Renormalization Group K-epsilon Research Articles

Numerical simulation of the effect of sulfide concentrate particle size on pollutant emission from flash smelting furnace

In this research, numerical simulation of three-phase flow (airflow, sulfide concentrate particles, and liquid fuel droplets) within a copper flash smelting furnace was conducted to investigate the effect of combustion of the sulfur present in the sulfide concentrates on temperature distribution and species production. The effect of sulfide concentrate size, amount of sulfur present in concentrates and air enriched with oxygen on sulfur combustion were numerically analyzed. The simulation was conducted using the Eulerian method for the continuous phase and the Lagrangian approach for discrete phases. The probability density function and the renormalization group K-epsilon model were used for combustion modeling and simulation of turbulence effects on the rate of chemical reactions. The discrete ordinate method was used to calculate the effect of radiative heat transfer. Results showed that when the amount of sulfur present in the concentrate particles increases, a higher level of sulfur release leads to an increase in the concentration of SO2, SO3, and SO. Also, by decreasing the concentrate particle size and increasing the rate of heat transfer to the particles, the amount of sulfur released increases. Since sulfur combustion occurs by high radiation, an increase in the sulfur released makes the temperature distribution more uniform within the furnace. Besides, by increasing the sulfur released, the concentration of CO2 decreases because gasoil competes with sulfur for oxygen consumption. Finally, it has been revealed that the amount of all species such as SO2, SO3, SO, CO2, and NOx, and the temperature increase using air enriched with oxygen.

Optimization of RANS turbulence models using genetic algorithms to improve the prediction of wind pressure coefficients on low-rise buildings

Being associated with natural ventilation, the pressure distribution on surfaces is relevant for energy consumption, thermal comfort, and air quality in buildings. The aim of this work is to present a simulation-based optimization methodology to recalibrate the closure coefficients of Reynolds-averaged Navier-Stokes (RANS) turbulence models in order to improve the prediction of wind surface-averaged pressure coefficients on a wide range of isolated low-rise buildings. To accomplish this, genetic algorithms and Computational Fluid Dynamics (CFD) simulations are dynamically coupled to find the closure coefficients set which minimize the CFD prediction error regarding wind-tunnel experimental data. The methodology is applied to two turbulence models, the renormalization group k-epsilon model (RNG) and the Spalart-Allmaras model (SA), considering as target cases buildings with different roof types (flat, gable and hip) and wind incidence angles. In order to show the strength of the novel optimal sets of closure coefficients obtained, an exhaustive validation is performed over other low-rise buildings (52 new cases) which were not calibrated against. Results validate using the optimal sets because the recalibrated RNG and SA models decrease the prediction error between 11-64% and 8–45%, respectively, regarding using the standard ones.

Model evaluation and experimental validation of thermal jet drilling for geothermal energy

Thermal jet drilling is a technology, which has the potential to be suitable for the exploitation of geothermal energy in relatively deep formations with low costs. Several investigations on this drilling method have been carried out for the depths of less than 1 km or deeper than 2 km. To the best of our knowledge, there is almost no specific study on simulation for thermal jet drilling at the depths between 1 km and 2 km. This paper focuses on investigating applications of different reaction (i.e., laminar, non-premixed, eddy dissipation concept, eddy dissipation model and finite rate), turbulence (i.e., standard k-epsilon, realizable k-epsilon, renormalization group k-epsilon and scale-adaptive simulation) and radiation (i.e., P1, discrete ordinate, discrete transfer radiation model and surface-to-surface) models to downhole reaction of thermal jet drilling. The objective is to identify the pros and cons of each model and determine a set of models that are the most appropriate for the reaction. Experiments are also carried out and data are collected as the benchmark for comparison. Relative errors and iteration for convergence are analyzed for each simulation model. Results show that the modified simulation temperature by considering the environmental temperature becomes more accurate compared with the experimental data. The laminar model over-predicts the temperature and yields unreasonable results. Finite rate and eddy dissipation model are the candidates with highest accuracy and acceptable computational time within selected model settings and boundary conditions. In addition, compared with renormalization group, realizable and scale-adaptive simulation turbulence models, the standard k-epsilon model is the most appropriate model under the conditions selected for this investigation. The discrete ordinate model can be applicable for the simulation if the error tolerance is 10%. The P1 model is the most suitable radiation model. Results in this paper can provide implications for the reaction simulation of thermal jet drilling.

