Fluids

The traditional way to model the statistics of turbulent flow and dispersion is through averaged conservation equations, in which the turbulent transport terms are described by semi-empirical expressions. A new development has been reported by Brouwers in a number of consecutive papers published over the last 15 years. The new development is that presented descriptions can be obtained through the application of fundamental principles of statistical physics and making use of the asymptotic structure of turbulence at a high Reynolds number. They no longer rely on empirical constructions, minimise calibration factors, and are not limited to specific flow situations. This article updates the contents of these works and presents them in coherent manner. The first derivations are presented as expressions for turbulent diffusion. These are subsequently implemented in a closed set of equations expressing the conservation of mean momentum, mean fluctuating energy, and energy dissipation rate. Predictions from these equations are shown to compare favourably with the results of direct numerical simulations (DNS) of the Navier–Stokes equations of highly anisotropic and inhomogeneous channel flow. The presented model equations provide a solid basis to calculate the main statistical parameters of turbulent flow and dispersion in engineering praxis and environmental analysis.

This study investigates the heat transfer coefficient (HTC) during flow condensation inside smooth inclined tubes, analyzing the combined effects of flow orientation, fluid properties and flow characteristics on the thermal performance. The literature review indicates that the channel inclination effect on the HTC remains insufficiently understood, highlighting the need for further investigation. Thus, a comprehensive experimental database comprising 4944 data points was compiled from 24 studies, including all flow directions, from upward, to horizontal, downward, and intermediate orientations. The study reveals that the influence of flow inclination on the HTC can be ruled by a criterion based on the liquid film thickness Froude number, ${\mathrm{Fr}}_{\delta }$. At ${\mathrm{Fr}}_{\delta }$ > 4.75, the effect of flow inclination becomes negligible, while under ${\mathrm{Fr}}_{\delta }$ < 4.75, the inclination can have a considerable effect on the HTC. The experimental data show that at low Froude numbers, upward flow typically exhibits higher HTC compared to downward flow, attributed to enhanced interfacial turbulence caused by opposing gravitational and shear forces. In contrast, under vertical downward flow, the annular pattern is more prominent, with reduced interfacial disturbances, limiting HTC performance. The compiled experimental database for inclined channels was compared against an update list of prediction methods, including seven correlations incorporating the inclination angle as an input parameter. Additionally, a new simple correction factor including the effect of inclined tubes was proposed based on the flow inclination angle and on the liquid film thickness Froude number. The proposed correction factor improved the prediction of well-ranked correlations in the literature by over 20% for stratified flow pattern conditions and by more than 5% for low Froude number values. These findings present new insights into how tube inclination can affect heat transfer in a two-phase flow.

The aim of this study is to compare submerged vortical structures for a pump mounted in a pump intake without any anti-vortex devices (AVDs), with a trident-like AVD or with a cone AVD. Another aim is to compare the pump characteristics (head, efficiency, power input and radial forces) of these pump arrangements via CFD simulation along with experimental measurements in a closed circuit. The numerical simulation of unsteady multiphase flow is established by means of computational fluid dynamics (CFD) and the volume of fluid (VOF) method. To predict vortical structures in the vicinity of the pump suction bell, the unsteady Reynolds-averaged Navier–Stokes equations (URANS) are solved together with the scale-adaptive simulation (SAS) turbulence model. For each AVD configuration, integral characteristics like the head, power input, efficiency and forces acting on the pump rotor are also evaluated. The numerical results show that the configuration with the cone AVD exhibits the best performance (from the point of view of both hydraulic efficiency and vorticity strength), but it requires a larger distance between the intake bottom wall and the pump bellmouth. The submerged vortices are quite stable when using an AVD, but rather unsteady without any anti-vortex tool.