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How do we write code for mean of reynolds stress tensor?

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Old   June 4, 2019, 05:38
Post How do we write code for mean of reynolds stress tensor?
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VL Srinivas
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In TKE equation, the production term consists of reynolds stress tensor multiplied by strain rate ?

The production term in tensor form = - <u_i u_j>*dU_i/dx_j ; here u=fluctuating component; U= mean component; d=partial derivative operator

While writing code for the TKE equation, do I have to add all the 9 components of the stress tensor and then average it over time ?

Production term: u'u' dU/dx + u'v'dU/dy + u'w'dU/dz + v'u'dV/dx + v'v'dV/dy + v'w'dV/dz + u'w'dW/dx + v'w'dW/dy + w'w'dW/dz

where U= U(x,y,z) and u'= u'(x,y,z,t)

Is this representation correct?
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Old   June 4, 2019, 09:51
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Yes the summation is correct. You do not need to time average because all the variables are already averaged. You can take the time-average. You'll just find out it doesn't do anything.


Maybe you got lazy and dropped the notation but if <> represents reynolds averaging then you should have:

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Production term: <u'u'> dU/dx + <u'v'>dU/dy + <u'w'>dU/dz + <v'u'>dV/dx + <v'v'>dV/dy + <v'w'>dV/dz + <u'w'>dW/dx + <v'w'>dW/dy + <w'w'>dW/dz
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Old   June 4, 2019, 10:12
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Thank you for the prompt reply. I will do that.

Regarding the <> for every element, I forgot to put that.


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programming, reynolds stress tensor, tke budget

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