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Currently, when the Reynolds-Averaged Navier–Stokes (RANS) equations are solved using turbulence modelling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been performed for similar performance with two-equation models of the k - ω type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k - ω type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically refined mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the model itself. Additionally, in this paper analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a welldefined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate (ω) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

Incipient wave breaking on a vertical circular pile is simulated with a Reynolds stress–$\\omega$ turbulence model. Comparison of results simulated with a stabilized two-equation turbulence model, as well as no turbulence model, demonstrates that the breaking point and the peak force on a vertical cylinder due to incipient breaking should not be affected by the turbulence closure model, provided that it is stable and the simulations are converged. Notably, the present results show that the build-up to peak force induced by incipient wave breaking can be accurately predicted without any turbulence closure model. However, for the prediction of the secondary load cycle (SLC), proper turbulence modelling is required, as this process involves both turbulence production and lee-side flow separation. The Reynolds stress–$\\omega$ model is demonstrated to predict the SLC more accurately than a stabilized two-equation $k$–$\\omega$ turbulence model, as the flow separation points and vorticity field are better predicted. Some existing studies indicate that the generation of the SLC does not necessarily result from flow separation, but is rather due to the suction force. The present work finds that the occurrence and point of flow separation significantly affect the magnitude of the suction force, which hence affects the SLC prediction significantly. For waves breaking on a vertical pile, proper turbulence modelling is therefore essential for accurate SLC predictions. (In the above, $k$ is the turbulent kinetic energy density and $\\omega$ is the specific dissipation rate.)

Scenario models of a moving subway train can help investigate the influence of different fire locations on smoke propagation characteristics in curved tunnels. To this end, this study adopts the three-dimensional Unsteady Reynolds Average Navier-Stokes equations method and the renormalization group k-ε two-equation turbulence model with buoyancy correction for numerical analysis. The motion of the train is replicated using the slip grid technique. The results indicate that when a fire breaks out on a moving train in tunnels, the piston wind leads the longitudinal movement of the smoke. If a fire erupts in the head or middle car of a moving train, the time of smoke backflow is delayed by 30 s or 17 s, respectively, compared to that for the tail car. The obtained results provide a theoretical basis for reasonably controlling the smoke flow in subway tunnels and reducing casualties in fire accidents.

In this paper, the k-έ two-equation turbulence model has been used to simulate ice accumulation under ice cover along a river bend. A 2D depth-averaged numerical model has been developed in a nonorthogonal coordinate system with nonstaggered curvilinear grids. In this model, the contravariant velocity has been treated as an independent variable. To avoid the pressure oscillation in the nonstaggered grids, the momentum interpolation has been introduced to interpolate variables at the interface. The discretization equations have been solved by using pressure correction algorithms. An equation has been developed for describing the deformation of ice jam bottom. The thickness distribution of ice accumulation (ice jam) along the bend has been simulated. The developed model has been applied to the experimental studies under different conditions carried out at the Hefei University of Technology. Results indicate that all simulated thickness of ice accumulation agrees reasonably well with the measured thickness of ice accumulation in laboratory.

The paper presents a comparative study based on the 3D computational simulations of the flow around a circular cylinder fitted with vortex generators, benefiting from a series of dedicated model tests conducted in a large circulating water tunnel. The effect of the vortex generators is presented with comparisons including the bare cylinder with no vortex generator case and related experimental data. Incompressible, unsteady Reynolds- Averaged-Navier-Stokes (URANS) computations were performed by using three different two-equation turbulence models, which were Realizable k-ε, Wilcox k-ω, and Shear-Stress-Transport k-ω models. The numerical calculations emphasized the effectiveness and the performance enhancing character of the vortex generators. Many key findings of the measurements such as the elongation of the near-wake, the extension of the shear layers, the decrease of the stress components and the weakening of the vortices were successfully reproduced with the computations. Significant drag reduction was observed in both experimental and computational study due to the application of the vortex generators.

This study aims to investigate how afterburning affects the thermal environment of the launch pad during a rocket launch. The thermal environment and launch pad flow field are studied using numerical simulations during the vehicle lift-off phase to achieve this goal. The launch vehicle exhaust plume model is constructed during the lift-off phase using the reaction model, the Realizable k-ε two-equation turbulence model, and the three-dimensional compressible Navier-Stokes equations. The results of the investigation demonstrate that the temperature field of the rocket exhaust plume is higher in the gas chemical reaction flow scenario compared to the frozen flow scenario. In addition, considering both the frozen and gas chemical reaction flows causes the launch pad surface temperature to rise. The research approach used in this study sheds important light on the launch pad’s thermal protection design.

The performance a valve has been frequently estimated with numerical methods owing to limitations such as cost and place. In this study, for the triple-offset butterfly valves, the different sizes in various disc-opening cases was numerically conducted using different turbulence models of the two-equation turbulence models of k–ε, k-ω, and Reynolds stress model. The numerical calculations were validated against experimentally obtained valve flow test results. The numerical effect with the different turbulence models were analyzed with respect to the disc-opening cases. From the numerical analysis, the Reynolds stress model exhibits the most pronounced turbulence effects among the various turbulence models showing higher value of Reynolds normal stress near the valve disc region. The sensitivity of the turbulence model constants was examined using the 300 mm valve to observe the sensitivity of the turbulence model parameters in the two-equation turbulence models.

The computational fluid dynamics (CFDs) models based on the steady Reynolds-averaged Navier–Stokes equations (RANSs) using the k−ω two-equation turbulence model are considered in order to estimate the wind flow distribution around buildings. The present investigation developed a micro-scale city model with building details for the Hail area (Saudi Arabia) using ANSYS FLUENT software. Based on data from the region’s meteorological stations, the effect of wind speed (from 2 to 8 m/s) and wind direction (north, east, west, and south) was simulated. This study allows us to identify areas without wind comfort such as the corner of the building and the zones between adjacent buildings, which make this zone not recommended for placement of restaurants, pedestrian passages, or gardens. Particular attention was also paid to the highest building (Hail Tower, 67 m) in order to estimate, along the tower height, the wind speed effect on the turbulence intensity, the turbulent kinetic energy (TKE), the friction coefficient, and the dynamic pressure.

Accurate prediction of wind turbine (WT) wake is essential for optimising wind farm layouts and maximising energy production. Traditional wake models, such as the Jensen and Park models, are commonly used in WT simulations but often struggle to capture wake characteristics accurately. Furthermore, high-fidelity Computational Fluid Dynamics simulations are computationally intensive, limiting their applicability for large-scale simulations. This research introduces an innovative approach to WT wake modelling using the Spalart-Allmaras (SA) turbulence model within a steady Reynolds-Averaged Navier-Stokes framework, specifically applied to horizontal-axis WT. The turbulent length scale, which is essential for wake predictions in SA turbulence model, has been derived from the standard k-ε turbulence model based on the neutral atmospheric boundary layer assumption. WT is modelled as actuator disk (AD), with thrust as a momentum source term distributed across the AD using a radial distribution function. Wake velocities are measured from 2.5 to 10 times the WT diameter downstream. The model’s accuracy is validated using four WTs of varying sizes and operational conditions. The average mean absolute percentage error (MAPE) of 5.5% confirming that the SA model effectively captures wake profiles at multiple downstream locations. Additionally, the SA model achieves these results with significantly reduced computational costs compared to traditional two-equation turbulence models. These findings offer valuable insights for optimising turbine placement and improving wind farm performance, positioning this research as highly relevant for both academic and industrial applications.