Power-law¶
A Power-law Fluid is a generalized non-Newtonian fluid where the shear stress, \(\tau\), is related to the shear rate, \(\dot{\gamma}\) , such that:
where \(\rho\) is the fluid density, \(K\) is the flow consistency, and \(n\) is the fluid behavior index. The units on \(\rho\) are taken to be \(kg/m^3\), the units on \(K\) are taken to be \(m^2/s^{2-n}\), and \(n\) is dimensionless. From this constitutive relationship, the apparent viscosity \(\nu_a\) of a power-law fluid is then defined as:
where the units \(\nu_a\) are \(m^2/s\). This definition of apparent viscosity is used to calculate the spatiotemporal variation in viscosity across the fluid volume due to spatiotemporal variations in strain rate.
Property Grid¶
Fluid Properties
¶
- Rheology Type
Apply Power-law rheology. Local fluid viscosity is calculated from the local shear rate using a user-defined flow consistency index, flow behavior index, and yield stress.
- Density
kg/m 3 | The density of the fluid.
- Yield Stress
Pa | Yield shear stress.
- Power Law K
m 2 /s 2-n | Flow consistency index.
- Power Law N
Flow behavior index n.
Rheology Limits
¶
These are user defined limits that provide a lower and upper bound on the viscosity realized in the simulation. Appropriate limits can help maintain simulation stability and maximize the allowable simulation time step.
- Min Viscosity
m 2 /s | The minimum fluid viscosity realized in the simulation.
- Max Viscosity
m 2 /s | The maximum fluid viscosity realized in the simulation.