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Abstract
Because of the introduction of a cylindrical swirling chamber into a neotype tundish, the Swirling Flow Tundish (SFT), the numerical simulation becomes difficult for this kind of tundish by the standard two-equation k-epsilon turbulence model. So another kind of k-epsilon turbulence model, the Renormalization Group (RNG) k-epsilon turbulence model derived from the theory of renormalization group, was adopted and compared with the standard one. Both of these two kinds of turbulence models were used to simulate the flow patterns in SFT on staggered grid systems based on Finite Volume Method (FVM) with SIMPLER algorithm for steady 3D and incompressible Newtonian turbulent flows. The comparison of simulation results from these two models shows that the RNG k-epsilon turbulence model for SFT leads quicker convergence than the standard one. Unsymmetrical flow patterns were obtained and the grid independence of this mathematical model for SFT was also discussed. The theoretical analyses of forces on particle, turbulent kinetic energy distribution and lower flow velocity behind dam and weir show that there will be a good effect for non-metal inclusion aggregation and separation with the swirling chamber.
... The k−ε model was chosen here: the idea is to introduce two equations governing the turbulent kinetic energy k and its dissipation rate ε. The more general model, derived from the NS equations [19] presents unknown constants, for which values are situation-dependent, and are available in literature [20]. There also exists a well established one equation model, the Spallart-Allmaras model [21], but on the one hand, it is more dedicated to external flows and on the other hand, the way to properly derive a turbulent conductivity has not been clearly investigated yet, so the following version of the k − ε model will be used here : ...
... x ∈ [a; s] (C. 19) y ∈ [F F ; F E; EF ; EE] (C.20) ...
... 19: 3d Empty cavity: streamlines along l c for Ra = 10 20: 3d Empty cavity: streamlines around x c for Ra = 10 21: 3d Empty cavity: streamlines along l c for Ra = 10 22: 3d Empty cavity: streamlines around x c for Ra = 10 4 ...
For heating and quenching operations occurring during material forming processes, thermal radiation is the the predominant physical phenomenon. Hence, when one tries to simulate such processes, it is important to have at disposal powerful tools for the numerical modelling of thermal radiation.The numerical simulation of these processes often rises numerous problems and questions, as the representation of a complex environment, involving several components ( ingots, burners, nozzles, walls), to deal with different coupled physical phenomena ( flow, heat transfer, boiling, thermal radiation). In this regard, some “immersed” numerical methods, allows a generalist treatment of these different problems, have gained popularity and drag interest of the scientific community in the recent years.The Thost project, aiming to produce a software for heat transfer during material forming processes, fits in the framework, and this PhD is part of this project. The goal is therefore to design tools for numerical modelling of thermal radiation within the immersed volume method of the Thost software. Two approaches are presented: one consisting in the adaptation of an existing method to the context of the immersed volume method, another concerning the development of a formulation for a specific model of radiation. These methods are then tested on industrial applications provided by our partners.
... RNG k − ε model is well suited for flows with large strain rates, large streamline curvature, low-Reynolds-number and near-wall flows [29], which has a similar form as the standard k − ε model. The transport equations for RNG k − ε model [30] are shown as: ...
... For the model constants the following values are chosen [30]: ...
The prediction of different shear stresses is one of the great challenges of turbulent–turbulentstratified two-phase flow in horizontal pipes. In this work, VOF method, near-wall differential viscosity and local turbulence viscosity distribution coefficient function are introduced and offer an efficient tool to correct the interface turbulence viscosity. The results show that the new method can better predict the shear stresses, liquid holdup and pressure drop of stratified two-phase flow. The fitting relationship between interfacial and wall friction factor (fi∕fW) is in good agreement with the experimental data. It is found that fi∕fW is predicted with a relative error of 12.62% by the new method, which is much less than that by any other method when the gas and liquid superficial Reynolds numbers are 8000≤ ReSG ≤90000 and 5000≤ ReSL ≤170000. It provides a reliable method for achieving the closure of stratified flow to predict the shear stresses.
... Comparing the results with experimental data, they concluded that the RNG model approximates the turbulence better in situations with high streamline curvature. Another study, by Hou and Zou (2005) using a swirling tundish, found that the RNG κ-ϵ model converges faster than the standard κ-ϵ model. ...
... The length of the nozzle is selected so that a fully developed profile forms at the port, as shown in Figure 7.9. The quantities of the turbulent properties at the inlet boundaries were calculated from equations 7.1 and 7.2, which have been used by several authors (Kumar et al., 2008;Hou & Zou, 2005;Solorio-Diaz et al., 2004) to obtain a good correlation between numerical and experimental results. It is also expected that due to the addition of the nozzle in the simulation, the results should be insensitive to the turbulent boundary conditions, since the turbulent properties will also develop along the nozzle. ...
In modern steelmaking a tundish serves as an important metallurgical reactor to remove inclusions and maintain thermal and chemical homogeneity in the product. In this study the flow behaviour in a four strand tundish was investigated by means of a 1/2 scale water model, based on Froude number similarity, as well as by using numerical modelling. Both the numerical study and physical model were used to characterise residence time distribution (RTD) in the vessel and to calculate properties pertaining to the tundish flow regime.
The three different tundish configurations investigated in this study are: a bare tundish with no flow control devices, a tundish with a turbulence inhibitor and a tundish using a turbulence inhibitor with holes in combination with dams. Preliminary investigations focussed on the framework for obtaining an accurate numerical solution within reasonable computational times. The effect of assuming symmetry and dynamically steady flow in the numerical model was shown to be small relative to the effect of grid size and justifiable by the savings in computational time. The grid independence study indicated the importance of using a finer mesh in areas of high velocity gradients to obtain realistic results and also to limit the number of computational cells. A procedure using gradient adaptation was used to refine the mesh automatically in the required regions for different tundish geometries. Results also showed that the inlet boundary of the numerical model should be selected at the ladle outlet, since assuming a flat velocity profile at the nozzle port resulted in significant changes in the RTD response.
Comparison of the results obtained using the numerical model with those from physical experiments yielded an average error of less than 10%. This was assumed to be a good prediction, considering the assumptions employed in the numerical model. Both the physical and numerical models showed that a tundish without flow control devices was prone to significant short circuiting. The addition of a turbulence inhibitor was shown to be successful in preventing short circuiting and provided surface directed flow, which is thought to aid inclusion removal in the slag. Additionally, the minimum, peak and mean residence times and plug flow volume fraction were increased significantly, while the dead volume fraction decreased. However, using a turbulence inhibitor with holes in combination with dams showed that this configuration may cause increased refractory wear together with increased risk of slag entrainment due to flow patterns with increased surface turbulence. It also showed that the short-circuiting might not be eliminated completely. This indicates that certain design changes to tundish flow control systems can introduce problems that outweigh the benefits of the altered flow patterns.
Furthermore, the numerical method, which was based on the water model, was modified to simulate the high temperature steel process. A very good match was obtained between the results using the two different numerical models. This serves as additional evidence that tundish water modelling based on Froude number similarity provides a good representation of the actual industrial process.
Using the numerical model based on the high temperature steel process the effect of turbulence inhibitor shape was studied for four different turbulence inhibitor designs. Results showed the best performance, based on flow characteristic properties and surface turbulence values, was achieved for the design using a rectangular box-like shape with flanges at the top. However, the comparison emphasized the effect of the turbulence inhibitor shape on the flow behaviour, as each design yielded completely different flow patterns. It was also observed that a good turbulence inhibitor provided an optimum amount of turbulent suppression. Insufficient suppression would cause fast flows, which will result in insufficient residence time for inclusion flotation and high surface turbulence values, which may cause slag entrainment. On the other hand, too much suppression may increase the variation between strands.
... Comparing the results with the available experimental data, they concluded, that the RNG model approximates the turbulence in flow situations with a high curvature of streamlines better than other models. Though the literature survey shows, that most of the simulation works were done by using the standard ε − k turbulence model, they [37] argued that this model, over predicts k values, because it does not take into account the fact that the strain rate of the flow field influences turbulence. Hou & Zou [37] reported the same type of conclusion. ...
... Though the literature survey shows, that most of the simulation works were done by using the standard ε − k turbulence model, they [37] argued that this model, over predicts k values, because it does not take into account the fact that the strain rate of the flow field influences turbulence. Hou & Zou [37] reported the same type of conclusion. They compared the standard ε − k turbulence model with the RNG ε − k turbulence model, while numerically simulating swirling flows in a tundish. ...
CFD modelling of melt flows in ladles and tundishes is an active area of research and has helped over the years in the understanding and improvement of the processes. The MMPC has been involved in the modelling and simulation of steel making ladle/tundish operations for the last 30 years, including review articles. In the last 3 years, the role of an overlaying slag in ladles was studied. Similarly, for the tundish, inert gas shrouding, alignment of the ladle shroud, and optimum configuration of dams and pads to improve the quality of liquid steel within the tundish, were all studied. The present paper summarizes the results obtained from numerical modelling with subsequent experimental validation, and reviews the general directions of modelling. Recommendations are made regarding amount of gas injection in shrouds, ladle change practices and positioning of flow control devices, for better tundish operations. Finally, the ultimate goal of these modelling efforts will be the development of a transient multiphase numerical simulator of the ladle-tundish system, which will be able to predict final cast temperature, residual ratios of inclusions, residence time distributions, amounts of slag entrained, and other important quantities of interest. For this, advanced computational facilities is a requisite.
