An assessment of streamline curvature effects on the mixing region of a turbulent plane jet in crossflow

The flow field of a turbulent plane jet in a weak or moderate crossflow, which is characterised by mild streamline curvature, has been investigated computationally. The values of the jet-to-crossflow velocity ratios chosen are 6, 9 and 10. The time-averaged Navier–Stokes equations are solved on a staggered Cartesian grid using the standard k–ϵ model and the k–ϵ model with streamline curvature modification. The predictions using both the models are compared with available experimental data. It has been shown that by accounting for the effect of streamline curvature in the k–ϵ model results in good prediction of this flow configuration.     

Numerical study of turbulent diesel flow in a pipe with sudden expansion

Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel flow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k–ε, the RNG k–ε and the two-scale k–ε models. The performance of the models is investigated with regard to the non-equilibrium parameter η and the mean strain of the flow, S. Velocity and turbulence kinetic energy predictions of the different models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The effect of more accurate near-wall modeling to the two-equation models is also investigated. The results of the study demonstrate the superiority of the second-moment closure in predicting the flow characteristics over the entire domain. From the two-equation models the RNG derived k–ε model also gave very good predictions, especially when non-equilibrium wall-functions were implemented. As far as η and S are concerned, only the closures with greater physical consistency, such as the two-scale k–ε model, give satisfactory results.     

Two-equation eddy viscosity models based on the Monin–Obukhov similarity theory

The present study is devoted for the development of two equation Reynolds-Averaged Navier–Stokes (RANS) closures for computational fluid dynamics (CFD) modelling of the atmospheric boundary layer. By using the inflow conditions based on the Monin–Obukhov similarity theory, the closure coefficients of the proposed models are derived from the analytical solutions of simplified turbulent transport equations. Modifications are conducted for three different turbulence models, which are standard $k-ϵ,$$k-\omega$ and Re-Normalisation Group (RNG) $k-ϵ$. Numerical experiments are performed for the homogeneous atmospheric boundary layer and the results are compared with the theoretical values in comparison to the standard versions of modified turbulence models. Developed models are implemented to open source CFD toolbox OpenFOAM.     

Coherent structure in flow over a slitted bluff body

The focus of the present investigation is resolution of the coherent structure in the near wake behind a slitted bluff body. The bluff body is two-dimensional with gap ratio from 0.12 to 0.48. The evolution of the structure was numerically investigated using the renormalization group (RNG) k–ε model at Reynolds number of 470,000. Two types of coherent structure are identified: At low gap ratio 0.12, the structure is characterized by a flip–flopping gap flow; at high ratio 0.22–0.48, the gap flow deflects to one side with an asymmetrical wake. The coherent structure is divided by the gap flow into two zones called the primary recirculation zone and the secondary recirculation zone. The coherent structure is intimately related to the gap ratio, and the structure of small gap ratio is different from that of large gap ratio because the interaction between two zones relates to the gap ratio. To explain the vortex shedding, a mechanism that single vortex of large size suddenly immerses between two shear layers was proposed. Experimental results using point-to-point method and particle-image velocimetry (PIV) measurements in a close wind tunnel were also carried out to confirm the observation from the numerical study. The evidence shows that the numerical results are of good agreement with the experiments. The comparison between the RNG k–ε model and the large eddy simulation also indicates that the RNG k–ε model is adequate in computing the bluff body flow.     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

Implication for Lie group symmetries for RANS modeling

Since the symmetries of fluid motion are admitted by all statistical quantities of turbulent flows as can be taken from the multipoint equations, we can derive conditions for turbulence models so that they capture the proper flow physics. Concerning these constraints we will exemplary investigate the k – ϵ – model for its capability to reproduce new scaling laws derived from symmetry methods. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of 3-D flow on porous broad crested weirs

Gabion weirs with optional design as a broad crested weirs are suitable structures to reduce flash flood with a minimal negative impact on the water environment. In the present study, the 3-D flow was simulated around gabion weirs with respect to free-surface water. The Reynolds-averaged Navier–Stokes equations are solved to predict water surface over the gabion weir. The VOF method with the geometric reconstruction scheme was applied to treat the complex free-surface flow. Simulations were performed using three variants of the k–ε and the RSM models to find the water level and velocity distribution profile and results are compared with several experimental data available in the literature. The structured mesh was used for all domains with high dense mesh near the solid region. A comparison between experimental data and simulations indicates that the k–ε model can be used to predict the complex flow and water level with high accuracy.     

