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.     

Numerical simulation of UV disinfection reactors: Evaluation of alternative turbulence models

Six turbulence models, including standard k–ε, k–ε RNG, k–ω (88), revised k–ω (98), Reynolds stress transport model (RSTM), and two-fluid model (TFM), were applied to the simulation of a closed conduit polychromatic UV reactor. Predicted flow field and turbulent kinetic energy were compared with the experimental data from a digital particle image velocimetry (DPIV). All of the predicted flow fields were combined with a multiple segment source summation (MSSS) fluence rate model and three different microbial response kinetic models to simulate the disinfection process at two UV lamp power conditions. Microbial transport was simulated using the Lagrangian particle tracking method. The results show that the fluence distributions and the effluent inactivation levels were sensitive to the turbulence model selection. The level of sensitivity was a function of the operating conditions and the UV response kinetics of the microorganisms. Simulations with operating conditions that produced higher log inactivation or utilized microorganisms with higher UV sensitivity showed greater sensitivity to the turbulence model selection. In addition, a broader fluence distribution was found with turbulence models that predicted a larger wake region behind the lamps.     

Performance of turbulence models for flows through rough pipes

The Reynolds-averaged Navier–Stokes (RANS) equations were solved along with turbulence models, namely k–ε, k–ω, Reynolds stress models (RSM), and filtered Navier–Stokes equations along with Large Eddy Simulation (LES) to study the fully-developed turbulent flows in circular pipes roughened by repeated square ribs with various spacings. Solutions of these flows were obtained using the commercial computational fluid dynamics (CFD) software Fluent. The numerical results were validated against experimental measurements and other numerical data published in literature. The performance of the turbulence models was compared and discussed. All the RANS models and LES model were observed to perform equally well in predicting the time-averaged flow statistics. However no instantaneous information can be obtained from the RANS results. Therefore, when a rough overview of the flow process in a pipe roughened by repeated ribs is needed, any one of the RANS models can be of value. On the other hand, the instantaneous as well as time-averaged flows could be studied with more insight using LES, albeit at a cost of CPU effort at least one order higher.     

Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle

In the present study, the turbulent gas flow dynamics in a two-dimensional convergent–divergent rocket nozzle is numerically predicted and the associated physical phenomena are investigated for various operating conditions. The nozzle is assumed to have impermeable and adiabatic walls with a flow straightener in the upstream side and is connected to a plenum surrounding the nozzle geometry and extended in the downstream direction. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and subsonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. The performance of the different turbulence models adopted has been assessed by comparing the obtained results of the static wall pressure and the shock position with the available experimental and numerical data. The dimensionless shear stress at the nozzle wall and the separation point are also computed and the flow field is illustrated. The various implemented turbulence models have shown different behavior of the turbulent characteristics. However, the shear-stress transport (SST) k–ω model exhibits the best overall agreement with the experimental measurements. In general, the proposed numerical procedure applied in the present paper shows good capability in predicting the physical phenomena and the flow characteristics encountered in such kinds of complex turbulent flow.     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

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.     

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.     

Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface

The present paper introduces a new interfacial marker-level set method (IMLS) which is coupled with the Reynolds averaged Navier–Stokes (RANS) equations to predict the turbulence-induced interfacial instability of two-phase flow with moving interface. The governing RANS equations for time-dependent, axisymmetric and incompressible two-phase flow are described in both phases and solved separately using the control volume approach on structured cell-centered collocated grids. The transition from one phase to another is performed through a consistent balance of kinematic and dynamic conditions on the interface separating the two phases. The topological changes of the interface are predicted by applying the level set approach. By fitting a number of interfacial markers on the intersection points of the computational grids with the interface, the interfacial stresses and consequently, the interfacial driving forces are easily estimated. Moreover, the normal interface velocity, calculated at the interfacial markers positions, can be extended to the higher dimensional level set function and used for the interface advection process. The performance of linear and non-linear two-equation k–ε turbulence models is investigated in the context of the considered two-phase flow impinging problem, where a turbulent gas jet impinging on a free liquid surface. The numerical results obtained are evaluated through the comparison with the available experimental and analytical data. The nonlinear turbulence model showed superiority in predicting the interface deformation resulting from turbulent normal stresses. However, both linear and nonlinear turbulence models showed a similar behavior in predicting the interface deformation due to turbulent tangential stresses. In general, the developed IMLS numerical method showed a remarkable capability in predicting the dynamics of the considered two-phase immiscible flow problems and therefore it can be applied to quite a number of interface stability problems.     

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.     

A 3D non-linear k–ε turbulent model for prediction of flow and mass transport in channel with vegetation

The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.     

The flow simulation of a low-specific-speed high-speed centrifugal pump

In this paper a general three-dimensional simulation of turbulent fluid flow is presented to predict velocity and pressure fields for a centrifugal pump. A commercial CFD code was used to solve the governing equations of the flow field. In order to study the most suitable turbulence model, three known turbulence models of standard k–ε, RNG and RSM were applied. The complex flow configuration required us to use around 5,800,000 cells, and 12 computational nodes (processors) for parallel computing. Simulation results in the form of characteristic curves were compared with available experimental data, and an acceptable agreement was obtained. Additionally, effect of number of blades on the efficiency of pump was studied. The number of blades was changed from 5 to 7. The results show that the impeller with 7 blades has the highest head coefficient. Finally, it was observed also that the position of blades with respect to the tongue of volute has great effect on the start of the separation. Thus, to analyze the effect of blade number on the characteristics of the pump, the position of blade and tongue should be similar to each other. Investigations of this kind may help to reduce the required experimental work for the development and design of such devices.     