Comparative study on turbulence models simulating inorganic particle removal in a Pista grit chamber

ABSTRACTNumerical simulations and experimental validations were conducted to determine grit removal efficiency and separation processes for inorganic suspended solids (ISS) with different particle sizes in a vortex-type grit chamber (Pista). The Euler–Lagrange method was used to simulate solid–liquid two-phase flow; the Unsteady Discrete Model was used to simulate the solid phase; and the Renormalization Group k-epsilon (RNG k-ε), Realizable k-epsilon (Real k-ε), and Shear Stress Transmission k-ω (SST k-ω) models were used to simulate the liquid phase. Results of the RNG k-ε model agreed well with the experimental results for particles with d ≤ 200 µm, with an average error of 7.10% (d < 100 µm) and 6.78% (100 µm ≤ d ≤ 200 µm). When particle size exceeded 200 µm, the Real k-ε model had the minimum average error (4.16%). Bed load transport and suspended load transport of the different size ISS particles presented in the grit chamber were important factors influencing grit removal efficiency. Pressure gradient and turbulence intensity distributions simulated by the three turbulence models were significantly different. Particles with diverse sizes reacted distinctly to the disturbance effect caused by pressure difference, which impacted on the accuracy and reliability of simulation results.

Performance study of erosion resistance on throttle valve of managed pressure drilling

The throttle valve designed for managed pressure drilling (MPD) is a core equipment of MPD technology. Due to the direct contact with drilling fluid at well site, the throttle valve's internal flow passage will be eroded and worn by the drilling fluid with high mobility, which would negatively affect the working performance and service life of the throttle valve. Therefore, based on the working principle and geometric structure of throttle valve, the computational fluid dynamics (CFD) technique is used to establish the three-dimensional fluid numerical model, and the renormalization group k-epsilon (RNG k-ε) model is selected for the turbulence model of liquid-solid two-phase flow in throttle valve of MPD. At the same time, the fluid flow in the wall region is solved by wall function which allows the physical quantity near the wall surface to connect with it in the core turbulence region. In addition, the discrete phase model (DPM) model is selected for the discrete phase model, and the Ahlert erosion model is selected for the erosion model. The finite volume method is used in discrete calculation, and the SIMPLE algorithm is applied in continuity equation, momentum equation, energy equation and turbulent kinetic energy equation when solving the control. The influences of drilling parameters (such as throttle valve opening, drilling fluid flow rate, drilling fluid density, mass flow rate of solid particle) on the erosion characteristics of throttle valve of managed pressure drilling are studied by CFD. The results show that the erosion of the solid particles on the wall of MPD throttle valve mainly occurs at the end of the valve spool. Meanwhile, the drilling fluid flow rate has the greatest impact on the erosion rate of solid particles, which is followed by the solid mass flow. Compared with the above two, the erosion rate of solid particles is less influenced by the throttle pressure difference between inlet and outlet which is caused by the change of throttle opening and drilling fluid density. In addition, the simulation result reaches a good agreement with the laboratory data of throttle valve erosion experiment. This study could give several advices for relevant throttle valve investigation work and operators who attempts to decrease the erosion in valves.

Numerical investigation of V-shaped riblets and an improved model of riblet effects

Symmetric V-shaped riblets are simulated by using the computational fluid dynamic method to understand the riblet effects on the turbulent boundary layer and the skin friction reduction. Three classical turbulence models, namely Spalart–Allmaras, shear stress transport, and re-normalization group k-epsilon models, are investigated under different grid densities. The re-normalization group model produces good results consistent with the experiment, as compared with the existing theoretical and experimental drag results of the flat plate and the V-shaped riblets with different sizes. Simulating V-shaped riblets yield the unexpected discovery that the shear stress transport model produces large errors, and the Spalart–Allmaras model even produces results of qualitative errors. Another finding is that von Kármán’s constants can no longer meet the requirement of describing velocity profiles in the logarithmic law layer. Aside from the traditional shift of the logarithmic law’s intercept, the slope is also changed by riblet height and spacing. Therefore, an improved model of riblet effects is proposed by redefining von Kármán’s constants.

Effect of Char Combustion Product Distribution Coefficient on the CFD Modeling of Biomass Gasification in a Circulating Fluidized Bed

A three-dimensional unsteady-state CFD (computational fluid dynamics) model is built to simulate biomass gasification in a circulating fluidized bed. The RNG (renormalization group) k-epsilon turbulence model is coupled with the enhanced wall treatment to describe the hydrodynamic regime of the gas-particle system. The conservation of momentum, mass, and energy equations are integrated with reaction kinetics to simulate chemical reactions in the gasifier. The impact of product distribution coefficient, θ, for char combustion on the CFD biomass gasification model is examined in nine cases. According to the simulation results, the coefficient of θ has a minor effect on the predictions of outlet gas compositions. However, it is found that the value of θ can influence the profile of gasifier temperature, and the peak temperature regions from the cases assigning 0.50 to the coefficient appear faster than those from the models using higher values of θ.

