Ansys Innovation Courses

4 Equations and 13 Unknowns

• Abubakar
Subscriber
Hi Karthik, nIn one of the basic turbulent flow video the instructor is saying that in Incompressible Navier stroke equation we have 4 equations and 4unknowns(u,v,w,p) which is correct but the instructor is saying that after averaging we are getting 13 unknowns how? We are getting only three additional unknowns so, total it becomes 7unknowns not 13 right? And the additional unknowns which we are getting after averaging is nothing but the fluctuations of velocity in each direction. nCan you please help me on this? For your reference I have attached the SS where the instructor is saying that we have 13 unknowns after averaging. nThank you, nAbubakar khann
• System_delete
Subscriber
This discussion was created from comments split from: Is it possible to remove a course from your dashboard?.
• Kalyan Goparaju
Ansys Employee
Hello Abubakar, nFor RANS equations, the unknowns are not the velocity fluctuations, they are infact the product of velocity fluctuations. Therefore, the total unknowns are u,v,w,p,u'u',u'v',u'w',v'u',v'v',v'w',w'u',w'v',w'w' = 13. Making use of the symmetric nature of the stress tensor, we can safely say u'v'=v'u', u'w'=w'u', v'w'=w'v'. Therefore, the actual number of unknowns are 10! nI hope this answers your question. nRegards, nKalyan nPS - I dropped the bar from the terms for simplicity. n
• Abubakar
Subscriber
Hi Kalyan Sir, nI got my answer, thanks for clearing my doubt. nI have a request, can you please make a video on a SIMPLE and PISO algorithm.nnnThank you, nAbubakar khann
• Abubakar
Subscriber
Hi Kalyan Sir, nI got my answer, thanks for clearing my doubt. I have a request, can you please make a video on SIMPLE and PISO algorithm.nThank you, nAbubakar khann
• Karthik R