Modeling turbulent flow in CFD simulations requires selecting a numerical technique that can account for nonlinear convective terms in the Navier-Stokes equations.
There are dozens of turbulence models, each with minor variations on each other, that are applicable in different types of systems and fluids.
Turbulence models are defined only after application of certain numerical methods that help simplify CFD problems.
Turbulence is one of the most mathematically demanding areas of engineering and physics to analyze, as it draws on mathematical techniques and concepts from multiple disciplines. Although many Ph.D. theses and scholarly articles have been published on this topic, there is no simple analytical theory that can be used to predict turbulent fluid flow and its evolution in every system. Only idealized cases can be used to simplify the governing equations and produce some general insights into turbulent flow behavior, but real systems involve demanding numerical techniques that are implemented in CFD simulation packages.
For systems designers and engineers, CFD simulations involving turbulent flows in real systems can be computationally demanding. Minimizing the computational costs of turbulence simulations requires pairing a turbulence model with an appropriate numerical solution technique. Many turbulence models have been published in the literature and are implemented in CFD simulation applications. In this article, we’ll look at some of the more popular turbulence models and where they tend to be most applicable.
The Challenge in Modeling Turbulence
Turbulence arises when a fluid’s viscosity becomes insufficient to provide enough damping to keep fluid flow steady along a prescribed direction. Turbulence is a nonlinear stability problem; due to lack of sufficient damping and excessive feedback, eddies begin to shear off from the main flow. This formation of eddies and the resulting chaotic behavior is highly dependent on initial conditions, as is generally the case in nonlinear stability problems that exhibit bifurcations.
The role of a turbulence model is to predict the resulting flow behavior in the presence of such nonlinear instabilities. This can be done statistically, by looking at the evolution of fluctuations about a long-term (time-averaged) mean, or by directly simulating this chaotic behavior for a range of initial conditions. The former can be used to examine the broader trend in turbulent flow while the latter provides much more detail on the flow behavior.
Choosing a Numerical Method
Turbulence models fall under the umbrella of a set of numerical techniques that can be used to solve the full Navier-Stokes equations in cases where turbulent flow is expected. The three broad classes of methods used to model turbulence are:
Direct numerical simulation (DNS) - This involves a direct simulation of the evolution of turbulent flow in space and time, starting from the full Navier-Stokes equations with specific initial conditions. In general, little or no simplification is applied, giving results that are highly accurate but require significant computational resources.
Large eddy simulation (LES) - This is the first level of simplification, where spatial averaging is applied to the Navier-Stokes equations in order to increase the size of the relevant length scale. The minimum size of eddies that can be resolved in turbulent flow is larger, but this reduces the computational costs in the resulting turbulence model.
Reynolds-averaged Navier-Stokes (RANS) - In these turbulence models and the associated numerical method, the Navier-Stokes equations are time-averaged such that a numerical simulation involves simulating fluctuations about the average flow rate. This greatly reduces the complexity of the problem and is most useful when a system’s behavior will be dominated by the long-term average of the flow rate.
Detached eddy simulation (DES) - This hybrid simulation method, also called hybrid RANS-LES, mixes the best aspects of RANS and LES through the use of spatial and temporal averaging. This methodology treats near-wall regions with a RANS approach while regions farther from a bounded region are treated with an LES approach. This provides greater efficiency without losing too much resolution and accuracy in the simulation results.
Momentum portion of the incompressible Reynolds-averaged Navier-Stokes (RANS) equations
These are four of the standard numerical approaches to developing a turbulence model. RANS models are most common in many industrial applications, or in techniques like design exploration, where computational efficiency is favored over very high resolution. In other applications, such as aerospace, higher resolution may be needed over certain length scales, as the appearance of turbulence can limit the maneuverability of an aircraft. In this case, RANS might not be preferred, and instead, something like DES, LES, or a hybrid approach would be used.
Selecting Turbulence Models
While we can’t provide a list of every turbulence model in this article, it’s important to note that the numerical schemes mentioned above are like categories of turbulence models. Within the above set of numerical approaches, turbulence models have been developed that are applicable in certain situations. For example, one of the more common turbulence models used in aerospace is the Spalart–Allmaras model, which has over a dozen variations. These models are RANS-based one-equation models that solve a transport equation for the kinematic eddy turbulent viscosity in compressible or incompressible flows in wall-bound systems.
RANS models with linearized eddy viscosity are often the best starting point to begin understanding fluid behavior in a complex system. As the required accuracy increases, so does the complexity of the system being simulated. Modern CFD simulation tools will have many of these turbulence models included as subsets of the standard numerical schemes listed above.
Working with turbulence models derived from the Navier-Stokes equations is much easier when you have an advanced set of CFD simulation tools. The mesh generation applications in Pointwise can help you create accurate simulation grids with high mesh order in complex geometries, helping you reduce computational complexity without sacrificing accuracy. Once a mesh is created and ready for further analysis, the set of CFD simulation tools in Omnis 3D Solver will determine the flow solution in your system accurately and efficiently.