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Flow Solver
Contains flow solver related guides, such as the reference and API guides.
Flow solver reference
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Modeling a gas mixture
The flow solver uses the scalar equation to model a gas mixed in any proportion with the main gas. The software supports up to five gases in the mixture. All gases are assumed to behave as ideal gases using the ideal gas law.

Flow Solver
Contains flow solver related guides, such as the reference and API guides.
- Flow solver guides
  Maya HTT's flow solver is included and distributed with Simcenter 3D and Simcenter Femap. This page contains links to flow solver guides, which help you understand how the flow solver works.
- Flow solver reference
  Insert short description here
  - Introduction
    The flow solver computes a solution to the non-linear, partial differential equations for the conservation of mass, momentum, energy, and general scalars in general complex 3D geometries. It uses an element-based finite volume method and iterative Krylov methods to discretize and solve the governing equations.
  - Nomenclature
    The nomenclature table offers a description and sample units or constant values of the variables used in the Flow Solver Reference Manual.
  - Governing equations
    A model can be comprised of multiple flow enclosures. Each enclosure is a separate group of three-dimensional elements that form a separate fluid domain from the remaining geometry. The physical scales of each enclosure, such as the length scale, time scale, pressure, and temperature are independent of the other enclosures. The flow solver solves governing equations separately for each flow enclosure.
  - Source term
    The source term can represent body forces or flow resistance forces to model different physical phenomena.
  - Turbulence models
    In the flow solver, the flow field can be solved as laminar or as turbulent using governing equations.
  - Boundary conditions
    This section outlines different boundary conditions supported by the flow solver and the associated considerations.
  - Modeling a gas mixture
    The flow solver uses the scalar equation to model a gas mixed in any proportion with the main gas. The software supports up to five gases in the mixture. All gases are assumed to behave as ideal gases using the ideal gas law.
    - Species enthalpy diffusion in the homogeneous gas mixture
      The flow solver allows you to include the enthalpy flux to the low-speed energy equation. This term should be included when species mass fraction gradients are significant as in combustion problems or for a gas mixture with different temperatures at low speed.
  - Modeling humidity
    The flow solver uses the gas mixture scalar equation to model humidity that is defined as a mixture of water vapor in air.
  - Modeling non-Newtonian fluid
  - Modeling particle tracking
    The following section describes the equations and forces that model particle trajectories, including treatment and effects of boundary conditions
  - Modeling fluid structure interaction
    Fluid structure interaction (FSI) computations account for motion or deformation of the solid structure boundaries that are interacting with the adjacent fluid flow. The flow solver handles both transient and static fluid structure interactions.
  - Discretization
    The following section describes the discretization methods used by the flow solver to discretize the governing equations.
  - Solver numerical methods
    The following section describes numerical methods used by the flow solver such as the linear equation solution, which acts as a preconditioning method to the basic iterative algorithm, and other solver methods, such as Krylov methods.
  - Flow solver files
    The following table describes the flow solver files, which are written in the run directory during the solving process.
  - Flow solver bibliography
    The following bibliography lists all sources used to explain how the flow solver works.
- Flow solver flowcharts
  This section consists of flowcharts that illustrate the methodology of the flow solver when you run a simple steady-state or transient simulation, and does not cover all features and situations. It also highlights how the flow solver is coupled to the thermal solver for a simple steady-state or transient coupled thermal-flow simulation.

Modeling a gas mixture

The flow solver uses the scalar equation to model a gas mixed in any proportion with the main gas. The software supports up to five gases in the mixture. All gases are assumed to behave as ideal gases using the ideal gas law.

The flow solver uses the conservation equations of mass, momentum, and energy to compute the gas mixture.

When modeling a gas mixture, the following properties are calculated at every iteration:

ρ the gas mixture density
C_p the specific heat at constant pressure of the gas mixture
k the thermal conductivity of the gas mixture
μ the dynamic viscosity of the gas mixture

This property update is based on the assumption that the two gases behave as ideal gases. Ideal gas equations of state for two gases, defined as follows:

p₁, p₂ represent the partial pressures of gas 1 and gas 2.
R₁, R₂ are the gas constants of gas 1 and gas 2.

Pressure and density of the gas mixture

The pressure of the gas mixture is given by:

The density of the gas mixture is given by:

Specific heat at constant pressure of the gas mixture

The specific heat of the mixture, C_p, is calculated from the following equations [18]:

Ĉ_p is the molar specific heat of the mixture, defined as:

is the molar mass of the mixture, defined as:

In these equations, and are the molar masses of gas 1 and gas 2.

Thermal conductivity and dynamic viscosity of the gas mixture

The thermal conductivity, k, and the dynamic viscosity, μ, of the mixture are calculated using the method of Wilke [19], which is valid for gases at low pressures.

The property η_m, that represents the the gas mixture thermal conductivity or the gas mixture dynamic viscosity, is given by:

where ϕ₁₂ and ϕ₂₁ are given by:

In these equations:

η_m, η₁, and η₂ represent the property, thermal conductivity or viscosity, of the gas mixture, gas 1, and gas 2, respectively.
X₁ and X₂ are the mole fractions of the two gases given by: