## How does the Reynolds Number affect my CFD model?

The Reynolds number (Re) is the single most important non-dimensional number in fluid dynamics and is recommended to be calculated before you begin any new CFD modelling project. The Reynolds Number is defined as the dimensionless ratio of the inertial forces to viscous forces and quantifies their relevance for the prescribed flow condition: Where U∞ and L are the characteristic velocity and length scale of the problem, ρ is the fluid density and μ is the dynamic viscosity. The use of the Reynolds number frequently arises when performing a dimensional analysis and is known as Reynolds principle of similarity. For example, air flow of U∞ = 1 [m/s] over a flat plate of L = 1 [m] will exhibit the same flow pattern as air flow of U∞ = 10 [m/s] over a flat plate of L = 0.1 [m]. This concept holds since the Re is equal and the flow is incompressible (i.e. the Mach number is low). The Re also allows us to characterize whether a flow is laminar or turbulent. Laminar flow is characterized by lower Re and high diffusion over convection. Turbulent flow on the other hand is characterized by higher Re where inertial forces dominate considerably, resulting in largely chaotic flow. The flow may also undergo a transitioning phase whereby the flow exhibits neither completely laminar nor completely turbulent characteristics. Note: Inertial forces are proportional to the square of velocity, while viscous forces vary linearly with velocity. Therefore as the Re → 0 it is reasonable to neglect convective terms (e.g. creeping flow). Similarly, as the Re → ∞ the viscous terms of the momentum equation can be neglected and the problem can be characterized purely by the generation of inertial forces (e.g. high supersonic and hypersonic flows). For flows in a pipe of diameter L or non-circular pipes with hydraulic diameter L, empirical studies have shown that laminar flow occurs for ReL < 2500 and fully developed turbulent flow occurs for ReD > 4000. In the interval between, transition occurs. For external flows (e.g. flow over a flat plate), laminar flow is observed up to approximately ReD ~ 1×105 to 5×105 (where D is the distance from the leading edge) before transition to turbulence takes place and turbulent flow is observed thereafter. Factors influencing transition include roughness and local acceleration. The Turbulence Modelling team at ANSYS Inc, led by Dr. Florian Menter, have developed world-leading capabilities to allow CFD users to accurately model these transition effects. Using the Reynolds number, we can determine whether or not it is necessary to include...

## Tips & Tricks: Turbulence Part 1 - Introduction to Turbulence Modelling

We will now focus on Turbulence Modelling, which is a critical area for any engineer involved with industrial CFD. There are a number of different approaches so it is important that you have solid grounding in this area to enable you to choose the appropriate model for your simulation requirements. It is worth noting that in August 2012, LEAP will be hosting Dr. Florian Menter to run a series of Advanced Turbulence Training courses in Melbourne, Sydney and Perth. Dr. Menter is a world recognised expert in turbulence modelling, and more information on his visit to Australia can be found here. The ANSYS CFD Solvers solve the Navier Stokes and conservation equations, but as direct solutions are not possible to resolve for any flows of an industrial Reynolds number then we need to do some modelling, as opposed to resolving the values directly. The equations that we used are not closed and so we need to use Turbulence Modelling to close the equation set and then iterate towards a solution. We can use what is called a Reynolds Averaged Navier Stokes (RANS) approach, or we can use an Eddy Simulation technique which resolves the larger eddies in the flow and is only really required when you have separation or large recirculating regions. The most commonly used models are the RANS models due to their low cost in terms of compute power and run times. The Eddy Simulation methods can be quite mesh sensitive but will yield much better results for separated and recirculating flow, albeit over much longer run times. The RANS models apply a Reynolds decomposition technique to the Navier Stokes equations which breaks the velocity down into its mean and fluctuating components. This decomposition leaves us with one unknown value, which is termed the Reynolds Stress. We use Turbulence Models to resolve the Reynold’s Stress and close the equation set. There are two ways we can go about resolving this, the first (and most commonly used approach) is to use an isotropic value for the turbulent viscosity value which is called the an Eddy Viscosity Model, the other way is to solve using the Reynolds Stress Model (RSM) for the 6 separate Reynolds Stresses, which results in an anisotropic solution. EDDY VISCOSITY MODELS The limitation with Eddy Viscosity models is that they use an isotropic value which may not be appropriate and hence can increase the diffusion in your result. Obviously solving for the 6 Reynolds Stresses and dissipation will be more accurate, but you are then solving extra equations which will increase your run time considerably. There are further modifications to the 2 equation Eddy Viscosity...