SpectraSim Documentation
Parameter · 04 Material

Dynamic viscosity

material.incompressible.mu Unit: Pa·s Step 04 · Material

The dynamic viscosity of an incompressible run. It follows the temperature through Sutherland's law until a value is typed over it; it is read-only for the compressible solver, which evaluates Sutherland's law itself in every cell.

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Theory

The incompressible solver uses the kinematic viscosity ν=μ/ρ\nu = \mu/\rho. Sutherland's law, equation (1), gives the viscosity of a gas as a function of the temperature only, with no pressure dependence; it rises with temperature (air: 18.2 µPa s at 20 °C, about 41 µPa s at 700 °C). The constants are those of Sutherland coefficient As and Sutherland temperature Ts, the same for air and exhaust gas.

A typed value replaces the computed one for the run, with a "user" badge, "reset to computed" and the report row "manual override".

Equations

μ=As T3/2T+Ts,ν=μρ\mu = \frac{A_s\,T^{3/2}}{T + T_s}, \qquad \nu = \frac{\mu}{\rho}
(1)
wheremeaningunit
μ\muDynamic viscosityPa s
AsA_sSutherland coefficient, 1.458e-6 by defaultkg/(m s K^0.5)
TsT_sSutherland temperature, 110.4 by defaultK
TTMaterial temperatureK
ν\nuKinematic viscosity the solver usesm²/s
ρ\rhoDensitykg/m³

Default and rule

Default
computed from the temperature (Sutherland's law)Computed by the program
Rule

Computed (the field is empty in the case file). Air at 20 °C: 1.81e-5 Pa s.

Source

Sutherland's law (Sutherland, 1893). The 2 % warning threshold is the program's own choice; it has no published basis.

Valid range > 0; warning when more than 2 % off the computed value

Values

Above 0.

Manual value

A typed viscosity more than 2 % away from the computed one is warned about.

Compressible solver

Ignored: the compressible solver applies Sutherland's law to the local temperature.

References 1

  1. Sutherland, W. (1893). The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 36(223), 507-531. DOI 10.1080/14786449308620508