k-epsilon_development

The given number has to have a 9 in the first place . Each digit after the 9 activates/deactivates the developments of the k-epsilon model since 2023. Default: COMP_development(1) = 91001010 (previous k-epsilon model, but with the bug corrections and restriction on turbulent length scale)

Digit	Description
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first	9 (compulsory, as leading entrance)
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second	correction factor A for the integration of velocity
	0 : A = 1
	1 : A determined by the layer distance to the wall (see Section 2.5 in DOCUMATH_NumericalIntegrationOfTurbulence.pdf)
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third	how to produce G
	0 : use Mises norm in the sense \( G = \lvert \frac{1}{2} \left( \nabla {\mathbf v}^T + (\nabla {\mathbf v}^T)^T \right) \rvert_{Mises}^2\)
	1 : use exactly \( G = 2 S_{ij} S_{ij}\) as given in the literature
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fourth	wall values according to ANSYS documentation
	0 : classical use of %BND_wall%
	1 : use Ansys wall values
	use the production term \( \bar{G}\) and apply a Dirichlet boundary condition \( \epsilon = \bar{\epsilon}\) as given in https://www.afs.enea.it/project/neptunius/docs/fluent/html/th/node100.htm
	Note: In this case, DEBUG_GeneralParameter(42), addressing the production term along the walls, has no significance and is ignored.
	2 : ONLY employ the ANSYS-formulation of G
	3 : ONLY employ the ANSYS-formulation of epsilon
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fifth	boundary formulation for BC_k and BC_eps which are subject to BC_k = %BND_wall% as well as BC_eps = %BND_wall%
	there was a bug for the diffusive terms of k and epsilon at walls. According to DOCUMATH_NumericalIntegrationOfTurbulence.pdf, the correct formulation is
	\( \left. \frac{\text{d}\left( \text{k} \right)}{\text{dt}} \right]_{add} = \frac{1}{\rho}\left( \frac{\partial \text{k} }{\partial \text{n}}-\frac{\text{k} }{\alpha \cdot h} \right)\cdot \frac{1}{\beta h}\) and \( \left. \frac{\text{d}\left( \varepsilon \right)}{\text{dt}} \right]_{add} = \frac{1}{\rho}\left( \frac{\partial \varepsilon}{\partial \text{n}}-\frac{\varepsilon}{\alpha \cdot h} \right)\cdot \frac{1}{\beta h}\)
	In the versions before beta2023.05.0, the terms \( \frac{\partial \text{k} }{\partial \text{n}}\) and \( \frac{\partial \varepsilon}{\partial \text{n}}\) were missing by accident.
	0 : use the incorrect formulation (as before beta2023.05.0)
	1 : use the correct formulation
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sixth	restriction of epsilon based on local length scale in the sense: increase epsilon such that \( L_{turb} < \gamma H\) . In fact \( \epsilon > \frac{ c_{\mu} k^{3/2} }{ \gamma H }\)
+ seventh	000 : do not employ this restriction
+ eighth	001 ... 999 : defines the value of \( \gamma\) . For example 123 defines \( \gamma = 1.23\) , or 008 leads to \( \gamma = 0.08\) .
	The smaller this value, the smaller the resulting turbulent viscosity.
	Thus this value can be used to set up and appropriate filter width for an LES-model
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ninth	restriction of epsilon for wall points , based on local length scale in the sense: increase epsilon such that \( L_{turb} < \gamma \cdot \alpha H\) . In fact \( \epsilon > \frac{ c_{\mu} k^{3/2} }{ \gamma \cdot \alpha H }\) the possible values 1 ... 9 define the value of \( \gamma\) . For example 7 defines \( \gamma = 0.7\) , or 002 leads to \( \gamma = 0.3\) . \( \alpha H\) is the virtual distance of the wall point in the tubulence sense.