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This turbulent model is a simple single-equation model that solves the modeled transport equation for vortex viscosity. In general, this model is used for low Reynolds numbers and areas affected by viscosity within the boundary layer. This model is used in aviation, low-separation flows (such as airfoil, wing and aircraft fuselage, and missile), and flows under a pressure gradient.
Two-equation turbulence models allow the determination of both, a turbulent length and time scale by solving two separate transport equations. The standard k-epsilon model in ANSYS Fluent falls within this class of models and has become the workhorse of practical engineering flow calculations in the time since it was proposed by Launder and Spalding. Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations. It is a semi-empirical model.
The standard k-epsilon model is a model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (e). The model transport equation for k is derived from the exact equation, while the model transport equation for e was obtained using physical reasoning
In the derivation of the k-epsilon model, the assumption is that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard k-epsilon model is therefore valid only for fully turbulent flows.
Standard Wall Function
If the k-epsilon turbulence model is used for the simulation, it is not possible to simulate flow vortex near the walls, a wall function must be defined to investigate the fluid behavior near the wall. These wall functions are near-wall analytical flow profiles obtained by explicitly solving the near-wall flow equations; hence, they are more accurate than numerical methods (in simpler models). Also, because of the need for no accurate mesh near the wall, they greatly reduce the computational time. It should be noted that when using the k-epsilon model, due to the lack of accurate mesh near the walls, it is necessary to check the wall functions using Y-Plus (Y+). The suitable Y+ should be between 30 and 300 for the standard model.
Enhanced Wall Function
When the k-epsilon turbulence model is used and it is not feasible to simulate flow vortices near the walls, a function of the wall must be defined to investigate the fluid behavior near the wall. These wall functions are near-wall analytical flow profiles obtained by explicitly solving the near-wall flow equations; hence, they are better than numerical methods and also due to the lack of the need for accurate mesh near the wall, they greatly reduce the computational cost. It should be noted that when using the k-epsilon model, due to the lack of meshing near the walls, it is necessary to check the wall functions using Y+ so that in enhanced mode the appropriate value for Y+ must be about 1. The enhanced wall function is mainly suitable for low Reynolds number and finer grid models.
The k-epsilon and Reynolds stress turbulence models do not have the ability to simulate vortexes near walls, and therefore, to model vortexes and solve flows near walls we should use the wall function. While the k-omega and Sparat-Allmaras turbulence models, with suitable meshing, have the ability to simulate and solve the flow directly near the walls. The k-omega model has different types including standard, GEKO, BSL, and SST. The standard type has applications such as better performance in low-velocity and reverse flows due to reverse pressure gradient, used incompressible flows, free and transient shear, suitable for mixing layers, plate and radial jets, suitable for wall enclosures and also suitable for aerodynamic and turbomachinery problems. While the SST (shear stress transport) model acts as a combination of the k-Ԑ model in the areas near the wall and the k-ω model in the open space. Capabilities of this type of turbulent flow are suitable in cases such as airfoils, transient shock waves and flows containing reverse pressure gradients, and of course, have disadvantages such as high probability of instability and weak convergences due to a transfer from one turbulence model to another. The k-epsilon model also has the ability to calculate shear flow corrections and low-Re corrections. In fact, this model can use shear flow corrections to increase accuracy in predicting fluid shear flow behavior.
The simulations that are related to the external flow, apply the K-Omega SST model. This model of k-omega operates as a hybrid function, which results in a gradual transfer of flow from the k-omega model for near-wall regions to the k-epsilon model in areas beyond the boundary layer. This model is used for reverse pressure gradient flows and in airfoil simulations. Since the wall function does not define in the k-omega model, finer grids should be used in areas close to the airfoil walls. However, in this turbulence model, the probability of divergence increases due to the transition from one model to another.
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