k-ε Predictions of the initial mixing of desalination discharges

Predictions from a k-ε model are compared with recently acquired experimental data from inclined negatively buoyant discharges. The k-ε model is part of a standard computational fluid dynamics package (CFX). Two approaches are taken when implementing the model. One involves using an essentially standard form of the model to predict flow behaviour. The other approach involves calibrating the model, through adjustment of the turbulent Schmidt number in the tracer transport equation, to achieve reasonable predictions for positively buoyant vertical discharges and then applying it to inclined negatively buoyant discharges. While the calibrated approach improves the predictions of some bulk parameters (notably the tracer spread and dilution) when compared to predictions from the standard model, the overall effect on the quality of the predictions is small. Comparisons with experimental data indicate that predictions from both the standard and calibrated simulations compare favourably with trajectory data, but integrated dilution predictions at the centreline maximum height are conservative (mean-integrated concentrations are over-predicted). The standard and calibrated k-ε predictions confirm the importance of buoyant instabilities on the lower (inner) side of the flow, the effects of which are clearly evident in the mean concentration profiles. However, these simulations have a tendency to overestimate the influence of stabilizing density gradients on the upper (outer) side of the flow and are unable to effectively predict the cross-sectional distribution of a tracer. In contrast to a previous study, the above comparisons indicate that predictions of bulk parameters from such models can be poor and indeed are no better than those obtained from relatively simple analytical solutions.     

RANS simulation of neutral atmospheric boundary layer flows over complex terrain by proper imposition of boundary conditions and modification on the k-ε model

In this study, a modelling methodology is proposed for RANS simulations of neutral Atmospheric Boundary Layer (ABL) flows on the basis of the standard k-ε model, which allows the adoption of an arbitrary shear stress model. This modelling methodology is first examined in the context of an open flat terrain in an empty domain to ascertain there are no substantial changes in the prescribed profiles. The results show that relatively good homogeneity can be achieved with this modelling methodology for various sets of inflow boundary profiles. In addition, to extend the solutions derived from the standard k-ε model to RNG k-ε model, the RNG k-ε model is in detail assembly and tuned. Finally, the topographic effects on surface wind speeds over a complex terrain are assessed with the combined use of the proposed methodology and the modified RNG model. The numerical results are in good agreement with wind tunnel testing results and long-term field observations. A discussion of the effects of horizontal homogeneity and turbulence models on the simulated wind flows over a complex terrain is also given.     

A One-Equation Turbulence Model for Geophysical Applications: Comparison with Data and the k−ε Model

A one-equation turbulence model is presented, in which the turbulent kinetic energy k is calculated with a transport equation whereas the turbulent length scale l is calculated with an algebraic expression. The value of l depends on the local stratification and reduces to the classical |z| scaling for unstratified flows near a wall, where |z| is the distance to the wall. The length scale decreases during stable stratification, and increases for unstable stratification compared to the neutral case. In the limit of strong stable stratification, the so-called buoyancy length scale proportional to k ^1/2 N ^–1 is obtained, where N is the buoyancy frequency. The length scale formulation introduces a single model parameter which is calibrated against experimental data. The model is verified extensively against laboratory measurements and oceanic data, and comparisons are made with the two-equation k- model. It is shown that the performance of the proposed k model is almost identical to that of the k- model. In addition, the stability functions of Launder are revisited and adjusted to obtain better agreement with recent data.     

A Fine-Scale <Emphasis Type="Italic">k</Emphasis>−ε Model for Atmospheric Flow over Heterogeneous Landscapes

A multi-purpose model for small-scale atmospheric flows over heterogeneous landscapes is being developed. The aim of this research is to build a tool able to predict the dynamical (wind, turbulence) and diffusive (gases, particles) fields over landscapes characterised by heterogeneous plant cover. In its present stage of development the model is based on the numerical integration of neutral atmospheric flow equations, using an energy-dissipation closure scheme and over a domain that may include vegetation layers. Three validation cases of the model are presented: (i) response of the airflow to a change in surface roughness; (ii) airflow within and above a horizontally homogeneous plant canopy; (iii) airflow over two complex forest-to-clearing and clearing-to-forest transitions. All simulations provide results in good agreement with the experimental data, except for turbulent kinetic energy just after a clearing-to-forest transition. This result is not surprising for a statistical k– model in a flow region characterised by strong distorsion and intermittent turbulence. However the overall good performance of the model is promising for environmental research at fine scales over heterogeneous landscapes.