VISCOSITY {SUTHERLAND | WILKE | KEYE | CONSTANT vis | TUNNEL9 | \ CUSTOM c_{1} c_{2} | CO2} |
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.
SUTHERLAND | Use Sutherland's law, designed for ideal gases with
T > 180 °R, as follows:
μ = 2.329 × 10^{−8} T^{3/2} / (T + 216) This is the default. | ||||||||||||||
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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:
μ_{n}/μ_{0} = (T/T_{0})^{3/2} (T_{0} + S) / (T + S) where T is the local static temperature, and μ_{0}, T_{0}, 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 = ∑^{N}_{i=1} [X_{i} μ_{i} / ∑^{N}_{j=1} (X_{j} φ_{i,j})] where φ_{i,j} is a mixing coefficient computed as φ_{i,j} = [8 (1 + M_{i} / M_{j})]^{−1/2} [1 + (μ_{i} / μ_{j})^{1/2} (M_{j} / M_{i})^{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 μ_{S} + (1 − f) μ_{K} where μ_{S} and μ_{K} 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)
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TUNNEL9 | Use a viscosity model obtained from AEDC Tunnel 9.
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CUSTOM | Use Sutherland's law with the constants c_{1} and
c_{2}, as follows:
μ = c_{1} T^{3/2} / (T + c_{2}) | ||||||||||||||
CO2 | Use a table lookup capability for CO_{2} gas. This requires the use of additional data files with the lookup information. |
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