A note on the prediction of liquid hold-up with the stratified roll wave regime for gas/liquidco-current flow in horizontal pipes.

This note presents a simple model for prediction of liquid hold-up in two-phase horizontal pipe flow for the stratified roll wave (St+RW) flow regime. Liquid hold-up data for horizontal two-phase pipe flow [1, 2, 3, 4, 5 and 6] exhibit a steady increase with liquid velocity and a more dramatic fall with increasing gas rate as shown by Hand et al. [7 and 8] for example. In addition the liquid hold-up is reported to show an additional variation with pipe diameter. Generally, if the initial liquid rate for the no-gas flow condition gives a liquid height below the pipe centre line, the flow patterns pass successively through the stratified (St), stratified ripple (St+R), stratified roll wave, film plus droplet (F+D) and finally the annular (A+D, A+RW, A+BTS) regimes as the gas rate is increased. Hand et al. [7 and 8] have given a detailed description of this progression in flow regime development and definitions of the patterns involved. Despite the fact that there are over one hundred models which have been developed to predict liquid hold-up, none have been shown to be universally useful, while only a handful have proven to be applicable to specific flow regimes [9, 10, 11 and 12]. One of the most intractable regimes to predict has been the stratified roll wave pattern where the liquid hold-up shows the most dramatic change with gas flow rate. It has been suggested that the momentum balance-type models, which give both hold-up and pressure drop prediction, can predict universally for all flow regimes but particularly in the case of the difficult stratified roll wave pattern. Donnelly [1] recently demonstrated that the momentum balance models experienced some difficulties in the prediction of this regime. Without going into lengthy details, these models differ in the assumed friction factor or shear stress on the surfaces within the pipe particularly at the liquid–gas interface. The Baker–Jardine model [13] when tested against the 0.0454 m i.d. data of Nguyen [2] exhibited a wide scatter for both liquid hold-up and pressure drop as shown in Fig. 1. The Andritsos–Hanratty model [14] gave better prediction of pressure drop but a wide scatter for liquid hold-up estimation (cf. Fig. 2) when tested against the 0.0935 m i.d. data of Hand [5]. The Spedding–Hand model [15], shown in Fig. 3 against the data of Hand [5], gave improved performance but was still unsatisfactory with the prediction of hold-up for stratified-type flows. The MARS model of Grolman [6] gave better prediction of hold-up (cf. Fig. 4) but deterioration in the estimation of pressure drop when tested against the data of Nguyen [2]. Thus no method is available that will accurately predict liquid hold-up across the whole range of flow patterns but particularly for the stratified plus roll wavy regime. The position is particularly unfortunate since the stratified-type regimes are perhaps the most predominant pattern found in multiphase lines.

Stochastic analysis of free surface flow through earth dams

This research investigated the unconfined flow through dams. The hydraulic conductivity was modeled as spatially random field following lognormal distribution. Results showed that the seepage flow produced from the stochastic solution was smaller than its deterministic value. In addition, the free surface was observed to exit at a point lower than that obtained from the deterministic solution. When the hydraulic conductivity was strongly correlated in the horizontal direction than the vertical direction, the flow through the dam has markedly increased. It is suggested that it may not be necessary to construct a core in dams made from soils that exhibit high degree of variability.

Polarisation independent split ring frequency selective surface

A frequency selective surface (FSS) is described which exhibits coincident spectral responses for TE and TM polarisation when the FSS operates at 45 degrees incidence. The structure consists of two closely spaced arrays of ring elements with the conductor split at one or two locations to provide independent control of the resonances for the vertical and horizontal field directions. The FSS is designed to diplex two channels separated by an edge of a band ratio of 1.7:1 and yield a common - 10 dB reflection bandwidth of 10.2%. Measured and numerical results are shown to be in good agreement over the frequency range 9-12 GHz.

Polarisation independent resistively loaded frequency selective surface absorber with optimum oblique incidence performance

This study presents the design of a thin electromagnetic absorber which exhibits radar backscatter suppression that is independent of the wave polarisation at large incidence angles. The structure consists of a metal backed printed frequency selective surface (FSS), with resistors placed across narrow gaps inserted in the middle of each of the four sides of the conductor loops. The geometry of the periodic array and the value of the vertical and horizontal resistor pairs are carefully chosen to present a real impedance of 377 Ω at the centre operating frequency for both TE and TM polarised waves. Angular sensitivity and reflectivity bandwidth have been investigated for FSS absorber designs with thicknesses of 1, 2 and 3 mm. Each of the three structures was optimised to work at a centre frequency of 10 GHz and an incident angle of 45°. The design methodology is verified by measuring the radar backscatter suppression from a 3 mm (l / 10) thick screen in the frequency range 8–12 GHz. The absorber construction was simplified by filling the four metal gaps in each unit cell with shielding paint, and selecting the ink thickness to give the two required surface resistance values.