Practical comparison of two turbulent models

A numerical study of a number of viscous compressible gas flows, using a one-parameter differential turbulence model of Spalart-Olmaras and another, obtained by changing the variables in the two-parameter SST model of Menter, is conducted. Calculations are based on Reynolds averaged two-dimensional Navier-Stokes equations, using a difference scheme of the fifth order of approximation. The problems of a subsonic flat plate, spoon-formed cavern, Jones airfoil overflow, separated flow in front of the angle of compression and dissipation of a single vortex are considered. These results permit me to better define the limits of applicability of the turbulence models considered, and to note their possible shortcomings.     

Improved parameterisation for the numerical modelling of air pollution within an urban street canyon

Numerical modelling for application to wind flow and dispersion in urban environments has noticeably progressed in recent years, to currently represent a widely used tool for simulating mechanical processes governing air pollution in complex geometries. In particular, Computational Fluid Dynamic (CFD) techniques based on RANS (Reynolds-Averaged Navier–Stokes equations) models, are extensively used to produce detailed simulations of the wind flow and turbulence in the urban canopy. However, several studies have indicated that RANS models, and in particular the widely used standard k–? turbulence model, are sensitive to the particular form of inlet profiles for turbulence and velocity. In the present study, simulations of the wind flow and dispersion within an idealised street canyon were carried out using the standard k–? turbulence model provided by the commercial software FLUENT. The aim of this study was to improve the standard k–? model performance by modifying the model parameters according to the chosen form of inlet profiles for velocity and turbulence. Capability of the model to reproduce real wind flow fields, turbulence and concentration patterns was evaluated by comparing the model results against recently published wind tunnel data. Results for turbulent kinetic energy and concentration showed that the redefinition of the default dispersive parameters can significantly enhance the model performance. The newly proposed parameterisations of the standard k–? turbulence model can be readily implemented within commercial CFD software packages, offering a reliable modelling tool for application to urban air pollution and other environmental studies.     

Simulation of the generation of turbulence motion in edge wakes

The process of generating turbulence in edge wakes has been simulated and the results of the simulation are presented. The proposed mathematical model follows from a special procedure, which aims to average the flow parameters on scales comparable with the free path of molecules. The examined mechanism of generating turbulence is described by an expended set of Euler and Navier-Stokes nonstationary equations, with additional dispersive summands of the third order, which are obtained, if one uses the averaging procedure. The basic hydrodynamic equations are integrated by means of the well-known Godunov procedure of the second order. The calculated averaged performances of the turbulent flows agree with the experimental data.     

An adaptive solver for the spherical shallow water equations

The shallow water equations (SWE), which describe the flow of a thin layer of fluid in two dimensions have been used by the atmospheric modelling community as a vehicle for testing promising numerical methods for solving atmospheric and oceanic problems. The SWE are important for the study of the dynamics of large-scale flows, as well for the development of new numerical schemes that are applied to more complex models. In this paper we present a finite difference p-adaptive method based on high order finite differences that is applied using an error indicator for solving the SWE on the sphere. A standard test set is used to evaluate the accuracy of the new method. The results obtained are compared with the pseudo-spectral method.     

Turbulence models and their applications to the prediction of internal flows: A review

The paper presents a brief account of various turbulence models employed in the computation of turbulent flows, and evaluates the application of these models to internal flows by examining the predictions of various turbulence models in selected important flow configurations. The main conclusions of this analysis are: (a) The κ-ε model is used in a majority of all the 2-D flow calculations reported in the literature. (b) Modified forms of the κ-ε model improve the performance for flows with streamline curvature and heat transfer. (c) For flows with swirl, the κ-ε model performs rather poorly; the algebraic stress model performs better in this case. (d) For flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well. Two important factors in the numerical solution of the model equations, namely false diffusion and inlet boundary conditions, are discussed. The existence of countergradient transport and its implications in turbulence modeling are examined. Finally, some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.     