... The choice of the turbulence model directly affects the accuracy of the numerical simulation. There are three types of k − ε turbulence model, namely standard k − ε, RNG k − ε and realizable k − ε Compared with the standard k − ε and realizable k − ε turbulence model, the RNG k − ε model is more suitable for predicting complex flow phenomenon, such as the flow in different shapes of pipelines (Mompean, 1998;Xia and Yadigaroglu, 1998), swirling flow (Hou and Zou, 2005;Xia and Yadigaroglu, 1998), turbulence line puffs (Lee and Chen, 1998), flow over backward-facing step (Darmawan and Tanukaya, 2019;Papageorgakis and Assanis, 1999) and confined co-flow jets (Papageorgakis 1999). In addition, the RNG k − ε turbulence model is usually considered to provide more accurate results than the standard k − ε model for flows with a well-defined air-water interface, flows with low turbulence intensity and flows with important shear regions (Bombardelli et al., 2011). ...
... where t is time,ṽ is velocity, p is pressure, r m is the density of liquid and m eff is the effective viscosity including the turbulent eddy viscosity and the laminar viscosity. The RNG k-e turbulence model was utilized to calculate the mean flow characteristics of the turbulent flow in tundish since this model showed significant advantages over the common standard one [33]. An enhanced wall function was also invoked to work with the RNG k-e turbulence model. ...
The baffle effect of inserting a filter within a tundish was investigated using a combination of water model experiments and numerical simulations. The filter, which is a cost-effective device used to enhance the quality of molten steel by removing inclusions, was studied for its impact on the removal rate of inclusions. In the water model experiments, a scaled-down model of the tundish system was created with a geometric ratio of 1:4. Polyethylene particles of varying sizes were used to simulate the inclusions. Additionally, a three-dimensional numerical model of the water model was developed to validate the experimental findings, provide supplementary data for analysis, and propose an optimized tundish configuration by moving the weir away from the filter by 50, 100, and 150 mm. The flow patterns were also thoroughly examined. The results revealed that the presence of the filter increased the flow resistance within the tundish, leading to changes in the residence time distribution. This resulted in the formation of a ‘dead zone’ with a significantly prolonged residence time. The higher flow resistance hindered the entry and exit of particles from the last chamber of the tundish. As a result, the distribution of particles in the last chamber became more dispersed, reducing the detrimental effects of inclusions in the steel. The removal efficiency of the seven types of particles was improved by 2–7%. Furthermore, by moving the weir away from the filter by 50 mm, the removal ratio could be further increased by approximately 2%.
... Based on the Navier-Stokes equations, various turbulence models, like k-e, RNG k-e, Realizable k-e, LES, etc., are available in calculating the flow and temperature field in the tundish. The Euler-Euler model or Euler-Lagrange model was often used to calculate the movement of inclusions [12][13][14][15]. In the prediction of electromagnetic field, the finite element method was widely adopted to solve the Maxwell equations [16][17][18][19]. ...
The key to acquire good metallurgical effects with induction heating tundish is to understand the flow field, temperature field and the movement of inclusions in the tundish with different induction heating power curves. Based on the production of a factory, this work established a multi-field coupling mathematical model to find out the link between the heating power curve and the metallurgical effects of the tundish. The results indicated that the heating efficiency of an induction heating tundish not only was affected by the heating power, but also related to the flow and temperature field in the tundish. When the induction heater was used intermittently and the induction heater was turned on, the molten steel was controlled by electromagnetic force, and the flow field basically remained stable. However, when the induction heater was turned off, the velocity of molten steel got small, and the thermal buoyancy could greatly change the flow, forming short-circuit flow; besides, large number of inclusions suddenly escaped from the outlet of the tundish. When the molten steel was heated continuously, the flow field, temperature field and inclusions behavior remained basically unchanged. Considering both energy saving and maintaining good metallurgical effects, continuous heating (the power increasing stepwise over time) should be selected.
... The initial numerical solutions of the model for the thermal accumulator, described in the next part of the paper, proved the advantage of Renormalization Group (RNG) k-epsilon turbulence model -it leads to a quicker convergence than the standard one. That is in accordance to the tips for the modeling of the turbulence in [10] and the conclusions of other research of turbulence flows with swirls [11]. The influence of the buoyancy on the turbulence is taken into account using Boussinesq buoyancy model in the production and dissipation terms in the RNG k-epsilon model. ...
Mathematical model for numerical simulation of the transient heat transfer and fluid flows in water thermal energy storage tanks is developed. The model allows analysis of the thermal fields in the accumulators at different schemes and modes of charging and discharging. It was verified and validated based on experimentally obtained information about the temperature stratification at charging of a thermal accumulator at a laboratory solar system. The proposed approach for numerical study of the thermal energy storage is convenient for parametrical estimation and improvement of the efficiency of the thermal systems.
... There are many turbulence models suitable for incompressible fluid flow. In the numerical calculation of pump devices, the standard k-ε model is widely used in engineering, and its numerical calculation results and model test results match well [22][23][24][25][26]. The modified turbulent viscosity of the model considers the rotation and rotation flow in the average flow, which can better deal with the flow with high strain rate and large streamline curvature [27]. ...
The deflection flow of inlet passage seriously affects the performance of axial flow pump devices, and reduces the operation efficiency and stability of pumping station systems. In this paper, the influence of different deflection angles on the internal flow characteristics and outlet pulsation characteristics of the inlet passage of the vertical axial flow pump are studied. Based on the Reynolds time-averaged N-S equation of the three-dimensional incompressible fluid and the standard k-ε turbulence model, the model axial flow pump device was numerically simulated. Under optimal working conditions (Qbep = 31.04 L/s), the internal flow field of the axial flow pump was analyzed to study the change law of the axial flow pump performance under different deflection angles. Under the flow conditions of 0.6 Qbep, 1.0 Qbep and 1.2 Qbep, the pulsation characteristics of the outlet of inlet passage in axial flow pump at different deflection angles were analyzed. The result shows that with the increase of the deflection angle, the flow pattern of the inlet passage becomes turbulent, forming vortices of different sizes, the hydraulic loss of the inlet passage increases continuously, and the uniformity of the outlet flow velocity of the inlet passage increases first and then decreases. The time-domain waveform of outlet of the inlet passage at the pressure pulsation monitoring point has obvious periodicity, and the dominant frequency of the monitoring point is four times the rotation frequency, which corresponds to the number of impeller blades. It shows that the numerical calculation is in good agreement with the experimental results, which proves the reliability and validity of the numerical simulation calculation.
... Therefore, the RNG turbulence model, which also gave the second best result in our study, is equally valid for both low and high Reynolds number flows. Effective use of this feature does, however, depend on an appropriate treatment of the nearwall region (Hou and Zou, 2005). A new k-eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, was proposed by Shih et al. ...
Experimental and numerical studies were carried out to determine the full-scale Oxidation Ditch (OD) hydrodynamics considering various turbulence models. Firstly, the experimental work was carried out in a full-scale plant by Acoustic Doppler Velocimeter (ADV) for field-measurements. Secondly, the experimental data was used to validate numerical models by using Computational Fluid Dynamics (CFD) software Ansys Fluent. Eight different turbulence models were compared in the numerical study to predict full-scale hydrodynamics. Results showed that standard k-ɛ, renormalization group k-ɛ, realizable k-ɛ turbulence models gave more accurate prediction results with relative errors of 13%, 17%, and 18% respectively, whereas the standard k-ω turbulence model gave the worst prediction results with 39% relative error. This study also shows that the velocities in the ODs are very low without external force such as air diffusers, rotors, and mixer and there is no homogeneous flow field distribution in the ODs. Moreover, the maximum wastewater velocities occurred at the inlet and outlet.
... The results showed that RTD parameters were completely different under isothermal and non-isothermal conditions. In a numerical investigation, Hou and Zou [68] have studied the molten steel flow patterns and inclusion separation in different designs of tundishes. Digital particle image velocimetry was used to measure the internal flow. ...
Continuous casting process is an important process to produce steel. Nowadays, steelmakers are focusing on improving the process capabilities, efficiency, and product performance in terms of mechanical properties. Hence, various ways have been devoted by researchers globally to improve the continuous casting process and final product quality. Mathematical modeling of steelmaking tundish is an important aspect to enhance process capability of continuous casting system especially improving the steelmaking tundish performance. In the present work, we have reviewed the recent progress made in the mathematical modeling of steelmaking tundish. Since tundish is an important last metallurgical reactor, so vast importance has been given to modify and enhance tundish performance to increase mechanical properties by reducing impurities. We have reviewed the most important aspects of mathematical modeling such as melt flow, heat transfer, turbulence modeling, grade mixing, and refractory wall study, etc. This review work would be helpful t understand the basic mathematical modeling practice of steelmaking tundish.
... Velocities indoors are usually low (under 0.1 m/s) and sometimes air flows may not be fully turbulent. Models employing modified versions of the k − ε model, such as the Renormalisation Group (RNG) model, seem to provide acceptable results [28], but there needs to be a critical reflection on the use of turbulence models in indoor heritage spaces. There are references to the adoption of SST (shear stress transport) k-ω models for application in indoor environments [29]. ...