Numerical evaluation of the suppression effect of a free-to-rotate triangular fairing on the vortex-induced vibration of a circular cylinder

The suppression of vortex-induced vibration (VIV) of a circular cylinder with a free-to-rotate triangular fairing in the Reynolds number range of Re = 1100–6100 is numerically investigated using computational fluid dynamics. The unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k–ω turbulence model coupled with an improved fourth-order Runge–Kutta method are used to solve the wake flow, the structure's vibration, and the fairing's rotation. The computational model is validated with the available experimental results for a cylinder with an attached short-tail fairing. The numerical results indicate that the triangular fairing has a positive role in suppressing vibration when it achieves a stable position deflected from the flow direction. The suppression effect is sensitive to the incoming flow velocity. The fairing shifts from a stable state to an unstable one when the flow velocity varies. Therefore, maintaining the hydrodynamic stability of the fairing is the key to achieving success in vibration suppression, and the stability is dependent on the characteristic length and the rotational friction. Although the strong flapping of the 70° triangular fairing excites a more vigorous vibration, it may be used as an amplifier of VIV for energy harvesting.     

Analysis of non-linear behaviour of shallow drought estuaries using the Stommel model

Shallow estuarine basins have small ocean exchange rates during periods of drought (when they are vertically mixed). This exchange is primarily due to convective processes. These are forced by a density difference between the basin and ocean produced by the surface buoyancy flux. This flux is dependent on the estuarine temperature, which is itself affected by the ocean exchange of heat. This creates a strong interaction between the buoyancy flux, and the density difference, and may be represented by a Stommel (H. Stommel, Tellus. 13 (2) (1961) 224–230) non-linear estuarine model. It involves a meteorological constant Γ, and a parameter ϵ, which measures the strength of the (buoyancy forced) convective exchange processes. The model has two stable states, or attractors, one of which corresponds to a classical, and the other to an inverse estuary. The analysis considers the range of (ϵ,Γ²) under which both of these steady states exist and investigates their comparative attractions. On seasonal time scales, the estuary may be in a transitory state (described here by manifold theory) in which the estuary may be `positive' or `negative' according to the sign of the buoyancy flux. For typical meteorological conditions, four categories of transitory estuary emerge which are dependent on the magnitude of ϵ.     

An assessment of turbulence models applied to the simulation of a two-dimensional submerged jet

This paper is concerned with the investigation of the performance of different turbulence models in the numerical prediction of transient flow caused by a confined submerged jet. Several widely used models, i.e., the standard k–ε, RNG k–ε, low Reynolds number k–ε models and the differential Reynolds stress model, as included in CFD codes, were compared with each other for a two-dimensional, incompressible, turbulent jet flow and with reported experimental data. A flapping oscillation was predicted regardless of the model used. A chosen Strouhal (St) number definition brought the fundamental frequencies from both the experiments and computations into close proximity. However, different turbulence models have exhibited quite different behaviours in terms of the frequency and regularity of the oscillation and in terms of the scale and duration of the vortices generated. All versions of the k–ε model yielded regular oscillations, which agree with experimental observations. On the other hand, the Reynolds stress (RS) model produced a complex pattern but a slower dissipation of vortices. In addition, some aspects of gridding and inflow representation are also discussed.     

On the modelling of bubble plumes in a liquid pool

Turbulent, bubble plumes are investigated numerically using the commercial, Computational Fluid Dynamics (CFD) code CFX-F3D. A six-equation, two-fluid model approach is adopted, in which interphase momentum exchange models include buoyancy, drag, added mass, lift and turbulent dispersion effects. Particular attention is paid to turbulence modelling, in which generation and dissipation resulting from interaction between bubbles and liquid are specifically taken into account within the context of an extended k − ϵ turbulence model. Results from a number of calculations are presented and compared against published, experimental bubble plume data. It is suggested that existing bubble/liquid interaction models for plumes may be grouped into three categories: those which produce lateral bubble spreading, those which diffuse the ambient liquid velocity field, and those which couple the plume to the surrounding liquid and thereby ultimately govern the pool mixing behaviour.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Modelling gas injection of a Peirce–Smith-converter

A commercial CFD-code PHOENICS was used to solve isothermal flow field of gas and liquid in a Peirce–Smith-converter. An Euler–Euler based algorithm was chosen for modelling fluid dynamics and evaluating controlling forces of a submerged gas injection. Predictions were made with a k–ε turbulence model in the body fitted coordinate system. The model has been verified with a 1/4 scale water model, and a parametric study with the mathematical model of submerged gas injection was made for the PS-process and the ladle injection processes. Limits of the modelling technique used were recognised, but calculated results indicate that the present model predicts the general flow field with reasonable accuracy. Predicted bubble distribution, pattern of the flow field and magnitude of flow velocities were used to evaluate scaling factors of physical models and general flow conditions of an industrial PS-converter.     

