Ansys 12.0 CFX 官方教程 9A.ppt

Chapter 9 Turbulence,Introduction to CFX,What is Turbulence?,Unsteady, irregular (non-periodic) motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space Identifiable swirling patterns characterize turbulent eddies Enhanced mixing (matter, momentum, energy, etc.) results Fluid properties and velocity exhibit random variations Statistical averaging results in accountable, turbulence related transport mechanisms This characteristic allows for turbulence modeling Contains a wide range of turbulent eddy sizes (scales spectrum) The size/velocity of large eddies is on the order of the mean flow Large eddies derive energy from the mean flow Energy is transferred from larger eddies to smaller eddies In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation,Is the Flow Turbulent?,External Flows,Internal Flows,Natural Convection,along a surface,around an obstacle,where,where,Other factors such as free-stream turbulence, surface conditions, and disturbances may cause transition to turbulence at lower Reynolds numbers,is the Rayleigh number,is the Prandtl number,Flows can be characterized by the Reynolds Number, Re,Observation by O. Reynolds,Laminar (Low Reynolds Number),Transition (Increasing Reynolds Number),Turbulent (Higher Reynolds Number),Turbulent Flow Structures,Energy Cascade Richardson (1922),Governing Equations,Conservation Equations,Continuity,Momentum,Energy,where,Note that there is no turbulence equation in the governing Navier-Stokes equations!,Overview of Computational Approaches,Direct Numerical Simulation (DNS) Theoretically, all turbulent (and laminar / transition) flows can be simulated by numerically solving the full Navier-Stokes equations Resolves the whole spectrum of scales. No modeling is required But the cost is too prohibitive! Not practical for industrial flows Large Eddy Simulation (LES) type models Solves the spatially averaged N-S equations Large eddies are directly resolved, but eddies smaller than the mesh are modeled Less expensive than DNS, but the amount of computational resources and efforts are still too large for most practical applications Reynolds-Averaged Navier-Stokes (RANS) models Solve time-averaged Navier-Stokes equations All turbulent length scales are modeled in RANS Various different models are available This is the most widely used approach for calculating industrial flows There is not yet a single, practical turbulence model that can reliably predict all turbulent flows with sufficient accuracy,RANS Modeling Time Averaging,Ensemble (time) averaging may be used to extract the mean flow properties from the instantaneous ones The instantaneous velocity, ui, is split into average and fluctuating components The Reynolds-averaged momentum equations are as follows The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the system of governing equations,Fluctuating component,Time-average component,Example: Fully-Developed Turbulent Pipe Flow Velocity Profile,Instantaneous component,(Reynolds stress tensor),RANS Modeling The Closure Problem,Closure problem: Relate the unknown Reynolds Stresses to the known mean flow variables through new equations The new equations are the turbulence model Equations can be: Algebraic Transport equations All turbulence models contain empiricism Equations cannot be derived from fundamental principles Some calibrating to observed solutions and “intelligent guessing” is contained in the models,RANS Modeling The Closure Problem,The RANS models can be closed in one of the following ways (1) Eddy Viscosity Models (via the Boussinesq hypothesis) Boussinesq hypothesis Reynolds stresses are modeled using an eddy (or turbulent) viscosity, T. The hypothesis is reasonable for simple turbulent shear flows: boundary layers, round jets, mixing layers, channel flows, etc. (2) Reynolds-Stress Models (via transport equations for Reynolds stresses) Modeling is still required for many terms in the transport equations RSM is more advantageous in complex 3D turbulent flows with large streamline curvature and swirl, but the model is more complex, computationally intensive, more difficult to converge than eddy viscosity models,A large number of turbulence models are available in CFX, some have very specific applications while others can be applied to a wider class of flows with a reasonable degree of confidence,Available Turbulence Models,The velocity profile near the wall is important: Pressure Drop Separation Shear Effects Recirculation Turbulence models are generally suited to model the flow outside the boundary layer Examination of experimental data yields a wide variety of results in the boundary layer,The above graph shows non-dimensional velocity versus non-dimensional distance from the wall. Different flows show different boundary layer profiles.,Turbulence Near the Wall,By scaling the variables near the wall the velocity profile data takes on a predictable form (transitioning from linear to logarithmic behavior) Since near wall conditions are often predictable, functions can be used to determine the near wall profiles rather than using a fine mesh to actually resolve the profile These functions are called wall functions,Linear,Logarithmic,Scaling the non-dimensional velocity and non-dimensional distance from the wall results in a predictable boundary layer profile for a wide range of flows,Turbulence Near the Wall,Fewer nodes are needed normal to the wall when wall functions are used,Turbulence Near the Wall,Turbulence Near The Wall,y+ is the non-dimensional distance from the wall It is used to measure the distance of the first node away from the wall,u,y,Boundary layer,y+,Wall functions are only valid within specific y+ values If y+ is too high the first node is outside the boundary layer and wall functions will be imposed too far into the domain If y+ is too low the first node will lie in the laminar (viscous) part of the boundary layer where wall functions are not