A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations

We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DG\linebreak method for the depth-integrated shallow water equations. The method described here is an extension of these ideas to non-depth-integrated models. The method and its implementation are discussed, followed by numerical examples on several test problems.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Zonal k-l based large eddy simulations

Zonal k-l based large eddy simulation (LES) approaches are presented. To reduce computational demands, near walls, Reynolds averaged Navier-Stokes (RANS) like modelling is used. The interface location for the differing models is either explicitly specified, or, based on length scale compatibility, allowed to naturally locate. With the latter approach the location is strongly grid controlled. When explicitly specified (based on turbulence physics grounds), to enhance results length scale smoothing is implemented. Using standard established LES and RANS model constants the zonal methods are shown to reproduce a satisfactory law of the wall. The approaches are implemented in both cell-vertex and cell-centred codes with similar results being found. Various other sensitivity studies are performed. These show that, as with standard LES, predictions are most sensitive to filter definition, first off wall grid node normal positions and temporal scheme order. For a non-isothermal periodic ribbed channel, the new zonal LES predictions are found to be significantly more accurate than those for an established RANS model and also LES.     

Multi-block lattice Boltzmann simulations of subcritical flow in open channel junctions

A two-dimensional lattice Boltzmann model (LBM) for subcritical flows in open channel junctions is developed. Shallow water equations coupled with the large eddy simulation model is numerically simulated by the lattice Boltzmann method, so that the turbulence, caused by the combination of the main channel and tributary flows, can be taken into account and modeled efficiently. In order to obtain more detailed and accurate results, a multi-block lattice scheme is designed and applied at the area of combining flows. The model is first verified by experimental data for a 90° junction flow, then is used to investigate the effect of the junction angle on flow characteristics, such as velocity field, water depth and separation zone. The objectives of this study are to validate the two-dimensional LBM in junction flow simulation and compare the results with available experimental data and classical analytical solutions in the separation zone.     

A computationally efficient particle-puff model for concentration variance from steady releases

This paper presents a computationally efficient particle-puff model that can be used to calculate both average concentration and concentration variance in turbulent flows. The model is self-contained in the sense that it does not need externally supplied parameterizations of puff spread, but rather calculates the spread with an internally-built module for relative dispersion of particles—all existing particle-puff models rely on parameterizations of puff spread derived from theoretical considerations and observational data for dispersion of a point source in isotropic turbulence.Preliminary evaluations show that the model performs as well as a computationally demanding two-particle trajectory model in predicting the mean concentration and concentration variance in two different flows: isotropic turbulence and a wind tunnel boundary layer. Because of its numerical efficiency, the present particle-puff model can be built into conventional, regulatory air quality models as a module to calculate the mean concentration and concentration variance in the near field.The reason for the numerical efficiency of present particle-puff model is that it needs to track only thousands of particle-pairs in order to calculate the puff spread, while (the original) two-particle Lagrangian stochastic (LS) models need millions of particle-pairs to achieve statistically stable predictions.     

twodee-2: A shallow layer model for dense gas dispersion on complex topography

twodee-2 is a Fortran 90 code based on previous code (twodee). It is designed to solve the shallow water equations for fluid depth, depth-averaged horizontal velocities and depth-averaged fluid density. The shallow layer approach used by twodee-2 is a compromise between the complexity of CFD models and the simpler integral models. It can be used for forecasting gas dispersion near the ground and/or for hazard assessment over complex terrains. The inputs to the model are topography, terrain roughness, wind measurements from meteorological stations and gas flow rate from the ground sources. Optionally the model can be coupled with the output of a meteorological processor which generates a zero-divergence wind field incorporating terrain effects. Model outputs are gas concentration, depth-averaged velocity, averaged cloud thickness and dose. The model can be a useful tool for gas hazard assessment by evaluating where and when lethal concentrations for humans and animals can be reached.     