An approximation algorithm for scheduling trees of malleable tasks

This work presents an approximation algorithm for scheduling the tasks of a parallel application. These tasks are considered as malleable tasks (MT in short), which means that they can be executed on several processors. This model receives recently a lot of attention, mainly due to their practical use for implementing actual parallel applications. Most of the works developed within this model deal with independent MT for which good approximation algorithms have been designed. This work is devoted to the case where MT are linked by precedence relations. We present a 4(1+ϵ) approximation algorithm (for any fixed ϵ) for the specific structure of a tree. This preliminary result should open the way for further investigations concerning arbitrary precedence graphs of MT.     

3D numerical simulation of ambient discharge of buoyant water

Waste heat and wastewater are frequently discharged into ambient water and become intermittent sources of buoyancy. In order to control and reduce the environmental impact of these discharges, the mixing characteristics of such discharge in ambient flow should be determined. In this work the transport, mixing and turbulence characteristics of intermittent discharge of buoyant fluid in ambient flow are simulated by a 3D numerical model incorporating a buoyancy extended k–ε model for turbulence. In the numerical model the governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by a characteristics-based scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly by using the Gauss–Seidel iteration method. The model has been applied to cases of instantaneous and continuous discharges of buoyancy in ambient water with or without current. Dimensional analysis is used to estimate the initial values. The estimated range of values are found not sensitive to the solution. Satisfactorily comparison between computed results and the experimental results is achieved for the trajectories and lateral widths of the buoyant discharge. The engineering applicability of the model is thus ascertained.     

Applying a non-equilibrium wall function in k–ε turbulent modelling of hydrodynamic circulating flow

Wall bounded flow with severe adverse pressure, separation, reattachment and stagnation has non-equilibrium (NE) exhibition. A wall function in turbulent flow is a remedy to avoid resolving near wall complex phenomena using predetermined functions as boundary conditions. The advantage of this case is permission to use a relatively coarse near wall cells and hence saving CPU time. Standard wall function (SWF) is a semi-empirical function that is just valid for constant shear near wall cell and local equilibrium flow. Popovac and Hanjalic introduced a non-equilibrium wall function as (PWF) with a blending method in v²–f model. To investigate PWF in circulating flow, standard k–ε model that has key role in complex and expensive industrial problems is used in this study. The approach derived by Popovac and Hanjalic retains the functional form of the SWF and can be easily implemented in existing code. Simulation results are validated against direct numerical simulation (DNS) on channel and experimental data on backward facing step (BS) and a sharp U bend flow. Prediction with PWF shows that use of this wall function in k–ε model has not any sensitive change in near equilibrium flow. However, produces an improvement in NE conditions like flow in circulation zones.     

The Propagation of Shock Waves in Incompressible Fluids: The Case of Freshwater

In this paper we investigate the basic features of shock waves propagation in freshwater in the framework of a hyperbolic model consisting of the one-dimensional Euler equations closed by means of polynomial equations of state extracted from experimental tabulated data available in the literature (Sun et al. in Deep-Sea Res. I 55:1304–1310, 2008). The Rankine–Hugoniot equations are numerically solved in order to determine the Hugoniot locus representing the set of perturbed states that can be connected through a k-shock to an unperturbed state. The results are found to be consistent with those previously obtained in the framework of the EQTI model by means of a modified Boussinesq equation of state.     

An ϵ-sensitivity analysis for semidefinite programming

We extend the concept of ϵ-sensitivity analysis developed for linear programming to that for semidefinite programming. First, the notion of ϵ-optimality for a given semidefinite programming problem is defined, and then a generic ϵ-sensitivity analysis for semidefinite programming is introduced. Based on the definitions, we develop an implementation of the generic ϵ-sensitivity analysis under perturbations of either the cost parameters or the right-hand side.     

A numerical algorithm for nonlinear parabolic equations with highly oscillating coefficients

A numerical algorithm is constructed for the solution to a class of nonlinear parabolic operators in the case of homogenization. We consider parabolic operators of the form d/dt + A_ϵ, where A_ϵ is monotone. More precisely, we consider the case when A_ϵu=−div (a(x/ϵ, e/ϵ^k) |Du|^p−2Du), where p≥2 and k>0. © 1996 John Wiley & Sons, Inc.