Since their excavation, a number of the sites listed as part of "The Megalithic Temples of Malta" inscription on the UNESCO World Heritage list have been afflicted by material and structural problems, including collapses. Therefore, three of these sites, the Ħaġar Qim, Mnajdra and Tarxien Temples, were protected by open-sided shelters, to address some of the principal causes of deterioration (e.g. direct rainfall, surface weathering, thermal stress). Environmental monitoring, condition assessments and biological surveys of the three sites took place before and after sheltering and are still in progress. To understand how the shelters are affecting these structures, a research programme has started aimed at analysing, through Computational Fluid Dynamics (CFD), the environmental data collected over a period of more than ten years. The aim of using CFD on the Temples is to provide detailed information on how different environmental conditions can affect the sites. For the CFD, macro and meso scale approaches will be used. The macroscale model represents the regional environment, including the all-terrain features around the Temples. Mesoscale modelling represents the Temple structures in a more detailed way. The final goal is to find confident correlations between CFD, and representative areas selected within the Temples showing particular deterioration patterns. All this information will be integrated with the results of in situ analyses to identify the causes of material deterioration and possibly mitigate against them.
... The equation constants that are found empirically in the standard k-ε model are derived explicitly in the RNG model. In particular, the RNG model is known to describe more accurately swirling flows, low intensity turbulence flows and flows having strong shear regions [19,20]. ...
A performance study of a stilling basin located downstream of 140 m high dam was attempted in the study using numerical simulation. The hydraulic characteristics of the stilling basin of 140-MW Tanahu (Upper Seti) Hydropower Project situated in Tanahu district in Nepal were investigated by numerical simulation using Computational Fluid Dynamics (CFD) modelling. The flow patterns, velocities at various locations with three different elevations: 293.00, 305.00, 309.00 masl and water levels along a main water course in stilling basin were recorded. A comparative study was made in order to evaluate the capability of the computational fluid dynamics on modeling stilling basin flow, by using results obtained from physical modeling and CFD simulation. FLOW-3D that solves Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup. The flow behavior inside the stilling basin was well represented by the numerical model and there was reasonably good agreements in flow characteristics between the physical and numerical models. The deviations in water levels between physical and numerical model were below 1.9 m and that in flow velocities were below 30%.
... The RNG k-e model was recommended for the simulation of strong swirling flow in tundish. [23] Furthermore, the Euler-Lagrange method was extensively employed to clarify the trajectory of the inclusion. It is seen that an ideal absorption condition has been applied to the slag-steel interface in most of the numerical model studies. ...
Multi-hole ceramic filter is regarded as an effective and cheap method of additional flow control device in tundish. In order to evaluate the performance of the ceramic filter, a transient three-dimensional (3D) comprehensive numerical model has been developed to study the flow pattern, temperature distribution and residence time of the molten steel, as well as the elimination of inclusion in a full size two-strand tundish. One-way coupled Euler–Lagrange approach with random walk model was adopted to track the inclusion motion trajectory. The gravity, buoyancy, drag, virtual mass, lift, pressure gradient, and rebound forces were included. The inclusion Reynolds number was utilized for the judgment of the inclusion separation at the slag-steel interface and the internal surface of the filter hole. Besides, the residence time distribution curve has been analyzed for figuring out the macroscopic mixing of the molten steel. The results indicate that the ceramic filter increases the flow resistance of the molten steel in the tundish, resulting in a longer residence time and a higher temperature drop. Except removed by the covering molten slag, the inclusion could also be trapped by the filter hole when the molten steel travels through the ceramic filter. The elimination of the smaller inclusion is significantly improved. The removal ratio of the 1 μm inclusion in the tundish without ceramic filter is only 59.3 pct, while the value is improved to 65.3 pct if we apply the ceramic filter with slenderness ratio of 3 to the tundish. And with the slenderness ratio changing from 3 to 5, the removal ratio of the 1 μm inclusion increases from 65.3 to 72.0 pct. Additionally, the ceramic filter could counteract certain side effects of the increasing inclusion density on the removal, especially for the smaller inclusion. With the inclusion density increasing from 3990 to 5000 kg/m³, the removal ratio of the 1 μm inclusion decreases by 14.5 pct in the tundish without ceramic filter, and after using the ceramic filter, the removal ratio decreases by 13.0, 7.4, and 5.0 pct with the slenderness ratio varies from 3 to 5.
... In this context, a sharp surface tracking technique, VOF, is adopted in this paper to study the splashing and sloshing phenomena in the slag stabilization process. The RNG k-e model is used in this work for the following reasons: (1) the choice of turbulence model is critical for simulation of the particle migration and mixing phenomena (Crowe et al., 1996;Jha et al., 2003); (2) the RNG k-e model outperformed the standard k-e model in rotating flows (Schwarze et al., 2001;Hou and Zou, 2005). In addition, the LES model, as an advanced turbulence model, is also applied for modeling the turbulence. ...
The hydrodynamics of a gas-viscous liquid flow is numerically studied by coupling the Volume of Fluid (VOF) method with the Renormalization Group (RNG) k-ɛ model or Large Eddy Simulation (LES) (VOF-RNG or VOF-LES). The simulations are validated by Particle Imaging Velocimetry (PIV) measurements. Averaged flow features are predicted by 2D and 3D VOF-RNG/LES models. Only the 3D VOF-LES model predicts the velocity fluctuation well. The Dynamic Smagorinsky-Lilly (DSL) Subgrid-scale model slightly outperforms the Wall-Adapting Local Eddy-Viscosity (WALE) subgrid-scale model. Subsequently, flow characteristics of a gas-viscous liquid flow are studied by the validated 3D VOF-LES-DSL model under industrially relevant conditions. Gas penetration depth, flow velocity attenuation, surface sloshing and slag splashing are quantitatively described. The flow regime is identified through the pressure data monitored in the lance and its Fast Fourier Transform (FFT) results. The study of the coherent structures shows strong vortices in the top part of the slag pot.
... Renormalization group k-ε turbulence model (RNG k-ε) is a turbulence model derived from the renormalization group theory. It has the advantage of higher precision and quicker convergence than the standard k-ε model [30]. Hence, it was used as the closure model in this study. ...
The hydrodynamic and thermodynamic characteristics of a heat exchanger muffler (HEM), which can reduce the size of a marine engine exhaust system with waste heat recovery, were investigated using a numerical simulation method that combines the porous media model and the dual cell heat exchanger model. The effect of the thermal conductivity and dynamic viscosity of the exhaust gas on the heat transfer and pressure loss of the equipment was studied. The relationship between the heat transfer and the pressure drop of the equipment for various mass flow rates of the exhaust gas was investigated. It is shown that heat transfer conditions of the HEM could be enhanced by increasing the thermal conductivity or dynamic viscosity of the exhaust gas. To further improve the performance of the HEM, a design modification for optimizing the structure of the guide blade was proposed and numerically validated.
... The renormalization group (RNG) k-e two-equation turbulence model is adopted in this work based on the previous study [11]. The governing equations for the steady flow are solved within a finite control volume are presented as follows. ...
... In order to obtain the solution of equations, the standard k ε − turbulence model is applied to calculate the complex turbulent problems with high Reynolds number. The turbulence equation can be written as [9] [10]: ...
... To model an impinging turbulent lubricant jet, a standard k-ε computational fluid dynamics (CFD) model is used. The governing equations for conservation of mass and momenta for each phase in a 3D Newtonian and incompressible turbulent flow are based on the approach outlined by Hou and Zou [13]. The interface between the immiscible liquid lubricant and the liberated vapour phase is monitored using the Volume of Fluid (VOF) method [14]. ...
Improved fuel efficiency is the primary objective in the optimization of modern drivetrain systems. Recently, the dry sump lubrication system is regarded as the lubrication system for high performance transmission systems. Dry sump lubrication enhances the system
efficiency by reducing the churning losses, whilst providing sufficient lubrication for the tribological contacts. One of the most important aspects of any dry sump system is assessment of the thermal performance. The generated heat in the contacts should be dissipated through impinging jets and air-oil mist in the transmission casing in an efficient manner. The present work incorporates a tribological model and a 3D CFD model into a finite element model. The aim is to evaluate the quantity of generated heat in the lubricated gear pair contacts, as well as heat removal rate due to an impinging oil jet. Furthermore, the transient circumferential temperature distribution on gear surfaces is determined. This provides an accurate input temperature for the entrant lubricant in the gear teeth-pair contacts. Such an approach has not hitherto been reported in literature.
To perform time-efficient system level analysis in the finite element model, extrapolated equations are obtained from a transient 3D CFD model using regression formulae.
... To model an impinging turbulent lubricant jet, a standard k-ε computational fluid dynamics (CFD) model is used. The governing equations for conservation of mass and momenta for each phase in a 3D Newtonian and incompressible turbulent flow are based on the approach outlined by Hou and Zou [13]. The interface between the immiscible liquid lubricant and the liberated vapour phase is monitored using the Volume of Fluid (VOF) method [14]. ...
Improved fuel efficiency is the primary objective in the optimization of modern drivetrain systems. Recently, the dry sump lubrication system is regarded as the lubrication system for high performance transmission systems. Dry sump lubrication enhances the system efficiency by reducing the churning losses, whilst providing sufficient lubrication for the tribological contacts. One of the most important aspects of any dry sump system is assessment of the thermal performance. The generated heat in the contacts should be dissipated through impinging jets and air-oil mist in the transmission casing in an efficient manner. The present work incorporates a tribological model and a 3D CFD model into a finite element model. The aim is to evaluate the quantity of generated heat in the lubricated gear pair contacts, as well as heat removal rate due to an impinging oil jet. Furthermore, the transient circumferential temperature distribution on gear surfaces is determined. This provides an accurate input temperature for the entrant lubricant in the gear teeth-pair contacts. Such an approach has not hitherto been reported in literature. To perform time-efficient system level analysis in the finite element model, extrapolated equations are obtained from a transient 3D CFD model using regression formula.
