# Fluid Configuration¶

## Conceptual Overview¶

Fluids are gases and liquids that flow when subject to an applied shear stress. For single-phase fluids, momentum transport is governed by the fluid density and viscosity. For multi-phase systems, the surface tension must also be defined to describe dynamics at the interface between two phases.

M-Star CFD can handle both Newtonian and non-Newtonian fluid rheology. The available fluid models, along with the relevant simulation parameters, are described in the sections that follow.

Laminar and transitional flows are typically modeled via direct numerical simulation. Turbulent fluid flows in M-Star CFD are modeled using implicit large eddy simulations (ILES) or large eddy simulation (LES). Additional theoretical details related to the LES model are provided in the Theory and Implementation section of this manual.

Users must select a fluid configuration. Four configurations are available:

Single phase

Free surface

Two-fluid immiscible

None

In the sections that follow, each of these configurations are discussed in detail.

## Single Phase¶

Single phase models, as the name suggests, are simulations involving a single base fluid with Newtonian or non-Newtonian rheology. Common applications include pipe flow simulations, well-baffled agitated tanks, jet mixing systems, and pumps. Within this configuration, users must specify the fluid density and define the constitutive relationship between fluid stress and fluid strain. As discussed in particleFields additional phases (such as discrete bubbles and discrete solid particle) can be added to the system and one- or two-way coupled to the fluid. Secondary miscible fluids with arbitrary densities and viscosities, as discussed in Miscible Fluids, can be also added to the base fluid. Thermal fields and scalar fields can also be superimposed on the single phase fluid, as discussed in Basic Concepts and Scalar Fields.

Within the single phase model, users can chose from one of five constitutive relationships:

Newtonian

Power law (with or without a yield stress)

Carreau

Custom expression

Briefly speaking, relationships (1)-(3) are familiar Newtonian and non-Newtonian rheology models. Relationship (4) represent custom expressions that may be more complex functions of strain, stress, age, species concentration, miscible fluid volume fraction, custom variables, particle concentration, and temperature. Additional details for each of these relationships are provided in Fluid Rheology

In single phase models, the entire interior zone of the lattice domain is assumed to be filled with the fluid.

## Free Surface¶

Free surface models are simulations involving a moving free surface with a single Newtonian or non-Newtonian rheology. Common applications include filling/draining simulations, jet sprays, sloshing, vortex formation, and coating processes. Within this configuration, users must specify the fluid density, surface tension and define the constitutive relationship between fluid stress and fluid strain. As discussed in particleFields, additional phases (such as discrete bubbles and discrete solid particle) can be added to the system and one- or two-way coupled to the fluid. Secondary miscible fluids with arbitrary densities and viscosities, as discussed in Miscible Fluids, can also be added to the base fluid. Thermal fields and scalar fields can also be superimposed on the single phase fluid, as discussed in Basic Concepts and Scalar Fields.

Within free surface model, users can chose from one of four constitutive relationships:

Newtonian

Power law (with or without a yield stress)

Carreau

Custom expression

Briefly speaking, relationships (1)-(3) are familiar Newtonian and non-Newtonian rheology models. Relationship (4) represent custom expressions that may be more complex functions of strain, stress, age, species concentration, miscible fluid volume fraction, custom variables, particle concentration, and temperature. Additional details for each of these relationships are provided in Fluid Rheology

Unlike the single phase fluid, which is assumed to fill the entire interior zone of the lattice, users must specify which portions of the interior zone (if any) are initially filled with the fluid. Any initial fluid configuration can be specified using any combination of parametric geometry and/or user-imported geometry. By default, the initial condition is a parametric “Fluid Height Box”. This cuboid geometry is anchored to the main lattice domain, but the height of the box aligned with the “UP-direction” can be adjusted. The background initial condition is assumed to be empty, while the Fluid Height Box is assumed to be fluid. Ad discussed in initialFluid, an arbitrary number of initial condition regions can be added to the model.

## Two Fluid: Immiscible¶

Immiscible fluid models, as the name suggests, are simulations involving a two immiscible fluids with Newtonian or non-Newtonian rheology. Common applications include two-phase gas flow simulations, colloid suspensions, and oil-water systems, Users must specify, for each fluid, the density and the constitutive relationship between fluid stress and fluid strain. The two immiscible fluids do not need to have the same constitutive relationships. Users must also specify a surface tension between the two fluids. As discussed in particleFields, additional phases (such as discrete bubbles and discrete solid particle) can be added to the system and one- or two-way coupled to the fluid. Secondary miscible fluids with arbitrary densities and viscosities, as discussed in Miscible Fluids, can also be added to the base fluids. Thermal fields and scalar fields can also be superimposed on the single phase fluid, as discussed in Basic Concepts and Scalar Fields.

For each fluid, users can chose from one of four constitutive relationships:

Newtonian

Power law (with or without a yield stress)

Carreau

Custom expression

Briefly speaking, relationships (1)-(3) are familiar Newtonian and non-Newtonian rheology models. Relationship (4) represent custom expressions that may be more complex functions of strain, stress, age, species concentration, miscible fluid volume fraction, custom variables, particle concentration, and temperature. Additional details for each of these relationships are provided in Fluid Rheology

Unlike the single phase fluid, which is assumed to fill the entire interior zone of the lattice, users must specify which portions of the interior zone are initially filled with each fluid. The “Background Fluid” describes the primary fluid in the tank. This background is typically defined as fluid1, but can be redefined by the user. The initial distribution of the secondary fluid (which is typically fluid2) can be specified using any combination of parametric geometry and/or user-imported geometry. By default, the secondary fluid condition is a parametric “Fluid Height Box”. This cuboid geometry is anchored to the main lattice domain, but the height of the box aligned with the “UP-direction” can be adjusted. The background initial condition is assumed to be Fluid 1, while the Fluid Height Box is assumed to be Fluid 2. Ad discussed in initialFluid, an arbitrary number of initial condition regions can be added to the model.

## No Fluid¶

In this set-up, which is typically paired with particle discrete element modeling (DEM), no fluid is modeled explicitly. Instead, the effects of any fluid on particle dynamics are modeled implicitly per the user-defined fluid viscosity and density. Within these calculations, the fluid velocity is always assumed to be zero.