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VISCOSITY - Specification of viscosity law

Structured Grids

 VISCOSITY {SUTHERLAND | WILKE | KEYE | CONSTANT vis | TUNNEL9 | \            CUSTOM c1 c2 | CO2}

Unstructured Grids

 VISCOSITY {SUTHERLAND | WILKE | CONSTANT}

This keyword allows you to specify the method of computing the transport properties.

The equations shown below are for the laminar viscosity coefficient μ. For all the options except WILKE, in Wind-US the laminar thermal conductivity coefficient k is equal to the viscosity coefficient, when non-dimensionalized. For WILKE, the form of the equations used for k is the same as those used for μ, but with different constants from the chemistry data (.chm) file.

In all of the equations, μ is in slug/ft-sec and T is in °R.

### Structured Grids

SUTHERLAND   Use Sutherland's law, designed for ideal gases with T > 180 °R, as follows:

μ = 2.329 × 10−8 T3/2 / (T + 216)

This is the default.

WILKE Use Wilke's law, designed for multi-species flow (real gases). First, the viscosity coefficient is computed for each individual species n using Sutherland's law, as follows:

μn/μ0 = (T/T0)3/2 (T0 + S) / (T + S)

where T is the local static temperature, and μ0, T0, and S are constants read from the chemistry data (.chm) file for species n. For N total species, the individual viscosity coefficients are combined using

μ = ∑Ni=1 [Xi μi / ∑Nj=1 (Xj φi,j)]

where φi,j is a mixing coefficient computed as

φi,j = [8 (1 + Mi / Mj)]−1/2 [1 + (μi / μj)1/2 (Mj / Mi)1/4] 2

X is the species mole fraction, and M is the species molecular weight.

KEYE Use Sutherland's law for T ≥ 180 °R, Keyes' law for T ≤ 160 °R, and a linear combination of the two for 160 °R < T < 180 °R. Sutherland's law is written as above. Keyes' law is given by:

μ = 2.32 × 10−8 T 1/2 / (1 + (220/T) × 10−9/T)

And the linear combination is given by

μ = f μS + (1 − f) μK

where μS and μK are the viscosity coefficients from Sutherland's and Keyes' laws, and f = (T - 160) / 20.

CONSTANT Use a constant molecular viscosity of vis (slug/ft-sec)

TUNNEL9 Use a viscosity model obtained from AEDC Tunnel 9.

 μ = 8.913 × 10−10 T 0.979 for T ≤ 227 °R μ = 2.144 × 10−8 T 3/2 / (T + 179.1) for 227 °R < T ≤ 795 °R μ = 6.050 × 10−9 T 0.659 for T > 795 °R

CUSTOM Use Sutherland's law with the constants c1 and c2, as follows:

μ = c1 T3/2 / (T + c2)

CO2 Use a table lookup capability for CO2 gas. This requires the use of additional data files with the lookup information.

### Unstructured Grids

For unstructured grids, only the Sutherland, Wilke, and constant viscosity models have been extensively exercised. The equations are the same as shown above for structured grids.

Last updated 30 Sep 2016