Turbulence Parameters Calculator at Inlet Boundary
Background Information
In case of CFD modelling of turbulent flow all CFD solvers needs turbulence quantities to be specified at inflow boundaries. The turbulent quantities at inlet depends on flow velocity, inlet geometry (area, perimeter and hydraulic diameter) and fluid properties.
There are many ways one can provide turbulence conditions at inlet. Most of the CFD solvers has one or all of below methods:
 Turbulent kinetic energy () and turbulent dissipation ()
 Turbulent kinetic energy () and specific rate of dissipation ()
 Intensity () and length scale ()
 Intensity () and viscosity ratio ()
 Intensity () and hydraulic diameter ()
When providing the turbulence values at inlet, one has to make sure to provide good approximation to avoid solution convergence issues and unphysical turbulence values. Following section gives details about equations used in this calculator to calculate the turbulence properties.
Reynolds Number ()
Reynolds number is the ratio of inertia forces to viscous forces. This number helps to determine if the flow is laminar or turbulent.
Where, is mean fluid velocity, is the density of fluid, is characteristic length (hydraulic diameter or traveled velocity of fluid) and is dynamic viscosity of fluid.
Turbulence Intensity ()
Turbulence intensity is defined as ratio of root mean square of the velocity fluctuations , to the mean flow velocity . A turbulence intensity of 1% or less is generally considered low and turbulence intensities and greater than 10% are considered high. The turbulence intensity at the core of a fully developed duct flow can be estimated as:
Turbulence Length Scale ()
Turbulent length scale represents the size of the large eddies in turbulent flows. In fullydeveloped duct flows, l is restricted by the size of the duct, since the turbulent eddies cannot be larger than the duct. An approximate relationship between l and the physical size of the duct is:
Where, is the diameter of pipe in case of circular ducts and hydraulic diameter () in case of noncircular ducts.
Turbulent Kinetic Energy ()
Turbulence kinetic energy is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured rootmeansquare (RMS) velocity fluctuations. Turbulence kinetic energy can be calculated (for smooth duct) using following equation:
Where, is the mean flow velocity and is turbulence intensity.
Turbulent Dissipation Rate ()
Turbulence dissipation, is the rate at which turbulence kinetic energy is converted into thermal internal energy. It is given by:
Where, is imperial constant specified in turbulence models (approximately 0.09), is turbulent kinetic energy and is turbulent length scale.
Specific Dissipation Rate ()
Specific dissipation rate is the rate at which turbulence kinetic energy is converted into thermal internal energy per unit volume and time. It is given by:
Where is imperial constant specified in turbulence models (approximately 0.09), is turbulent kinetic energy and is turbulent length scale.
Turbulence Viscosity Ratio ()
The turbulent viscosity ratio is simply the ratio of turbulent to laminar (molecular) viscosity. Turbulent viscosity ratio is given by:
Where is imperial constant specified in turbulence models (approximately 0.09), is density, is turbulent kinetic energy, is dynamic viscosity of fluid and is turbulence dissipation.
Related Reading
Turbulence Modeling for CFD 

A First Course in Turbulence 

Turbulent Flows 

Computational Fluid Mechanics and Heat Transfer 
The Tool Creators
Sanket Dange 
Sanket is working as a CFD engineer in CCTech. He has worked on numerous CFD projects in the filed of automobile and HVAC. He has worked as a tutor at LearnCAx and taught to students through LeanrCAx online as well as offline course modules. Currently he is working in the field of CFD software development which is mainly based on ANSYS FLUENT. Sanket has written blogs on various topics in CFD. He also has interest in open source CFD technologies. Sanket holds a Bachelors degree in Mechanical engineering from University of Pune. 
Subhransu Majhi 
Subhransu is man of all treads. He has worked on almost all aspects of CFD. Started with CCTech's education brand LearnCAx, he is now moved into cloud based CFD simulation product. Subhranshu has unique combination of skill sets including strong knowledge of physcis, numerical methods and an excellent programming skill sets. Subhranshu has extensively worked on CFD software customization and automation. He has worked on data center cooling software development. He has great passion for automation and customization and has written many blogs covering complex topic like UDF and CFD software automation. 