Variable Property Support

The different material properties that can be modeled are discussed in the following sections.

Density

The density models can be specified for all types of media supported by AcuSolve (solid, fluid and shell). They are:

Constant Density: A constant density for the media. This is generally used for incompressible flow simulations.
Boussinesq Model: Use of the Boussinesq approximation, where the variation in density is assumed to be a linear function of temperature and the density variation is accounted only in the body force terms.
Isentropic Model: The constant entropy gas model, where the variation in density is taken into account for all the terms in the momentum equations.
Ideal Gas Model: The density is based on the ideal gas law. The variation in density is taken into account for all the terms in the momentum equations.
Customized Models: Custom variable property functions for density can be specified using curve fit options (piecewise linear and cubic spline) as a function of single independent variable. User functions can be used to model more complex density models. In case of customized models the density variation is applicable to all the terms.

Viscosity

The molecular viscosity models used in the flow (momentum) equations, specified for the fluid medium are:

Constant Viscosity: A constant viscosity for the fluid medium. This is the simplest case of a Newtonian model for calculation of the stress tensor.
Ramped Viscosity: The viscosity is ramped down 1,000 times from the viscosity value specified at time step one to the viscosity value at time step ten, after which the value from time step ten is used.
Non-Newtonian Models: Non-Newtonian viscosity models based on Power Law, Bingham model, Carreau-Yasuda model can be specified.
Customized Models: Custom variable property functions for viscosity can be specified using curve fit options (piecewise linear and cubic spline) as a function of single independent variable. User functions can be used to model more complex viscosity models.

Porosity

AcuSolve uses the Darcy-Forchheimer porosity model for the flow (momentum) equations, specified for the fluid medium. The porosity model modifies the momentum equation as follows: (1)

\frac{ρ}{\emptyset} \frac{\partial \vec{u}}{\partial t} + (ρ \vec{u} \cdot \nabla) \vec{u} + R \vec{f} = - \nabla p + ρ b + \nabla \cdot τ

where

$\vec{f}$ is the field vector contribution due to porous media, also referred to as porous media forces.
$R$ is the rotation tensor which rotates $\vec{f}$ to the global coordinate system.

The porous media forces are given by: (2)

f_{i} = (\frac{C_{D a r c y} μ}{k_{i}} + \frac{C_{F o r c h} ρ}{\sqrt{k_{i}}} | u |) u_{i}

where

$C_{D a r c y}$ and $C_{F o r c h}$ are the Darcy and Forchheimer coefficients, respectively.
$k_{i}$ is the permeability in the principal direction $i$ .

Viscoelasticity

AcuSolve supports simulations involving viscoelastic materials using the Upper Convected Maxwell Model and the Upper Convected Maxwell Log Model. The viscoelastic models used in the flow (momentum) equations, have various sub models to determine the rate of stress build up and rate of stress decay. These include:

Oldroy-B Model: Stress build up and decay rate obtained by defining the relaxation time and polymer viscosity of the fluid.
Giesekus Model: Stress build up and decay rate obtained by defining the mobility factor along with the relaxation time and polymer viscosity of the fluid.
Phan-Thien-Tanner Model (PTT): Stress build up and decay rate obtained by defining the PTT extensibility factor and the diffential ratio along with the relaxation time and polymer viscosity of the fluid.
Customized Models: Customized models based on a user function.

Additional Properties

AcuSolve also supports the modeling of several additional properties such as Surface Tension, Conductivity, Diffusivity, Contact Angle and Specific Heat of the fluid medium.

All of these material properties except Contact Angle can be specified using customized models based on curve fit options (piecewise linear and cubic spline) as a function of single independent variable or by using user functions.

The Conductivity can be additionally specified to be based on an Isotropic Prandtl number Model, ramped to a value or set as anisotropic using the customized models.

The Diffusivity can be additionally ramped to a value.

Contact Angle for free surfaces with surface tension can be set to a constant value or automatically computed from the boundary conditions.