WIND User's Guide - Keyword Reference, VISCOSITY

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VISCOSITY - Specification of viscosity law

VISCOSITY {SUTHERLAND | WILKE | KEYE | CONSTANT vis}

This keyword allows you to specify the method of computing the transport properties. The equations shown below are for the laminar viscosity coefficient mu. For all the options except WILKE, in WIND 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 mu, but with different constants from the chemistry data (.chm) file.

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

      mu = 2.329 × 10^-8 T^3/2 / (T + 216)

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:

      mu_n / mu₀ = (T / T₀)^3/2 (T₀ + S) / (T + S)

where T is the local static temperature, and mu₀, 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

      mu = sum^N_i=1 [ X_i mu_i / sum^N_j=1 ( X_j phi_i,j ) ]

where phi_i,j is a mixing coefficient computed as

      phi_i,j = [ 8 ( 1 + M_i / M_j ) ] ^-1/2 [ 1 + ( mu_i / mu_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:

      mu = 2.32 × 10^-8 T^1/2 / (1 + (220/T) × 10^-9/T)

And the linear combination is given by

      mu = f mu_S + (1 - f) mu_K

where mu_S and mu_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)

In all of the above equations, mu 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: mu = 2.329 × 10^-8 T^3/2 / (T + 216)
	`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: mu_n / mu₀ = (T / T₀)^3/2 (T₀ + S) / (T + S) where T is the local static temperature, and mu₀, 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 mu = sum^N_i=1 [ X_i mu_i / sum^N_j=1 ( X_j phi_i,j ) ] where phi_i,j is a mixing coefficient computed as phi_i,j = [ 8 ( 1 + M_i / M_j ) ] ^-1/2 [ 1 + ( mu_i / mu_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: mu = 2.32 × 10^-8 T^1/2 / (1 + (220/T) × 10^-9/T) And the linear combination is given by mu = f mu_S + (1 - f) mu_K where mu_S and mu_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)