Learning Forum

[ABUBAKAR]

Hi,

Name of the video-Closure of RANS Equations - Lesson 5, Basic of Turbulent flow course. "The instructor is saying that quite often we ignored the kinetic energy term due to the negligible contribution of normal stress compared to turbulent stress" I think it should opposite, right? because the contribution of turbulent stress is more there will be more kinetic energy since they are directly proportional to each other.

I hope you understand my question.

Thank you,

Abubakar khan

[Kalyan Goparaju]

Hello,
Turbulent kinetic energy is defined as ­Øæÿ=0.5((­ØæóÔÇ▓ ­ØæóÔÇ▓ ) +(­ØæúÔÇ▓ ­Øæú' ) + (­ØæñÔÇ▓ ­ØæñÔÇ▓ ) ). The terms inside the brackets are referred to as the normal stresses. Based on the Boussinesq approximation, Reynolds stress can be written as a combination of the Strain rate tensor (made up of the mean flow velocity gradients) and the turbulent kinetic energy. Because the velocity fluctuations (uÔÇÖ,vÔÇÖ,wÔÇÖ) and the normal stresses are generally very small compared to the mean flow velocity gradients, the turbulent kinetic energy part of the Reynolds stress formulation can be ignored.
Hope this helps.
Thanks Kalyan

[ABUBAKAR]

Thank you sir for your quick support. I have two follow-up questions:
Let's say we consider the turbulent kinetic energy and it's defined as ­Øæÿ=0.5((­ØæóÔÇ▓ ­ØæóÔÇ▓ ) +(­ØæúÔÇ▓ ­Øæú' ) + (­ØæñÔÇ▓ ­ØæñÔÇ▓ ) ) so, my question is since we don't have an equation for fluctuations velocity then how does the solver calculate these fluctuations components.
How does the turbulent kinetic energy is ignored I mean does the user have to do something or the solver itself will ignore these terms based on the mean flow velocity gradients.

[Kalyan Goparaju]

Hello,
Fluctuations are always calculated. Each solver may have its own way of calculating time varying fluctuations, such as tracking a running average of a quantity and subtracting it from the instantaneous value.
The user doesn't have to do anything. Everything is taken care off by the solver. For e.g.,in Fluent, when using the Spalart-Allmaras Turbulence Model, the Reynolds stresses are calculated without using the TKE term. However, for all the other turbulence models where an evolution equation for TKE is used (like k-e, k-w etc.), the effect of TKE is included in calculating the Reynolds stresses.
Kalyan

[ABUBAKAR]

Got it sir thank you for your help.