There is the inconsistency in units for non-Newtonian viscosity calculations in the Herschel-Bulkley model. The inconsistency arises because the model expresses shear stress (tau) in units of N/m^2 (Pascals), while the shear rate (gamma_dot) is in units of s^-1 (reciprocal seconds).
Here's the breakdown:
* Shear stress (tau): N/m^2 (measures force per unit area)
* Shear rate (gamma_dot): s^-1 (measures rate of deformation)
Kinematic viscosity (nu) has units of m^2/s, which combines units from both shear stress and shear rate. However, the Herschel-Bulkley model directly outputs kinematic viscosity below the yield stress threshold, while it calculates a dynamic viscosity (eta) above the threshold (eta = nu * rho, where rho is density).
The solution you propose is indeed correct:
* tau0 and k parameters should be pre-divided by density (rho). This ensures that the units cancel out correctly and the final result is kinematic viscosity (m^2/s) as expected.
The documentation oversight you identified is a common issue. Many resources don't explicitly mention this pre-division because it's assumed as a standard practice in computational rheology.
Here's a recommendation:
* Before implementing the model, consult the OpenFOAM user guide or community forums for confirmation.
* Look for examples or tutorials on implementing the Herschel-Bulkley model in OpenFOAM to see how others handle the units.
* If the documentation remains unclear, consider contacting the OpenFOAM developers for clarification.
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