decelerating pipe flows are studied using a well-established CFD code developed specifically for modelling unsteady turbulent flows. The suitability of the turbulence model used was demonstrated previously and re-confirmed by comparison with recent experimental data. The response of the wall shear stress to the deceleration is shown to exhibit features in common with responses in accelerating flows, but also indicates strong differences. Turbulence delays are shown to be important, causing, in effect, a frozen-turbulence response at early times. Also, flow reversal and increasing turbulence timescales prevent the development of asymptotic conditions at larger times. It is demonstrated that, at intermediate times, the instantaneous wall shear stress may be either larger or smaller than the corresponding quasi-steady value, thereby explaining features of existing experimental data that were previously regarded as conflicting. It is shown that the amplitude and timing of key features of the wall shear stress history can be correlated by means of a single non-dimensional parameter.

Fatigue Performance of Two Structural Adhesives

Abstract The fatigue performance of two toughened epoxy adhesives suitable for use in heavy structural engineering is assessed using a purpose-built fatigue rig. One adhesive is of the single-part, hot-cure type and the other is a two-part, cold-cure system. It is found that the single-part adhesive performs better than the two-part adhesive in fatigue even though the latter has the higher fracture toughness. Crack growth rates in both adhesives are found to satisfy the Paris Law as closely as any other crack growth model, and no dependence is found on the frequency of load cycling in the range studied (0.5Hz-5Hz). The fatigue performance of both adhesives is very promising for their likely uses in large-scale structures.

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.

On the Suppression of Coupled Liquid/Pipe Vibrations

The vibration of liquid-filled pipe systems can be caused by internal (pressure surges) or external (rotating machinery) sources, or a combination of both. Liquid pulsations can be diminished by devices like an air chamber, whereas pipe vibrations can be reduced by suitable supports. The performance of vibration suppression devices in the system under consideration can be investigated by numerical simulation. This is usually done with conventional waterhammer or pipe-stress computer codes. Present-day software also permits fully-coupled liquid-pipe analyses. The analysis of suppression devices and their interaction with the entire system is an important tool in design and trouble shooting.