... In the present case, we have used the version of the K -Ɛ model of Launder and Spalding [17]in which K is the specific turbulence energy and Ɛ is the rate of turbulence energy dissipation. Turbulent kinetic energy [5,6,8,14]: ...
... The RNG model, developed using methods by Yakhot and Orszag (1986), renormalizes the Navier-Stokes equations to focus on smaller scales of motion over the standard k-, thus leading to improved simulation performance regarding highly strained flows. This model is employed also due to its improved accuracy for capturing the effect of swirl on turbulence, and flows with strong streamline curvatures, vortices, and rotation (ANSYS R Fluent R , 2012; Hou & Zou, 2005;Jawarneh, Tlilan, Al-Shyyab, & Ababneh, 2008;Papageorgakis & Assanis, 1999). This simulation shows regions of highly strained flow near the inlets, thus making the choice of this model appropriate for this simulation. ...
Removal of volatiles and other unwanted products in a polymer mix is a critical step in polymer manufacturing. This process serves many purposes, such as improvement in the physical and chemical properties of the polymer, elimination of odours, recovery of monomers and solvents, and fulfilment of environmental regulations. In this study, the mixture of polymer and solvent, or cement, is mixed with superheated steam which causes the unwanted solvent to evaporate. As the cement droplets lose solvent and dry out, they are ejected as cement ‘crumb’ from the mixing device. This process is modelled using computational fluid dynamics (CFD) to gain insight into the complex phenomena. The model simulates the heat transfer and phase changes associated with cement and steam, via 3D axisymmetric calculations. Using an Eulerian–Lagrangian approach, the superheated steam is modelled as the continuous phase and tracked in an Eulerian frame, while the cement droplets are treated using a Lagrangian tracking method, thus as a whole allowing us to track the particle sizes, temperatures, and solvent content. Furthermore, a parametric study is carried out to analyse the effect of initial polymer temperature on final polymer product. The simulation is carried out with three different initial polymer temperatures and the resulting solvent concentration, and the size of the cement particles between the three cases are compared. By increasing the cement operating temperature, the solvent concentration in the cement crumb is significantly lower, and the final cement crumb sizes shows a slight decrease, which indicates better production performance. Indeed, full 3D CFD calculations, presented to verify the axisymmetric assumption, show differences in the particle statistics, which could have implications for design considerations. Such studies can provide further insights into control parameters that can potentially enhance the efficiency of such a manufacturing process.
... [14] New proposals to control steel flows in tundishes include the use of a rounded wall in a delta tundish, which smoothes the steel flow and improves the performance of the tundish. [15] Hou et al. [16][17][18] proposed a swirling flow tundish (SFT), whose main objective is to give the entry jet a swirling motion by entering through a cylindrical swirling chamber. It was shown that the SFT was more efficient in the removal of small inclusions (20 lm) than a turbulence inhibitor. ...
A new concept for a ladle shroud was tested and compared to the performance of a conventional ladle shroud. For that purpose, an experimental study was carried out which included physical modeling using red dye tracer and flow fields determinations obtained through PIV techniques. From the results the following conclusions can be drawn: 1. The bare tundish with the conventional LS produces strong short circuiting to the inner strands. The average residence times increase in the order, Case 1, Case II, Case III and Case IV. 2. The best fluid flow uniformity (homogeneity of distribution of tracer to the four strands) was obtained using the Case II arrangement. However, larger mixing volumes in the inner strand may be useful such as those obtained in the case IV. 3. The entry jet into the tundish using the LS provides a characteristic one-phase straight jet with small interactions with the surrounding flow unless the input of kinetic energy is high. Using the DLS, transient jet deformation flows are developed whose frequency of oscillation increase with increases in the kinetic energy input, or steel throughput. 4. Downward kinetic energy and fluid velocities are radically decreased by the DLS, thanks to the dissipation rate of energy spent in creating intermittent-turbulent boundary layers with the surrounding fluid, resulting from deforming jet motions. 5. The feasibility of substituting flow control devices in current tundishes using the alternative DLS appears promising.
... This would include the removal of all dams, weirs, and turbulence inhibiters. Hou and Zou [165] studied the flow patterns in a new type swirling flow tundish fitted with a swirling chamber. Numerical simulations suggested that the RNG k–e model was the most suitable turbulence model for this new type of tundish and can get convergent results more easily than the standard k–e model for strong curvature flows and flows with different Reynolds numbers in different areas (see Figure 4.3.16). ...
Section 4.3 provides an updated literature review and discussion of the many metallurgical processes that have been modelled using Computational Fluid Dynamics (CFD). Following a brief introduction to CFD techniques, their application to flows in Iron Blast Furnaces and to the design of these impressive reactors, and to others, such as COREX, FINEX, and HIsarna, are presented. These latter reactors are succeeding in by-passing the coke production step needed for the blast furnace route. CFD applications in Basic Oxygen Furnaces and in its off-gas management are next reviewed, followed by flows in ladles, in tundishes, and in continuous casting moulds. It is concluded that the advent of CFD and ever increasing computing “power” has created a revolution in the field of liquid metal processing, and that this will lead to better processes, and to better quality products.
... [14] New proposals to control steel flows in tundishes include the use of a rounded wall in a delta tundish, which smoothes the steel flow and improves the performance of the tundish. [15] Hou et al. [16][17][18] proposed a swirling flow tundish (SFT), whose main objective is to give the entry jet a swirling motion by entering through a cylindrical swirling chamber. It was shown that the SFT was more efficient in the removal of small inclusions (20 lm) than a turbulence inhibitor. ...
The aim of this research work is to study a new ladle shroud concept and design to assist in the reduction of slag emulsification in the tundish during ladle change-over operations. For this, a tundish analogue water model is designed and constructed based on Froude similarity criterion; a deeper analysis of the flow behavior is undertaken by mathematical simulation. Tap water and silicon oil are employed to simulate molten steel and slag. The modeling results show that using a conventional ladle shroud, the water is delivered with an excessive amount of turbulent kinetic energy which is dissipated inside the tundish bath, generating strong mixing flow patterns and entrapping a massive amount of oil. Furthermore, during this transient operation the conventional shroud induces oil dragging into the bath at zones next to the entry volume, producing continuous oil emulsification. In contrast, the proposed ladle shroud dissipates the turbulent kinetic energy before the water enters the tundish model, promoting less intense mixing patterns. Also, the dragging zone disappears; thus, the amount of oil emulsification is reduced significantly. Consequently, if the turbulent kinetic energy is dissipated before the steel enters the tundish, it will be possible to reduce the slag emulsification and the slag opening area.
... Generally, three kinds of FCDs can be classified depending on their locations: (1) located at the outlet of tundish, for instance, stopper rods; 1) (2) located in the tundish, such as turbulent inhibitors, weirs and dams; [2][3][4] (3) located at the inlet of the tundish, i.e., ladle shrouds. [5][6][7][8][9][10][11] The first two kinds of FCDs have earned widespread attention and gotten significant development. For the ladle shroud, it is a new research field to employ it as a flow control device for tundish operation and even replace other FCDs. ...
Flow structures were investigated in a dissipative ladle shroud (DLS) and a tundish using Large Eddy Simulation. The numerical results were validated inside the DLS and the tundish with PIV experiments. Velocity distribution, vorticity islands and strain rate were analyzed in the DLS respectively, compared with that of a bell-shaped ladle shroud (BLS). The results showed that the three chambers of the DLS gave rise to velocity differences, fluctuating strain rates and vortices, and promoted an increase on turbulence dissipation rate; and the average velocity of outflow ranged from 0.25 to 0.5 m/s when the inlet velocity was 0.708 m/s. In the BLS, the stream flowed straightforward with relatively consistent velocity; apparent vortices were only formed in the bell end; and the outflow went down with high speed and turbulent kinetic energy. The dissipative effect of the DLS was also validated by the flow structure in the tundish. When the stream left the outlet of the DLS, it swung, got twisted and was mixed with more surrounding fluid in the tundish which decreased the mean skin friction coefficient of tundish wall and the velocity of free surface, and finally contributed to a better tundish performance.
... In a recent work of Siddiqui and Jha (2014), the predicted F curve showed a good agreement with KCl tracer measurements when using the RNG k-ε model. Besides, the RNG k-ε model was recommended for simulations of strong swirling flows in tundishes (Hou and Zou, 2005). It should be mentioned that, in all of the models, the tracer is treated by scalar transport equations without coupling the density of a tracer (at least they did not mention that the density was coupled). ...
In an earlier research (Chen et al. 2015a) a mathematical model was established to simulate tracer mixing (a KCl solution). The predicted Residence Time Distribution (RTD) curves showed good agreements with experimental RTD curves for larger amounts of tracer additions. However, for smaller additions (50mL) of a KCl solution into water, the predicted RTD curves tended to deviate from the experimental RTD curves for a tundish (a continuous flow reactor). The current paper focuses on the possibilities that the predictability for smaller additions could be resolved by using a suitable turbulence model. The performance of five different turbulence models representing different modelling techniques and levels of complexity were tested in combination with using a density-coupled mixed composition fluid model to simulate the mixing, i.e. the following models: LVEL, Chen-Kim k-ε, MMK k-ε, Explicit Algebraic Reynolds Stress Model (EARSM), and Large Eddy Simulation (LES): Wall-Adapting Local Eddy-viscosity (WALE). The results indicate that models that tend to resolve turbulence structures renders better predictions of the mixing process of smaller tracer amounts. In addition, the influence of different tracer amounts on the flow in tundish was assessed. The simulation results for 75mL, 100mL, 150mL, and 250mL KCl tracer additions were compared. The results showed that in an upward flow the tracer will, sooner or later (dependent on the tracer amount), sink to the bottom. This is due to the higher density of the tracer compared to the density of water. From a physical modeling perspective, this issue is like the “butterfly effect”. It is showed that for a slight increase of the amount of tracer, the flow field might be disturbed. This, in turn, will result in a shifted RTD curve.
