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  1. AcuSolve supports a variety of turbulence modeling options ranging from steady RANS to LES. The following list provides a description of each model. 1.) Spalart-Allmaras (spalart_allmaras or spalart) This is a general purpose single equation RANS model that solves for the transport of a modified eddy viscosity. This model has been shown to perform extremely well for a broad class of industrial flows. This model can be run in steady or transient mode. By default the model utilizes the rotation and curvature correction proposed by Spalart. Users may disable this feature by deactivating the -trc command line option of AcuSolve. 2.) Classical LES (large_eddy_simulation or les) This model corresponds to the fixed coefficient Smagorinsky subgrid scale LES model. This is an algebraic closure that requires no stagger to solve. Using this model, the large scale turbulent fluctuations in the simulation are resolved in time and space. This models requires that the Smagorinsky coefficient be changed for different types of flows. The Smagorinsky coefficient may be modified via the -smagfctcommand line on AcuSolve. This model may only be run in transient mode and requires sufficient mesh density to resolve the turbulent structures for accurate results. 3.) Dynamic LES (dynamic_model or dynamic) The dynamic subgrid LES model uses a filtering procedure to determine the appropriate Smagorinsky constant to use for specific flows. The filtering process is based on the Germano identity, and was further refined for unstructured meshes by Carati and Jansen. Using the dynamic model, the model coefficient varies in time and space to set the appropriate level of viscosity at each location in the flow. This model is also an algebraic closure that requires no stagger to solve. This model may only be run in transient mode and requires high levels of mesh density to resolve turbulent structures. 4.) Detached Eddy Simulation (detached_eddy_simulation or des) This model is a hybrid RANS/LES model based on the single equation Spalart-Allmaras RANS model. This model treats attached flow regions in RANS mode, and separated flow regions as LES. Starting withAcuSolve V1.7c, the default DES model uses the Delayed Detached Eddy Simulation (DDES, 2005) closure of Spalart. If users prefer the original DES formulation of Spalart (1997), the -ddes command line option of AcuSolve can be set to false. The DES models also utilize a constant coefficient subgrid model in LES regions. The value of this coefficient can be modified via the -desfct command line option ofAcuSolve. This model does require the solution of a turbulence stagger. This model may only be run in transient mode, and requires high levels of mesh density in separated flow regions to resolve turbulent structures.
  2. General Applications The starting point for most applications should be the steady state Spalart-Allmaras model. For most industrial applications, this model provides sufficient accuracy. For applications involving massive separation, the DES model may be used if a higher level of accuracy is required. Unsteady Simulations For the simulation of unsteady flows, users have the option of unsteady RANS (URANS), DES, or LES. Depending on the goal of the simulation, different turbulence models may be used. If the unsteadiness in the flow is driven by some type of thermal transient, then the use of URANS (i.e. the Spalart-Allmaras model in unsteady mode) is typically sufficient. If the unsteadiness is due to large scale separation and bluff body vortex shedding, the DES model or LES model should be used. For cases where small scale turbulent structure is of interest, the Dynamic LES model should be used.
  3. Advantages: (a) Computational efficiency: The standard k-ε model is a classical model developed by turbulence researchers in the early 1970's, whereas the SA model is a recent model developed in the early 1990's with the objective of numerical efficiency and robustness. The SA model can perform much faster than the k-ε model for the same or better level of accuracy. ( Accuracy as Low-Re Model: Inherently, the SA model is effective as a low-Reynolds number model and provides a superior accuracy than the standard k-ε model for wall-bounded and adverse pressure gradients flows in boundary layers. The k-ε model does not perform well in boundary layers and requires additional terms to be added to the governing equations to produce boundary layer profiles. © Mathematics & Numerics: The standard k-ε model involves a two equation coupled differential system, which can lead to stiff algebraic system for non-diffusive & accurate flow solver like AcuSolve. Some numerically dissipative solvers can easily handle such stiff differential equations. On the contrary, the SA model possess a well-behaved one equation differential system.