Development of a landslide component for a sediment budget model

Most erosion models focus on overland-flow erosion with fewer incorporating landslide erosion although it is common on hillslopes. Landslide models are typically dynamic, spatially distributed simulations with large data requirements for parameterisation and are often computationally intensive. The Australian SedNet model represents a middle ground between process-based and empirical models and is being modified for New Zealand conditions by incorporating shallow landsliding.We describe a method for implementing a model within SedNetNZ to provide the long-term annual average sediment contribution from shallow landsliding and its spatial distribution. The mass of soil eroded over a defined period is calculated from the landslide probability for each slope class, slope class area, failure depth, soil bulk density, and sediment delivery ratio. Landslide probability is derived from mapping a time series of landslides intersected with DEM-derived slope. The conceptual approach and methodology for parameterisation are suitable for landslide modelling where rainfall-triggered shallow landslides occur.     

Explicit algebraic Reynolds stress model of incompressible turbulent flow in rotating square duct

An explicit algebraic Reynolds stress model (EARSM) is proposed for the simulation of the incompressible three-dimensional Reynolds averaged Navier-Stokes (RANS) equations. The spatial discretization of the RANS equations is performed by a finite volume method with nonstaggered variable arrangement.The EARSM model which accounts for rotational effects is used to compute the turbulent flows in rotating straight square duct. The Reynolds number of 48,000 is based on the bulk velocity and the hydraulic diameter of the duct and is kept constant in the range of the rotational numbers. The second order closure (EARSM) yields an asymmetric mean velocity profile as well as turbulence properties. Effects of rotation near the cyclonic (suction side) and anticyclonic (pressure side) walls are well observed. Direct numerical simulation and large eddy simulation data are available for this case. The comparison of EARSM results with these accurate simulations shows a very good agreement.     

A Godunov-type scheme for modelling 1D channel flow with varying width and topography

One-dimensional (1D) numerical models have long been used in simulating fluvial hydrodynamics. While most of these models are based on the solutions to some approximate forms of the fully 1D St. Venant equations, it is desirable to have a 1D code that can deal with those highly dynamic and complex flows under certain flood conditions, with full consideration of the convective and source terms. This paper therefore presents a Godunov-type alternative for solving the 1D inhomogeneous shallow water equations with complex source terms. The model is also implemented with a wetting and drying condition to avoid producing negative water depth. The proposed model is validated by a selection of steady and transient hydraulic problems with reference solutions.     

Coupled lattice Boltzmann and discrete element modelling of fluid–particle interaction problems

Particle–fluid systems encountered in many scientific and engineering applications impose a significant modelling challenge. This paper outlines a new solution strategy that couples lattice Boltzmann (LB), large eddy simulation (LES), and discrete element (DE) methodologies for the simulation of particle–fluid systems at moderately high Reynolds numbers. The following main computational issues are considered: (1) the use of the standard LB formulation for the solution of fluid flows; (2) the incorporation of the one-parameter Smagorinski turbulence model in the LB equations for turbulent flows; (3) the utilisation of one immersed boundary scheme for computing hydrodynamic interaction forces between the fluid and moving particles; and (4) the use of DE methods accounting for the interaction between solid particles. The new contributions made in the current work include the application of the Smagorinski turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling in order to ensure an overall stable LB–DE solution. A complex transport problem involving 70 large moving particles with moderately high Reynolds number (around 56,000) is provided to demonstrate the capability of the presented coupling strategy.     

Enhanced predictive modelling process of broadband services adoption based on time series data

In this paper, the importance of the predictive modelling process of broadband services adoption is described. A detailed overview of different analytical models used for prediction, i.e., fitting and forecasting processes of broadband services adoption are presented. Furthermore, a comparison of several analytical models commonly used for prediction of broadband adoption is conducted. In order to more accurately fit to the existing broadband adoption time series data, and to forecast the future broadband services adoption paths, the features of the most accurate common predictive models have been identified for different phases of broadband services adoption. Considering the given results, usage of additional models in the predictive modelling process is analyzed. The objective of these analyses is set to improve the accuracy of the existing predictive modelling process. The accuracy of the predictive modelling process using additional models is tested and compared in different phases of broadband adoption. The model which gives the most accurate results is identified. Finally, in order to enable the usage of this model within a whole broadband service life cycle, as well as to include a greater number of explanatory parameters in predictive modelling process, an enhanced predictive modelling process is proposed.     