Flow efficiency in a two‐strand continuous casting tundish is studied by analyzing the residential time distribution (RTD) curves in a small‐scale tundish water model using a conductive NaCl solution tracer. The velocity fields in the tundish water model are measured by particle image velocimetry, which is used to validate the results of the mathematical model in the article. It is found that the tracer concentration has a significant impact on the predicted dead volume fraction in the RTD analysis. Validated mathematical modeling of the computational fluid dynamics (CFD) technology is performed to explore the root cause of the defective results in the RTD analysis. It is found that the flow inside the tundish is sensitive to density variations caused by the injected tracer. A denser tracer will stay lower in the tundish by gravity and flow out of the tundish more quickly. A proper tracer concentration in the water model experiments is discussed to visualize the dead volume and improve tundish furniture design efficiently for future work, a new method using CFD modeling is proposed in this article, which can directly demonstrate the dead volume's location.
The swirling flow generated by the swirling chamber of the split swirling flow tundish can effectively promote the collision and growth of inclusions. The split swirling flow tundish can promote the removal of inclusions by improving the flow field. In this work, the CFD-PBM coupling model was applied to simulate the transport, aggregation, and floating removal of inclusions in the split swirling flow tundish, and compared with a same-size T-type tundish. The results indicated that the swirl flow can effectively promote the collision-coalescence of inclusions. Comparing the flow field of the split swirl tundish and the T-type tundish, the dead flow fraction of the two tundishes is similar, but the plug flow fraction of the split swirling flow tundish is 4.5% larger than the T-type tundish. Monitoring the volume concentration of inclusions at the outlet of the two tundishes, the inclusion removal rate of the T-shaped tundish and split swirling flow tundish are 29.28% and 34.33%, respectively. Therefore, the split swirling flow tundish is stronger than the T-shaped tundish in removing inclusion. Especially in the removal of small inclusions, the number density of 1.00–28.64 µm inclusions at the outlet of the split swirling flow tundish is 29.97%–65.91% lower than the T-type tundish, the split swirling flow tundish enhances the removal of small inclusions.
Computational Fluid Dynamics (CFD) is often used for analyzing natural ventilation but is limited in early design stages due to its high computational demands and the need for detailed inputs. To overcome such limitations of CFD simulation, this paper proposes a method using a conditional Generative Adversarial Network (cGAN)
based image-to-image translation (Pix2Pix) to predict the indoor airflow condition. Compared to other traditional machine learning models that predict averaged values like indoor air velocity, Pix2Pix can predict contour plot of indoor airflow for the given building floor plan image, which provides more intuitive feedback to designers. The
proposed method was tested to understand indoor air movement caused by wing-walls attached to the windows. The model was trained using 1,153 pairs of floor plan images, incorporating variations in window widths, wing-wall depth, wing-wall angle, wind speed, and wind direction. It achieved a prediction accuracy of 94% and produced results in less than a second. Moreover, the model showed relatively better performance with the changes in windows and wing-walls properties rather than wind properties. This high performance indicates that Pix2Pix can serve as an efficient proxy model of conventional CFD simulations, helping designers optimize ventilation in building designs at an early stage without the need for complex inputs.
Bu çalışmada bitki örtüsünün, dikdörtgen bir açık kanal üzerindeki akım özelliklerine olan etkisi, Hesaplamalı Akışkanlar Dinamiği analizi kullanılarak incelenmiştir. Hesaplamalı Akışkanlar Dinamiği (HAD) için ANSYS Fluent yazılımı kullanılmıştır. Akımın üç boyutlu, sıkışmayan, türbülanslı ve kararlı olduğu kabul edilmiştir. Sayısal çalışma literatürde yapılan deneysel bir çalışma ile doğrulanmıştır. Sayısal çalışmanın deney sonuçlarını başarılı bir şekilde tahmin ettiği gözlemlenmiştir. Sayısal çalışma ve ölçüm sonuçları arasındaki bağıl hata %10’un altında bulunmuştur. Yapılan sayısal çalışmalar sonucunda, bitki örtüsünün kanalın akım ve türbülans özelliklerini önemli ölçüde değiştirdiği gözlemlenmiştir. Bitki örtüsü olan bölgelerde, su yüzeyinde hızların çok düşük olduğu, yaprak örtüsünün altında kökler arasında ise hızların yüksek olduğu ve maksimum hızın 0,1177 m/s ile bu bölgede gerçekleştiği tespit edilmiştir. Ayrıca türbülans viskozitesinin serbest alanlarda fazla olduğu gözlemlenirken türbülans enerji kırılımının katı-sıvı temas bölgelerinde fazla olduğu görülmüştür. Bu çalışma, açık kanal akışının bitki örtüsüyle etkileşimini anlamak ve açık kanal sistemlerinin hidrolik açıdan performansını geliştirmek için önemli bilgiler sağlamaktadır.
The evolution of in-cylinder flow involves small and large-scale structures during the intake and compression strokes, significantly influencing the fuel-air mixing and combustion processes. Extensive research has been conducted to investigate the flow evolution in medium to large-sized engines using laser-based diagnostic methods, computational fluid dynamics (CFD) simulations, and zero-dimensional (0-D) based modeling. However, in the present study, we provide a detailed analysis of the evolution of flow fields in a small-bore spark ignition engine with a displacement volume of 110 cm3. This analysis employs a unique methodology where CFD simulation is performed and validated using measured particle image velocimetry (PIV) data. Subsequently, the validated CFD results are utilized to develop and validate a 0-D-based model as it is computationally more efficient. The validated CFD simulation and 0-D-based model are used to evaluate the quantified strength of the flow fields by calculating the tumble ratio and turbulent kinetic energy (TKE). The streamlines and velocity vectors of the flow fields obtained from CFD simulations are utilized to explain the evolution of these parameters during intake and compression strokes. The study is further extended to analyze the effect of engine speed on the evolution of flow fields. With an increase in engine speed, relatively higher values of tumble ratio and TKE at the end of the compression stroke are observed, which is expected to improve the fuel-air mixing and combustion efficiency.
Abstract
Purpose:
The purpose of this paper is to investigate the impact of near-wall treatment approaches, which are crucial parameters in predicting the flow characteristics of open channels, and the influence of different vegetation covers in different layers.
Design/methodology/approach:
Ansys Fluent, a computational fluid dynamics software, was used to calculate the flow and turbulence characteristics using a three-dimensional, turbulent (k-e realizable), incompressible and steady-flow assumption, along with various near-wall treatment approaches (standard, scalable, non-equilibrium and enhanced) in the vegetated channel. The numerical study was validated concerning an experimental study conducted in the existing literature.
Findings:
The numerical model successfully predicted experimental results with relative error rates below 10%. It was determined that nonequilibrium wall functions exhibited the highest predictive success in experiment Run 1, standard wall functions in experiment Run 2 and enhanced wall treatments in experiment Run 3. This study has found that plant growth significantly alters open channel flow. In the contact zones, the velocities and the eddy viscosity are low, while in the free zones they are high. On the other hand, the turbulence kinetic energy and turbulence eddy dissipation are maximum at the solid–liquid interface, while they are minimum at free zones.
Originality/value:
This is the first study, to the best of the author’s knowledge, concerning the performance of different near-wall treatment approaches on the prediction of vegetation-covered open channel flow characteristics. And this study provides valuable insights to improve the hydraulic performance of open-channel systems.
Bu çalışmada bitki örtülü kanalların akım özelliklerinin sayısal olarak tahmin edilmesinde önemli parametrelerden biri olan yakın duvar davranışı yaklaşımlarının sonuçlara etkisi incelenmiştir. Bu amaçla sayısal çalışmalar, Hesaplamalı Akışkanlar Dinamiği (HAD) metodu ile analiz yapabilen Ansys Fluent yazılımı kullanılarak üç boyutlu, türbülanslı, sıkıştırılamayan ve kararlı akım koşullarında bitki örtülü dikdörtgen kesitli bir kanal için gerçekleştirilmiştir. Sayısal çalışmalarda yakın duvar davranışı için farklı yaklaşımlar kullanılarak kanaldaki hız dağılımları tahmin edilmeye çalışılmış ve sayısal çalışmalardan elde edilen sonuçlar literatürde yapılmış deneysel bir çalışmayla karşılaştırılarak en başarılı metot ortaya konulmuştur. Yapılan karşılaştırma sonucunda “geliştirilmiş duvar fonksiyonu” yaklaşımıyla kurulan sayısal çalışma en başarılı tahmin sonucu veren yaklaşım olmuştur. Ayrıca HAD analizi sonucunda elde edilen kanaldaki hız dağılımları verilerek, bitki örtülü açık kanal akımında hidrolik özellikler incelenmiştir.
