Derivation of boundary condition for turbulent dissipation

FluidKo · August 23, 2022, 01:12

Hello everybody!

I'm wondering how below boundary condition is derived.
$\epsilon =\frac{C_{\mu }^{0.75}k^{1.5}}{L}$

I know below formula.
$\epsilon=\frac{C_{\mu }k^{2}}{\nu _{T}}$ .

But I don't know how upper formula is derived from lower formula.

Thank you~!

LuckyTran · August 23, 2022, 01:52

The first formula is the so-called equilibrium law. It is not an exact result but one worth knowing. There was a somewhat recent discussion in Annual Revs. Fluid Mechanics. People often use this formula to calculate a reasonable value for epsilon to be applied as an inlet boundary condition. For super accurate simulations, you have to get the real value of epsilon via even more accurate simulation or measure it directly.

The second formula is the k-epsilon turbulence model itself.

FluidKo · August 23, 2022, 02:06

Quote:

Originally Posted by LuckyTran

The first formula is the so-called equilibrium law. It is not an exact result but one worth knowing. There was a somewhat recent discussion in Annual Revs. Fluid Mechanics. People often use this formula to calculate a reasonable value for epsilon to be applied as an inlet boundary condition. For super accurate simulations, you have to get the real value of epsilon via even more accurate simulation or measure it directly.

The second formula is the k-epsilon turbulence model itself.

Aha that is just derived from dimensional analysis.

Thank you~!

August 23, 2022, 01:12	Derivation of boundary condition for turbulent dissipation	#1
FluidKo Senior Member Sangho Ko Join Date: Oct 2021 Location: South Korea Posts: 135 Rep Power: 4	Hello everybody! I'm wondering how below boundary condition is derived. $\epsilon =\frac{C_{\mu }^{0.75}k^{1.5}}{L}$ I know below formula. $\epsilon=\frac{C_{\mu }k^{2}}{\nu _{T}}$ . But I don't know how upper formula is derived from lower formula. Thank you~!

August 23, 2022, 01:52		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,672 Rep Power: 65	The first formula is the so-called equilibrium law. It is not an exact result but one worth knowing. There was a somewhat recent discussion in Annual Revs. Fluid Mechanics. People often use this formula to calculate a reasonable value for epsilon to be applied as an inlet boundary condition. For super accurate simulations, you have to get the real value of epsilon via even more accurate simulation or measure it directly. The second formula is the k-epsilon turbulence model itself. FluidKo likes this.

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