Model-based reasoning: a principled approach for software engineering

The software engineering industry suffers from almost unmanageable complexity both in the products it produces and in the processes of production. One of the current shortcomings in the software production process is the weakness of the models used. This paper makes observations on the role of knowledge in engineering and examines the central role of models and simulation. We develop an argument for the application of certain new forms of modelling methods in software engineering in order to impose more discipline and give a principled framework for building models that can support the software life-cycle. The concept of a model is examined in depth and different characteristics and types of model are defined. This introduces the relatively new concept of qualitative models and their use in the field known as model-based reasoning. Unlike previous knowledge-based methods, model-based reasoning has several important advantages. Although very few model-based software projects exist, we illustrate how this approach can be developed by drawing on applications from traditional engineering. It is argued that, because qualitative modelling offers great power for addressing the issue of complexity, such models have considerable potential as high-level abstractions of software products. These could form the core of tools for the management and support of the software development process through the whole product life-cycle.     

The development and application of CFD models for water treatment flocculators

The use of CFD to simulate turbulent flows in laboratory and full scale flocculation processes commonly found at water treatment works is reported. The paper considers a range of modelling strategies and simulation techniques including, inter alia, steady and unsteady flow, two-equation and Reynolds stress turbulence modelling, sliding mesh and multiple reference frames approaches to rotational flow simulation, and mesh density optimisation. Through analysis of turbulence dissipation rate, this work considers the development of models for environmental engineering problem solving and demonstrates clearly the benefits to be gained from the use of CFD in flocculation vessels.     

Artificial neural network modelling in simulation of complex flow at open channel junctions based on large data sets

The flow characteristics in open channel junctions are of great interest in hydraulic and environmental engineering areas. This study investigates the capacity of artificial neural network (ANN) models for representing and modelling the velocity distributions of combined open channel flows. ANN models are constructed and tested using data derived from computational-fluid-dynamics models. The orthogonal sampling method is used to select representative data. The ANN models trained and validated by representative data generally outperform those by using random data. Sobols' sensitivity analysis is performed to investigate contributions of different uncertainty sources to model performance. Results indicate that the major uncertainty source is from ANN model parameter initialization. Hence an ANN model training strategy is designed in order to reduce the main uncertainty source: models are trained for many runs with random model parameter initializations and the model with the best performance is adopted.     

Numerical study of stress-transport turbulence models: Implementation and validation issues

The primary goal of this work is to implement, validate and compare in shear-free and simple wall-bounded turbulent flows the performance of five stress-transport turbulence models that have recently appeared in the open literature. A secondary goal of this work is to analyze and study the effort and difficulties encountered by programmers when implementing turbulence models developed by other researchers. The need for standardized procedures and for the development of efficient numerical techniques is advocated as a means to reduce the model-variance and code dependency of turbulent models. The second-order models chosen for this study are the Launder-Shima, the Jakirlic-Hanjalic, the elliptic-blending model of Manceau, the Turbulent Potential Model proposed by Perot and an unidentified model. For comparison reasons, Wilcox k-ω eddy-viscosity model was included in the study. The validation and the study of the performance of the models were performed through the comparison of the numerical solutions with experimental data and analytical solutions. The five benchmark flowfields considered in this study encompass the shear-free and wall-bounded regimes and are the flat plate without pressure gradient, the flow over a plate with a moderately adverse pressure gradient, and the self-similar flows of the mixing layer, the plane jet and the axi-symmetric jet. The tested stress-transport models produced results in general agreement with the experiments. However, no clear advantage of the stress-transport model over Wilcox k-ω model was noticed in these simple flowfields. The Launder-Shima model could not predict accurately the skin friction on a flat plate but it performed well in all the other cases. Although the test cases used were simple, a major difficulty encountered in this effort is the unreliability of the open literature as a resource for turbulence model implementation. A general lack of consistency was observed between model versions published in different journals or at different times. The detrimental effect that such a lack of structure and consistency has on the CFD community is discussed.