This paper introduces an evaluation of the hydrodynamic performance of the flow in the screens used on the physical unit operations in a selected full-scale wastewater treatment plant (WWTP) based on Computational Fluid Dynamics (CFD) simulations. The numerical study was carried out with the ANSYS Fluent, CFD software by using the three-dimensional (3 D), steady, incompressible flow based on the Reynolds-Average Navier-Stokes equations with three different turbulence modeling. The hydrodynamic behavior of the screening facility, combined with head pond-upstream channel-bar screens was evaluated under different conditions of the mass flow rate and velocity fields. Also, the numerical study was validated against the experimental study, which implemented in-situ measurements by Acoustic Doppler Velocimeter (ADV), and consistent results were obtained between the numerical and experimental study. Interestingly, while the Realizable (real) k-ε turbulence model with the relative error of 9.31% gave the best predicting results in the head pond, the renormalization group (RNG) k-ε turbulence model with the relative error of 9.05% gave the best predicting results in the upstream channel and through bar screens. As a result of the experimental measurements and CFD analyses carried out in the full-scale WWTP, the function of the screening facility was found to be incomplete. Moreover, a hydraulically improved new geometry was presented to operate the existing WWTP efficiently.
The SFT (swirling flow tundish) is a kind of tundish with SC (swirl chamber) placed in the flow injection zone. The gravity potential energy of the molten steel is converted into rotation kinetic energy as entering into the tundish from the bottom of the SC along the tangential direction. The inclusions tend to collide and aggregate as following the rotating molten steel in the SC. In this work, the collision-coalescence behavior of inclusion was investigated by the mathematical simulation with PBM (population balance model) model, and the removal rate of the inclusion was investigated by the DPM model. The results show that, under the same operating conditions, the average diameter of inclusion at the outlet of the tundish increases from 4.25 μm to 4.35 μm with the introduction of the SC, which means that the SC promotes the collision and aggregation of inclusion. The inclusion removal rate of SFT is 33.09% without considering the collision-coalescence, and it increases into 43.20% as considering the collision-coalescence. The results of considering the collision-coalescence of inclusion is more consistent with the actual movement of inclusion in the tundish.
One of the key factors to improve steel quality is the steel cleanliness. In the continuous casting process, the tundish serves as a reservoir and a distributor of molten steel, but also as a metallurgical reactor to diminish the inclusion content in the final product. This research is aimed to study the flow behavior inside the ladle shroud. commercial computational fluid dynamics software, SOLID WORKS, was used for simulation. The data of geometry and operating parameters were collected from the steel plant at Bokaro Steel Plant (BSP), SAIL JHARKHAND INDIA. The simulations were performed under isothermal conditions. The results show that, with the implementation of flow control mechanisms, the velocity of the steel through ladel was decreased whichiwould enhance the chance of inclusion removal and promoteithe steel cleanliness. Different cases have been analyzed, including a conventional ladle shroud (LS). Similarly, the new design ofithe shroud was studied under equivalent conditions. LS at different bore designs, showing the detailed jetting characteristics of steel leaving the three types of ladle shroud. Ladle shroud is a small but significant device in tundish metallurgy to facilitate both the production process and steel quality. Past decades have witnessed its evolution from a simply shrouding tube to a multi-functional device in continuous casting processes. Advances in the functions of ladle shroud in tundish metallurgy have been reviewed in this work, including shrouding the teeming stream, fluid flow control, slag carry-over detection, and the potential of heating and additive feeding. The features of various commercialized and novel ladle shrouds are discussed. The effect of practical operations, such as argon injection and misalignment, on the performance of ladle shrouds, is also analyzed in this review.
The coal‐based flash ironmaking furnace is designed to industrialize the novel flash ironmaking technology (FIT), which is recognized as a cleaner and efficient alternative ironmaking process. To realize gas‐particle contact, researchers use the cocurrent downer to reduce bonding, and the reactor structure has a significant effect on the flow pattern. Herein, a 3D computational fluid dynamics (CFD) model is developed to obtain an in‐depth understanding of the geometry parameters, including ore feeding position (r/R), shaft diameter (D), and height‐to‐diameter ratio (L/D). The simulation results show that the secondary gas flow caused by the dropping hematite particles might enhance or destroy the primary turbulence structure when r/R was below or above 0.6. The increased shaft diameter D expanded the recirculation zone, which helps to prolong the residence time and improve the species exchange. The particles’ reduction degrees first rise and then fell, and the highest value (90.89%) is attained at D = 2.2 m. On the contrary, the increased L/D ratio does not change the turbulence structure but prolongs the length of the plug zone. It also shows a positive but declining effect on the reduction degree from 89.7% to 99.8%. The coal‐based flash ironmaking furnace is redesigned by computational fluid dynamics (CFD) method to industrialize cleaner flash ironmaking technology (FIT). An in‐depth understanding of the geometry parameters is obtained, including ore feeding position, shaft diameter, and height‐to‐diameter ratio. The simulation results predicate the new founding in the coupling process, such as secondary gas flow caused by ore feeding.
Dry sump lubrication is a key feature in transmission systems of high-performance racing applications. While it provides adequate oil for gears contact, it reduces churning losses. Moreover, provision of continuous oil for gear contacts under harsh conditions during a race, makes dry sump lubrication systems more reliable. One of the most important aspects of any dry sump system is the assessment of its thermo-tribological performance and its capability to remove the generated heat from highly loaded high-shear gear contacts. In this paper, a multi-physics integrated numerical method of a dry sump transmission, considering a system approach is presented. The method provides a validated predictive tool to assess thermal functioning of dry sump lubrication systems.
There is a relevant hydraulic potential in Amazon rivers, from which it is generated most of the energy available for the largest part of Brazil. One of the most important hydropower plants in the Amazon is Tucuruí dam, which can produce 8370 MW through Francis turbines. This kind of turbine often presents hydrodynamic issues due to the vortex rope formation, which can induce vibrations and reduce assembly operating life. The present work concentrates in a computational study to determine the frequency pressure fluctuations in a hydraulic generation unit of the Tucuruí hydroelectric power plant. A numerical technique is applied for modeling the turbulent flow throughout the generation unit in a transient regime using finite volume method. For the analysis of velocity and pressure fields on the hydrogenerator, a 3D fully turbulent transient modeling for characterizing the pressure fluctuations at the runner outlet is performed. The structure of vortex rope formed is investigated in order to evaluate the hydrodynamic phenomena resulting from the turbine operating condition. Low-frequency pressure pulsations are caused by the movement of the vortex rope at the runner outlet. Additionally, vortex shedding dynamics is heavily influenced by the turbine operating conditions, demonstrating the importance of such investigation. For 63% distributor opening, the structure of the vortex rope reaches a big size in the suction duct, increasing the possibility of vibration. For 89% distributor opening, the turbine operates under overload condition, and the vortex rope becomes unstable. Comparisons with field data show the efficiency and validity of the numerical modeling, demonstrating good agreement.
The swirling flow in the submerged entry nozzle (SEN) is found to significantly improve the flow pattern in the mold, as well as the quality of the steel products. However, the devices generating swirling flow designed so far are mostly limited to be applied in the industries due to the cost, lifetime, external facility, and so on. Herein, a novel swirling flow generator (SFG) is intended to be installed in the conventional tundish to generate a swirling flow in the SEN driven by the gravitational potential energy of the molten steel. The computational fluid dynamics (CFD) simulations are performed to investigate the effects of the SFG by comparing the flow pattern in the conventional tundish. The result shows that a swirling flow is produced in the SEN without bringing a serious disturbance to the flow distribution in the tundish. The flow in the SEN becomes much even by adopting the SFG and the swirling velocity is found to decrease with the increasing distance from the bottom of the tundish. A parameter called swirling intensity is proposed to quantitatively evaluate the intensity of the swirling in the SEN. A novel swirling flow generator is intended to generate a swirling flow in the submerged entry nozzle (SEN). Computational fluid dynamics simulation indicates that the device has limited effect to the flow pattern in the tundish. The flow characteristics in the SEN were discussed and a parameter is proposed to evaluate the intensity of the swirling flow.
We perform the theoretical analysis of the process of motion of liquid metal in the tundish ladle of a continuous casting machine (CCM) in the course of inert-gas blowing. The hydrodynamic parameters of the flow of liquid metal in the confined space of a continuous casting machine in the process of blowing with inert gases are determined by the method of mathematical modeling. As the regulated parameters of blowing, we consider the distance of a tuyere from the center of the tundish ladle and the angle of inclination of the gas jet to the vertical.
Fuel efficiency is one of the main concerns in the optimisation of modern racing transmissions. The dry sump transmissions are the preferred choice for high performance racing applications. While it provides adequate lubricant for gear contacts, it minimises the system churning losses, and therefore enhances the system efficiency. An important aspect is assessing its thermal performance in removing the generated frictional heat. The generated heat in the highly loaded high shear contacts of racing transmissions should be dissipated through use of directed impinging oil jets and in an air–oil mist environment. The paper presents an integrated tribological and three-dimensional computational fluid dynamics analysis for a spur gear pair, incorporated into an overall finite element model to evaluate the quantity of generated heat and its removal rate from the rotating gear surfaces. Furthermore, the temperature distribution in the circumferential direction is predicted and used to evaluate transient temperature distribution over representative race laps. Such an approach has not hitherto been reported in literature.
Improved fuel efficiency and reduced emissions are key drivers for modern drivetrain systems. Therefore, in recent years, dry sumps with air-oil mist lubrication have been used for efficient transmission design in order to reduce the churning losses. With dry sumps appropriate cooling measures should be implemented to dissipate the generated contact heat in an efficient manner. This paper integrates a tribological model with three- dimensional thermofluid analysis in order to predict the heat generated in the lubricated meshing gear contacts and its dissipation rate by an impinging oil jet in air-oil mist environment. Such an approach has not hitherto been reported in literature. The results show that the generated heat under realistic conditions cannot be entirely dissipated by the impinging oil jet in the air-oil mist transmission casing. Numerical results are used to derive extrapolated regressed equations for heat transfer purposes for time-efficient analysis. These conform well with the detailed numerical results.