Experimental and Numerical Investigation of Flow under Sluice Gates

AbstractThe flow characteristics upstream and downstream of sluice gates are studied experimentally and numerically using Reynolds averaged Navier-Stokes two-dimensional simulations with a volume of fluid method. Special attention was brought to large opening and submergence, a frequent situation in distribution canals that is little seldom addressed in the literature. Experimental results obtained by ADV measurements provide mean velocity distributions and turbulence characteristics. The flow is shown to be mostly two-dimensional. Velocity fields were simulated using renormalization group k-epsilon and Reynolds stress model turbulence models, leading to an estimation of energy and momentum correction coefficients, head loss, and bed friction. The contraction coefficient is also shown to increase with gate opening at large submergence, which is consistent with the energy-momentum balance. This result can be used to derive accurate discharge equations.

Studies of the flow of air in a mixed-flow pump using numerical simulations

This article presents an investigation of the three-dimensional (3D) turbulent flow through the impeller passages and surroundings of a mixed-flow pump. Rotating passages of turbomachinery contain some very interesting and complex fluid flow phenomena. The model tested has five impeller blades mounted on a conical hub and nine stator blades in a diffuser which brings the diagonally outward flow back to the axial direction. Numerical calculations of the unsteady flow were carried out with the code Fluent, using air as the working fluid. Three models have been applied for turbulence closure: standard k-epsilon, renormalization group k-epsilon, and Reynolds stress model, using conventional wall functions near solid surfaces. For this transient 3D computation, the numerical grid has been decomposed into eight separate regions in order to process these in a parallel cluster of desktop computers. The results obtained show entirely reasonable correlations with previously published experimental data, as detailed in the performance curve comparisons and also in the numerical and experimental flow fields. These outcomes confirm that such a complex transient phenomenon may be reasonably captured by means of a commercial computational fluid dynamics code.

Simulation of mixed convection flow in a room with a two-layer turbulence model.

Most indoor airflows are mixed convection. In order to simulate mixed convection accurately and efficiently, this paper uses a two-layer turbulence model. The two-layer model combines a one-equation model for near wall flow together with the standard k-epsilon model for outer-wall flow. The model has been used to predict the mixed convection by displacement ventilation in an office. The computed results agree well with the corresponding airflow pattern and the distributions of air temperature, air velocity, air velocity fluctuation, and tracer-gas concentration. The model can predict correctly heat transfer from a wall where the standard k-epsilon model and re-normalization group (RNG) k-epsilon model with wall functions often fails. The computing cost required by the two-layer model is comparable to that of the standard k-epsilon model and RNG k-epsilon model and is significantly less than that by a low-Reynolds number model.

COMPARISON OF LINEAR AND NONLINEAR RNG-BASED k-epsilon MODELS FOR INCOMPRESSIBLE TURBULENT FLOWS

Linear and nonlinear renormalization group (RNG) k-epsilon models are compared for the prediction of incompressible turbulent flows. The multidimensional finite-volume code KIVA-3 \\[1] is used to explore the alternative models versus the standard k-epsilon model. Test cases include the classic backward-facing step and the confined co-flow jet flows. Our results suggest that the linear RNG k-epsilon model can yield significant improvements over the standard k-epsilon model for recirculatory flows, because of its less dissipative nature. While the nonlinear RNG k-epsilon model can also improve predictions compared to the standard k-epsilon model, its greatly increased cost compared to the linear RNG model renders it less attractive. However, for the case of shear flows, such as for confined co-flow jets, the RNG-based k-epsilon models are in less favorable agreement with experiments compared to the standard k-epsilon model. Overall, it is concluded that combining the claimed universality of the RNG-based k-epsilon model constants with the anisotropies introduced by the nonlinear k-epsilon model cannot enhance predictions of both recirculating and shear incompressible flows.

Numerical simulations of wind forces on Troll B

A three-dimensional computational fluid dynamics model is used to examine the air flow and forces (pressure and viscous) on a simplified geometrical description of the offshore production platform Troll B. The Navier–Stokes equations are used to describe the air flow except for flow through some specific regions of the platform such as the flare tower, where a Darcy formulation has been employed. The turbulence is modeled using the ‘two-equation’ renormalization group k-epsilon formulation. The equations are solved on an unstructured mesh using a control-volume based technique. The model is forced by prescribing wind velocity and turbulence level on the inflow open boundary where the vertical wind profile is designed to fit experimental data from wind tunnel tests. A no-slip boundary condition is applied at the sea surface and at the surface of the platform itself. To include effects of the presence of surface waves on the wind profile, a surface roughness length corresponding to a wave height of 2 m is introduced. Heeling of the platform due to wind forces is neglected. Flow fields and total drag/lift forces are computed for various wind directions. The results are compared with data from wind tunnel experiments of Troll B.

Asymptotic behavior of solutions of the renormalization group k-epsilon turbulence model

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.