CFD studies on burner secondary airflow

In many fossil power plants operating today, there is insufficient means to assure the proper balancing of the secondary airflows between the individual burners of wall-fired units. This mismatch leads to decreased boiler efficiency and increased emissions. In this study, a computational fluid dynamics (CFD) modeling of a fossil power plant wind box was performed. The model solved the three-dimensional Reynolds averaged Navier–Stokes equations with the k–ε turbulence model. The CFD results were validated by the experimental data taken from a 1/8th scale model of a wall-fired fossil unit. Simulations under various mass flow rates specified at inlet, various baffle positions and two opening conditions of the burners were obtained to identify the optimum design in terms of the equalization of the secondary airflow through the burners. This study demonstrated that the combination of experimental and CFD approach can be an effective tool in the research of burner secondary airflow balancing.     

Mathematical modeling of coupled turbulent flow and solidification in a single belt caster with electromagnetic brake

A mathematical model has been developed to simulate turbulent fluid flow and solidification in the presence of a DC magnetic field in an extended nozzle for metal delivery to a single belt caster. This paper reports on predicted effects of DC magnetic field conditions in modifying flows and solidification behavior in the metal delivery system. It is shown that the application of a DC magnetic brake to the proposed system can result in a reasonably uniform feeding of melt onto the cooled moving belt. This, in turn, optimises the rate of even shell growth along the chilled substrate. In order to account for the effects of turbulence, a revised low-Reynolds k–ε turbulent model was employed. A Darcy-porosity approach was used to simulate fluid flow within the mushy solidification region. Simulations were carried out for plain carbon steel strip casting. The fully coupled transport equations were numerically solved using the finite volume method. The computed flow patterns were compared with those reported in the literature. The performance of the magnetic flow control device proposed in this work is evaluated and compared with flow modifications obtained by inserting a ceramic filter within the reservoir.     

Stability and non-normality of the k-ε equations

The analytical and numerical solutions of the equations of the k-ε turbulence model are analyzed. Under certain conditions on the boundary values and the interior values of k and ε the analytical and numerical solutions are bounded. If the steady state solution is obtained numerically by a Runge-Kutta time-stepping method, then severe constraints on the time-step and the non-normality of the jacobian matrix make the convergence very slow. The simplifications and conclusions are supported by data from a numerical solution of flow over a flat plate.     

Assessment of an improved turbulence model in simulating the unsteady flows around a D-shaped cylinder and an open cavity

Most engineering flows are still predicted by the conventional Reynolds-averaged Navier-Stokes method because of the low requirements of the computational quantities. However, the resolution capability of Reynolds-averaged Navier-Stokes models is still open to deliberation, especially in the recirculation and wake regions, where the vortical flows dominate. In the present work, an improved turbulence model derived from the original shear stress transport k-ω model is proposed and its superiority is assessed by our modeling the unsteady flows around a D-shaped cylinder and an open cavity, corresponding to two different Reynolds numbers. The results are compared with results from experiments and other turbulence models in terms of the flow morphology and mean velocity profiles. This shows that the predictive accuracy of the modified turbulence model is increased significantly in the bluff body wake flows and in the shear layer and separation flows of the cavity. Some special vortex structures can be captured in the open cavity, in which the secondary vortex emerging from the shear layer and the separation vortex near the trailing edge can induce large flow instability, and this phenomenon should be eliminated in engineering applications. It is believed that this improved turbulence model can be used for the more complex turbomachinery flows with better prediction of the hydrodynamic/aerodynamic performance and the unsteady vortical flows, which can provide some guidelines to design or optimize rotating machines.     

Development of boundary transfer method in simulation of gas–solid turbulent flow of a riser

Computational fluid dynamics (CFD) is used to simulate the behavior of two phase gas solid in a fluid catalytic cracking (FCC) riser. Gas and particle phases are considered as separate fully interpenetrating continuous media within each control volume. Each phase described in terms of its own separate mass and momentum conservation equations. Simple k–epsilon (k_g–?_g) turbulence model is used for the gas phase and the solid phase is handled with the kinetic theory of granular flows. Source terms are used to account for the influence of hydrodynamic drag on the production, dissipation and exchange of turbulent kinetic energy between the phases. For the particles partial slip condition is considered at the wall.     

Computational fluid dynamics modelling of gas jets impinging onto liquid pools

Gas jets impinging onto a gas–liquid interface of a liquid pool are studied using computational fluid dynamics modelling, which aims to obtain a better understanding of the behaviour of the gas jets used metallurgical engineering industry. The gas and liquid flows are modelled using the volume of fluid technique. The governing equations are formulated using the density and viscosity of the “gas–liquid mixture”, which are described in terms of the phase volume fraction. Reynolds averaging is applied to yield a set of Reynolds-averaged conservation equations for the mass and momentum, and the k–ε turbulence model. The deformation of the gas–liquid interface is modelled by the pressure jump across the interface via the Young–Laplace equation. The governing equations in the axisymmetric cylindrical coordinates are solved using the commercial CFD code, FLUENT. The computed results are compared with experimental and theoretical data reported in the literature. The CFD modelling allows the simultaneous evaluation of the gas flow field, the free liquid surface and the bulk liquid flow, and provides useful insight to the highly complex, and industrially significant flows in the jetting system.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

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.     

Turbulent diffusion of mass in circular pipe flow

An implicit finite difference scheme was used to solve the convective-diffusion equation to predict the steady-state transport of a conservative, neutrally bouyant tracer injected along the centreline into a fully developed turbulent pipe flow. Three different distributions for the radial mass diffusivity have been compared with two independent sets of experimental data. The results indicate that the distribution based on the turbulent kinematic eddy viscosity predicted by a k?l model produces the closest agreement between the numerical model predictions and the experimentally observed tracer distribution.