The separation of inclusions with sizes less than several micrometers is very difficult because the flotation speed of such small inclusions is slow. Thus, increasing the volume of inclusions is essential for accelerating the removal of inclusions, and several methods for enhancing collision frequency of inclusions have been proposed hitherto. Their collision behavior, however, has not been directly observed yet. In this study, by using a water model, the collision rate of particles was quantified by directly observing the particle collision behavior in a turbulent flow. The collision rate of particles directly counted by use of image analysis was compared with a theoretical collision rate, which was calculated by substituting the turbulent energy dissipation rate obtained in a numerical analysis into the Saffman-Turner's equation. In the range with large turbulent energy dissipation rate beyond 0.06 m ²/s ³, the observed collision rates deviated above the theoretical values. In view of this, the Saffman-Turner's equation has been modified for applying to the range with the large turbulent energy dissipation rate.
Tundish metallurgy is critical in continuous casting process, and it has much to do with the clean steel technology. And the most effective and convenient way to evaluate the tundish designing or tundish metallurgy is to calculate different regions' volume fraction in the tundish, such as plug flow region, backmix flow region, bypass flow region and dead region. Till now this can only be solved through some calculation models based on the analysis of residual time distribution (RTD) curve, and RTD is referred from chemical reaction engineering. But RTD is far away from metallurgy field because complicated mathematical calculation and analysis are covered. Few metallurgists do further research about its applicability and correctness since modified mixed model and combined model are proposed and widely used in tundish metallurgy. In this paper, the short-coming of these two calculation models are pointed out and explained. Then it finds to irrationally define the dead region's volume fraction equals to 1-theta(av) the reason is that this equation doesn't definitely describe the definition of dead region, which is defined the region where tracers spend more than twice mean residual time, so this equation does not characterize the property of dead region. In some case, minus value of the dead region's volume fraction are obtained if this equation is adopted; and it is also not reasonable to define plug flow's volume fraction equals to 1/2(theta(min) + theta(max)) or theta(min), because theta(min) is also influenced by backmix flow. Even when theta(min) and theta(max) have the same value, the plug flow volume fraction is different according to variance sigma(2). Then in this paper, these two models are further proved based on mathematical simulation, it suggests to calculate the different regions' volume fraction in tundish inadequately through the present models available, and to trustless use the results to guide the tundish designing and tundish metallurgy process. At last it suggests that another new calculation model should be attempted to calculate the different regions' volume fraction in the tundish.
So far, there are two widely used approaches to calculate different regions' volume fraction for single-strand tundish, but they are proved to have some limitation. Few people do research about approach of calculating different regions' volume fraction for multi-strand tundish. These will greatly inhibit the development of tundish designing and tundish metallurgy. In this paper, further study about the application of residual time distribution (RTD) concept in tundish metallurgical field is carried on, including the case of single-strand tundish and the case of multi-strand tundish. Then, basing on mathematical simulation, a completely new calculation approach is attempted to propose for the first time, and it is easy to calculate the different regions' volume fraction in tundish. In the new approach, the standard is proposed definitely for dealing with RTD-curve. It is much complete and helpful for the application of RTD concept in metallurgy field. Definition of all regions in tundish flow field are further specified in the new approach, and especially, dead region's definition is made more clear, which concept was always ambiguous for people before, and it can be adaptable to redefine according the actual demand. Newly proposed approach can distinguish different flow patterns sensitively. Especially, new approach is suitable for both of single-strand tundish and multi-strands tundish, but no other approach can do it so far. What's more, new approach has considered the bypass flow, which is critical for tundish metallurgy, and new approach is able to calculate the bypass flow 's volume fraction, and other approach can do it neither. So new approach will be more complete and reasonable to evaluate and improve the tundish designing and tundish metallurgy.
The article presents the results of computer simulations of steel flow in the tundish. During numerical simulation six different turbulence model were applied. At work authors tested: κ-∈, RNG κ-∈, Realizable κ-∈, κ-Ω, RSM and DES turbulence models. To research fragment of tundish with other form of tundish internal space equipment was chosen. Numerical computations were based on the control volumes method, using the computer program Fluent. As a result of computations, fields of steel flow, turbulence intensity, residence time were obtained. For all turbulence models mean residence time, variance of the time of residence and RTD curves (type E and F) were calculated.
A new design of a ladle shroud, obtained through water modeling, that controls turbulence of the entry jet in continuous casting tundishes is proposed. Particle Image Velocimetry (PIV) measurements indicate that this design decreases the impact velocity on the tundish bottom to close to 1/3 of that provided by a conventional ladle shroud. This achievement is due to a swirling jet that promotes a recirculatory flow in the horizontal planes of the tundish. The swirling effects help to dissipate the turbulence energy of the jet before it impacts the tundish bottom making possible decreases of fluid velocities that impact the back and front walls of the tundish. Turbulence models like k-epsilon, k-omega and RSM were applied to simulate the experimental PIV measurements of velocities in the fluid flow. Only the RSM model yielded results that agree remarkably well with the experimental determinations. These results make possible to avoid the employment of flow control devices such as dams, weirs, turbulence inhibitors and the like in tundishes.
A water model of a typical 60 t slab tundish was designed and constructed to determine flow patterns characteristics when using a turbulence inhibiting device and dams; the patterns observed were compared with those predicted by a numerical model. Parameters studies included minimum residence time, volume fractions of piston (plug), perfect mixed, and dead flow, and tracer dispersion. From the quantitative results obtained by water modelling, an optimum flow control system was identified. Further evaluations were carried out to determine the system's performance under different flowrates and during a change of steel grade. The bare tundish and the selected arrangement were mathematically simulated to compare the tracer dispersion of the water model with the flow patterns predicted by the computer model. The results show the importance of using these flow control devices to increase productivity and steel quality.
Spiral separators are used globally in the fine coal and heavy mineral processing industries as gravity-concentration devices. Consisting of an open trough that spirals vertically downwards in helix configuration about a central axis, a slurry mix of particles and water is fed to the top of the concentrator. Particles are then separated radially on the basis of density and size as they gravitate downwards. To enhance performance, the geometric design has evolved historically by experimental trial-and-error investigations to develop a prototype suited to the given industrial application. This approach has proved somewhat prohibitive for design purposes however, and researchers have accordingly turned to numerical techniques in an attempt to develop a fully predictive and reliable model for use in the design process. Towards this end, the present paper uses Computational Fluid Dynamics (CFD) analysis to simulate fluid and dilute particulate flows on one operational spiral unit. The free-surface Volume-of-Fluid (VOF) algorithm, isotropic RNG k–ε turbulence model and Lagrangian method have been used for this purpose. Satisfactory predictions have been obtained with respect to a collaborative experimental program, and the model forms the basis for future examination of the two-way fluid-particle coupling processes and inter-particle effects.
The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.
This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management. © Springer-Verlag Berlin Heidelberg 2006. All rights are reserved.
Mixing phenomena in a six strand billet caster tundish has been studied by numerically solving the Navier Stokes equations along with the species concentration equation in a boundary fitted coordinate system comprising the geometry of the tundish. The solution of the species concentration equation has been utilized to compute the mix, dead and plug volume of the tundish under different flow conditions. The numerical procedure and solution algorithm has been first verified by comparing the numerically obtained residence time distribution curve, which agree well with that of the experiments done for a single strand bare tundish by Singh and Koria.44) It has been observed that the ratio of the mix to dead volume for the six strand tundish has a maximum value for a particular position of the outlets. At that particular position of the outlets (where mixing is best), an APB is placed on the bottom of the tundish surrounding the incoming inlet jet and the height of the APB has been varied to see the effect on mixing in the tundish. It has been observed that the ratio of mix to dead volume further increases with the use of APB and attains a peak value after which it decreases with the increase of the height of the APB signifying the existence of an optimum APB height. At this optimum height of the APB, the shroud immersion depth was made to change from 0 to 400 mm. It was also observed that there exists an optimum immersion depth of the shroud where the ratio of mix to dead volume still attains another peak signifying still better mixing. However, increasing the immersion depth to higher values spoils mixing significantly.
Extensive water modelling was carried out to ascertain the influence of various types of baffle designs on the hydrodynamic performance of three different designs of steelmaking tundish systems. These included, a two-strand slab casting tundish, a six-strand billet casting tundish and a five-strand, skewed, delta shaped tundish. Plant scale operating conditions were scaled down respecting both geometric and Froude similarity and on the basis of the latter, the inflow rate of water into the model tundish systems was estimated via: Qm = Λ5/2Qf.s. To quantify the hydrodynamic performance, residence time distribution (RTD) characteristics were measured using the conductivity measurement technique for a wide range of baffle designs. From such measurements as well as from flow visualisation studies, the following general observations have been made.
This paper reports the outcome of our research for resolving the very severe disagreement between the computed and measured results of the 90 deg duct flow with strong curvature. Three kinds of turbulence models (standard κ − ε eddy-viscosity turbulence model, RNG κ − ε model and RNG κ − ε model with Cμ modification) have been used to predict the abovementioned flow. The results demonstrate that RNG model and the revised model can provide satisfactory computed results. Both of the mean velocities and Reynolds shear stresses are in quantitative agreement with the experimental data. We feel that the RNG κ − ε model suggested in this paper can be a useful turbulence model for practical engineering and scientific computations.