valid,In some situations, such as boundary layer separation, wall functions do not correctly predict the boundary layer profile In these cases wall functions should not be used Instead, directly resolving the boundary layer can provide accurate results Not all turbulence models allow the wall functions to be turned off,Wall functions applicable,Wall functions not applicable,Turbulence Near the Wall,Standard k- Model The “industrial CFD” standard since it offer a good compromise between numerical effort and computational accuracy Wall functions are always used y+ should typically be 300 for the wall functions to be valid There is no lower limit on y+ CFX uses Scalable wall functions If your mesh results in y+ values below the valid range of the wall functions, the nodes nearest the wall are effectively ignored This ensures valid results, within the model limitations, but is a waste of mesh Known limitations: Separation generally under predicted since wall functions are used Inaccuracies with swirling flows and flows with strong streamline curvature,k-epsilon Model,k- Model One of the advantages of the k- formulation is the near wall treatment for low-Reynolds number computations Here “low-Reynolds” refers to the turbulent Reynolds number, which is low in the viscous sub-layer, not the device Reynolds number In other words “low-Reynolds number computations” means the near wall mesh is fine enough to resolve the laminar (viscous) part of the boundary layer which is very close to the wall A low-Reynolds number k- model only requires y+ = 2 If a low-Re k-e model were available, it would require a much small y+ In industrial flows, even y+ = 2 cannot be guaranteed in most applications and for this reason, a new automatic near wall treatment was developed for the k- models,k-omega Model,k-omega Model,k- Model (continued) The Automatic wall treatment for the k- models switches between a low-Reynolds number formulation (i.e. direct resolution of the boundary layer) at low y+ values and a wall function approach at higher y+ values This lets you take advantage of a fine near-wall mesh when present,Airfoil at Mach 0.5 showing the mesh and y+ values. y+ values are 2. A finer near wall mesh is required to achieve y+ 2.,Shear Stress Transport (SST) Model The SST model is based on the k- model and has the same automatic wall treatment It accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation This is a good default choice,SST Model,y+ for the SST and k-omega Models,When using the SST or k- models y+ should be 300 so that the wall function approach is valid This will not take advantage of the low-Reynolds formulation, which is necessary for accurate separation prediction However, the model can still be used on these coarser near-wall mesh and produce valid results, within the limitations of the wall functions To take full advantage of the low-Reynolds formulation y+ should be 2,Estimating y+,It is useful to estimate y+ before obtaining a solution Saves time! Use the following formula based on flow over a flat plate: Dy is the actual distance between the wall and first node L is a flow length scale y+ is the desired y+ value ReL is the Reynolds Number based on the length scale L See the documentation for a derivation of this formula ANSYS CFX-Solver Modeling Guide Turbulence and Near-Wall Modeling Modeling Flow Near the Wall Guidelines for Mesh Generation,Other Turbulence Models,When RANS models are not adequate, Eddy Simulation models can be used As already mentioned, these are more computationally expensive Large Eddy Simulation (LES) Resolves the large eddies, models the small eddies Problem: Requires a very fine boundary layer mesh, making it impractical for most flows Detached Eddy Simulation (DES) Uses a RANS model in the boundary layer, switches over to LES in the bulk flow A “standard” boundary layer mesh can be used Problem: the RANS to LES switch depends on the mesh, which can give unphysical results on the “wrong” mesh Scale-Adaptive Simulation (SAS) Like DES, but without the mesh dependency problems,Inlet Turbulence Conditions,Unless turbulence is being directly simulated, it is accounted for by modeling the transport of turbulence properties, for example k and Similar to mass and momentum, turbulence variables require boundary condition specifications Several options exist for the specification of turbulence quantities at inlets (details on next slide) Unless you have absolutely no idea of the turbulence levels in your simulation (in which case, you can use the Medium (Intensity = 5%) option), you should use well chosen values of turbulence intensities and length scales Nominal turbulence intensities range from 1% to 5% but will depend on your specific application The default turbulence intensity value of 0.037 (that is, 3.7%) is sufficient for nominal turbulence through a circular inlet, and is a good estimate in the absence of experimental data,Inlet Turbulence Conditions,Default Intensity and Autocompute Length Scale The default turbulence intensity of 0.037 (3.7%) is used together with a computed length scale to approximate inlet values of k and . The length scale is calculated to take into account varying levels of turbulence. In general, the autocomputed length scale is not suitable for external flows Intensity and Autocompute Length Scale This option allows you to specify a value of turbulence intensity but the length scale is still automatically computed. The allowable range of turbulence intensities is restricted to 0.1%-10.0% to correspond to very low and very high levels of turbulence accordingly. In general, the autocomputed length scale is not suitable for external flows Intensity and Length Scale You can specify the turbulence intensity and length scale directly, from which values of k and are calculated Low (Intensity = 1%) This defines a 1% intensity and a viscosity ratio equal to 1 Medium (Intensity = 5%) This defines a 5% intensity and