  4. AcuSolve contains a set of boundary conditions that automatically sets a boundary layer profile at an inlet boundary. When using the inflow boundary condition types of mass_flux, flow_rate, and average_velocity,AcuSolve computes an appropriate boundary layer profile for the velocity and turbulence fields based on the the distance from no-slip walls, and estimated Reynolds Number. The profile is re-computed at each time step such that deforming meshes are properly accounted for in the calculation. This boundary condition provides a robust method of automatically specifying physically realistic inlet conditions. It is much more realistic than specifying a constant velocity condition for internal flow applications.
  5. AcuSolve supports three different techniques of modeling turbulent boundary layers. The first, and most accurate technique is to fully integrate the equations directly up to the no-slip wall. When the user selects "Low Reynolds Number" for the turbulence wall type, AcuSolve uses this procedure to model the boundary layer. When using this technique, it is important that the user constructs the mesh such that the first node off of the wall is within the laminar sublayer (i.e. y+ <= ~8). If the y+ exceeds this value, large errors in the accuracy of the shear stress can be introduced. Note that these guidelines are valid for the DES models and Spalart-Allmaras RANS model. When using LES, the first node off the wall should be at a y+<1.0. The wall normal mesh spacing should increase with a stretch ratio of ~1.3 until it smoothly blends into the surrounding volume mesh. The second type of treatment for turbulent boundary layers is the use of a wall function. When the Turbulence Wall Type is set to wall function, AcuSolve uses the well known "Law of the Wall" to model the boundary layer. When employing this technique, the first node off the wall should be placed between a y+ of 1-300. For extremely high Reynolds Number flows, the upper bound of the y+ limit may be extended beyond 300 without sacrificing accuracy. Note that AcuSolve has no lower limit on the near wall spacing when using the wall function. When in the viscous sublayer, the wall function recovers the Low Reynolds Number solution. This type of wall function can be used with either the DES or RANS models, but is not suggested for use with LES models. The third type of wall model that is offered by AcuSolve is the running average wall function. When this model is employed, the wall function is evaluated using the running average velocity field and not the instantaneous field. The meshing requirements for this model are the same as for the standard wall function. This approach is typically used with LES and DES models, but may also be used with RANS if appropriate. Note that this requires the Running Average field to be turned on in the simulation.
  6. The Spalart-Allmaras model incorporates some of the recent advances in turbulence modeling that make it an excellent choice for prediction of industrial turbulent flows. Comparisons between the k-ε model and Spalart-Allmaras models regularly show that Spalart-Allmaras has equal or superior accuracy for nearly all classes of flows. In addition to this, the Spalart-Allmaras model is more computationally efficient than k-εbecause it only solves a single transport equation. Bardina, et. al. provide an excellent overview of some leading turbulence models that users can use as a reference.
  7. Theory: We derived our turbulence wall roughness formulation from "Viscous Fluid Flow" Second Edition, by Frank M. White, ISBN: 0-07-069712-4; Pages 426-429. Basically, the law of the wall is given by u+ = 1/k ln( y+ ) + B(k+) + Pc(Grad_P) Where u+ = u / u* y+ = y * mu / u* k+ = k * u* / mu u = velocity y = distance to the wall mu = kinematic viscosity k = average roughness height u* = sqrt( tau_w / dens ) tau_w = shear at the wall dens = density k = 0.41 (Karman constant) B = wall function constant Pc = pressure correction For smooth walls, B = 5.5. For rough walls, B is a function of k+, which is a function of wall shear (or u* to be exact). The exact equations are written in White's book above. Given the above, effectively the roughness shifts the u+ curve down. Practice: In practice, one must consider the following: 1. The first mesh point MUST be larger than the roughness height. That is, other than the nodal point on the wall, all other points need to have y > k. Otherwise, the theory is incorrect; since the u+(y+) curve will go below zero. 2. On the other hand, we like to mesh such that y+ of the first node should not be over 300. At times, this criteria will contradict y > k condition. In this case, y+ of 300 should be sacrificed in favor of y > k. 3. All of the roughness theory and measurement come from experiments performed in air over sand paper (usually associated with the aero-space field). Hence, there is an assumption of Gaussian distribution of roughness, leading to a self similarity solution.
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