Three-dimensional mathematical models are currently being used successfully to model liquid steel flow and turbulence behavior in continuous casting tundishes. Traditionally, this information is used to calculate the residence time distribution (RTD) of liquid metal in the given tundish configuration. The RTD curve provides the effectiveness of a tundish to produce cleaner steel in an indirect and qualitative manner. Recently, some computational models have been developed to predict inclusion trajectories and their rate of flotation in a semi-quantitative manner. In the present work, a model that addresses the inclusion transport and removal phenomena from the molten metal has been developed. The model examines three modes (flotation to the surface, coalescence of particles to form larger inclusions, and sticking to the solid surfaces) of inclusion density reduction from molten steel in the tundish. The effect of various flow control devices, such as dams, weirs and baffles with holes on each of these inclusion reduction modes was investigated and their inclusion removal efficiencies were compared. The role of different flow control devices in producing cleaner steel has been discussed.
In GOTHIC, the standard k–ε model is used to model turbulence. However, for practical reasons, one usually employs relatively large meshes near physical boundaries (walls). In an attempt to enhance the turbulence modelling in the code for simulation of mixing driven by highly buoyant discharges, in the framework of this simplified approach appropriate for containment analysis codes, we have implemented three additional models which are modifications/extensions of the standard k–ε model: the renormalization group k–ε model, and the non-linear (quadratic and cubic) eddy viscosity k–ε models. These models which for the time being, are only implemented in the ‘gas’ phase, were tested with different simple test-problems and their predictions were compared to the corresponding ones of the standard k–ε model. Furthermore, a simple study was performed to assess the sensitivity of the predictions to the mesh size.
The Navier-Stokes equation and the species continuity equation have been solved numerically in a boundary fitted coordinate system comprising the geometry of a single strand bare tundish. The solution of the species continuity equation predicts the time evolution of the concentration of a tracer at the outlet of the tundish. The numerical prediction of the tracer concentration has been made with nine different turbulence models and has been compared with the experimental observation for the tundish. It has been found that the prediction from the standard k-? model, the k-? Chen-Kim (ck) and the standard k-? with Yap correction (k-? Yap), matches well with that of the experiment compared to the other turbulence models as far as gross quantities like the mean residence time and the ratio of mixed to dead volume are concerned. It has been found that the initial transient development of the tracer concentration is best predicted by the low Reynolds number Lam-Bremhorst model (LB model) and then by the k-? RNG model, while these two models under predict the mean residence time as well as the ratio of mixed to dead volume. The Chen-Kim low Reynolds number (CK low Re) model (with and without Yap correction) as well as the constant effective viscosity model over predict the mixing parameters, i.e. the mean residence time and the ratio of mixed to dead volume. Taking the solution of the k-? model as a starting guess for the large eddy simulation (LES), a solution for the LES could be arrived after adopting a local refinement of the cells twice so that the near wall y+ could be set lower than 1. Such a refined grid gave a time-independent solution for the LES which was used to solve the species continuity equation. The LES solution slightly over predicted the mean residence time but could predict fairly well the mixed volume. However, the LES could not predict both the peaks in the tracer concentration like the k-?, RNG and the Lam-Bremhorst model. An analysis of the tracer concentration on the bottom plane of the tundish could help to understand the presence of plug and mixed flow in it.
A mathematical model, based on the SOLA-SURF scheme and k-? two equation model (where k is the turbulence kinetic energy and ? is its dissipation), has been developed to simulate the fluid flow and mass transfer phenomena as well as inclusion removal rate for a single strand stainless steel continuous casting tundish under various designs of flow control device (FCD). A physical model, one-third the scale of the actual slab continuous casting tundish, has also been constructed to observe/measure the fluid flow and mass transfer phenomena directly. The experimental observations/measurements have been used to validate the mathematical model. Satisfactory consistency is noted when the simulated results are compared with the experimental results. The verified mathematical model has been applied to the actual slab continuous casting tundish to evaluate the effects of FCD design on the fluid flow-mass transfer phenomena and inclusion removal rate. It has been found that incorporation of a pouring pad underneath the long nozzle can enhance the opportunity for inclusions to float, and achieves the highest removal rate of inclusions among the four FCD designs evaluated.
The turbulence structure of a water flow in the branch exit of a tee pipe junction has been investigated experimentally and numerically. A mass flow rate branch exit-to-inlet ratio of 50% was used. The Reynolds number based on the inlet bulk mean velocity and the pipe diameter D=50 mm was 1.26×105. The numerical solution was conducted employing three models for turbulence, k–ε, renormalization group theory (RNG) and Reynolds stress model, using a refined grid to model the smooth chamfer of radius, r=0.25D as part of the physical tee junction. Within the branch exit the flow has a separation region with recirculation, which extends up to half of the diameter. In this paper the differences noticed between the numerical and experimental results and between the results from each model are discussed. The predicted recirculating flow was attached to the pipe wall up to 2.05D downstream from the separation region, contrary to the 0.65D experimentally observed. In the vertical direction, the experimental data gave evidence that the near-wall flows are substantially asymmetric.
We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumC
K=1.617; turbulent Prandtl number for high-Reynolds-number heat transferP
t
=0.7179; Batchelor constantBa=1.161; and skewness factorS
3=0.4878. A differentialK-
[`(e)]\bar \varepsilon
model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/
[`(e)]\bar \varepsilon
, decay of isotropic turbulence asK=O(t
–1.3307), and the von Karman constant[`(e)]\bar \varepsilon
, and[`(e)]\bar \varepsilon
is finite. This latter model is particularly useful near walls.
A mathematical model to represent turbulent fluid flow and mixing in continuous casting tundishes has been developed. The
model involves solution of the three-dimensional turbulent Navier-Stokes equation, turbulence being modeled by the so-calledK-ε, two-equation model. Fluid flow parameters and residence time distribution has been predicted in a tundish of rectangular
cross section. The model is later extended to predict fluid flow in typical industrial tundishes where walls are not vertical,
but rather slightly inclined from the vertical. This results in an interresting variation in fluid flow, which may have important
technological implications. The theoretical predictions are compared with measurements obtained in water models. The detailed
understanding of the hydrodynamics of the tundish flow can be used to optimize their design for steel cleanliness.
In the interest of designing an efficient and acceptable indoor air environment in modern buildings, it is important to resolve the relationship between geometric room parameters and the air flow patterns produced by mechanical ventilation systems. Toward this end, we compare results from relatively simple three-dimensional numerical simulations (CFD) with laser Doppler anemometry (LDA) and particle image velocimetry (PIV) experimental measurements of indoor air flows in a one-tenth sub-scale model room. Laminar, k–ε turbulence, and RNG k–ε turbulence numerical models are used and evaluated with respect to their performance in simulating the flow in the model room, and results of the numerical simulations and velocimetry measurements show how obstructions can greatly influence the air flow and contaminant transport in a room. It is important, therefore, that obstructions be considered in ventilation design. Simulations predict the measured trends in a model room very well, with relative errors not much larger than 20%. In this study, the RNG model most accurately predicts the flow in a partitioned room, capturing the gross effects of a large flow obstruction.
The present paper describes a numerical and experimental investigation of strongly swirling flow in a water model combustion chamber equipped with a swirler of special design. The turbulence models used for the numerical calculations are the standard κ—ε model, the RNG κ—ε model and a differential Reynolds stress model (DRSM). In the water model, local mean velocity components and normal stresses are measured using a laser Doppler anemometer. Comparison of numerical predictions against experimental data reveals the superiority of the DRSM over the standard and RNG κ—ε models. The DRSM captures all the major features of the swirling flow, while the other two models do not. For instance, both the experimental data and the DRSM predictions reveal complex, interesting flow behaviour: a corner recirculation zone, and a central toroidal recirculation zone connected to a central reverse zone, which persists all the way to the outlet of the chamber. However, the other two turbulence models predict that the swirling flow evolves into a solid-body-rotation-type flow downstream. The RNG κ—ε model gives very little improvement over the standard κ—ε model for the swirling flow case considered.
A numerical simulation has been performed with the non-linear turbulence model proposed by Speziale (1987)On non-linear k–l and k–ε models of turbulence, Journal of Fluid Mechanics, 178, 459–475, coupled with the K–ε equations coming from the renormalization group theory (RNG) derived by Yakhot et al. (1992) Development of turbulence models for shear flows by a double expansion technique, Physics of Fluids A, 4, 1510–1520. The fully developed turbulent flow through a straight square duct, involving secondary motion, is simulated. The results are compared with the DNS data and measurements. The non-linear model was capable of predicting secondary flows, but underpredicted their intensity. The comparison between model predictions, DNS data and measurements are shown and commented for the streamwise, spanwise velocities and Reynolds stress tensor. The terms of the streamwise vorticity equation are computed and compared with DNS data. The predictions obtained with the RNG K–ε model show small improvements when compared with the standard K–ε.
The renormalization-group (RG) analysis of turbulence, based primarily on KG Wilson's coarse-graining procedure, leads to suggestive results for turbulence coefficients and models. Application of the method to turbulence evolved from the contributions of many authors and received widespread attention following the 1986 work of V Yakhot and SA Orszag. The Yakhot-Orszag method involves the basic renormalization-group scale-removal procedure, as well as additional hypotheses and approximations; their analysis is reviewed here with an attempt to clarify those approximations. Discussion of some related and subsequent literature is also included. Following the work of M Avellaneda and AJ Majda, a simpler version of the method is appplied to a model passive scalar problem wherein it is seen that, in certain cases, the RG method can recover exact results.
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