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Flow Solver
Contains flow solver related guides, such as the reference and API guides.
Flow solver reference
Insert short description here
Modeling particle tracking
The following section describes the equations and forces that model particle trajectories, including treatment and effects of boundary conditions
Particle slip correction factor
Understand how the flow solver corrects the particle traction force when the no-slip assumption cannot be used.

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.
  - 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 of the particle motion
      The flow solver uses a one-way coupling between the flow field and the injected particles. Thus, the flow field is not affected by the particle transport problem.
    - Drag force
      The drag force on a particle is defined using the local Reynolds number, which considers the local fluid velocity field unaffected by the particle's presence or motion. By default, the flow solver uses a specific drag coefficient correlation, but you can also specify a fixed drag coefficient for the calculations.
    - Buoyancy
      The flow solver models buoyancy force acting on a spherical particle as a function of the particle's volume and density, as well as the fluid density.
    - Non-drag forces
      The non-drag force on a particle consists of the force due to the pressure gradient in the fluid surrounding the particle, and the added mass force to accelerate the virtual mass of the fluid in the volume occupied by the particle.
    - Brownian and turbulent diffusion
      The phenomenon of small scale chaotic motion of particles through a fluid, due to the sub‑continuum interactions with individual fluid particles, is known as Brownian motion. In the case of a turbulent flow, chaotic motion of particles is also observed. It is due to the instantaneous forces arising from the turbulent, continuum-scale fluctuations of the velocity and pressure fields. This chaotic motion is estimated within the boundaries of an element during a particle time step.
    - Particle motion equations
      The flow solver uses many equations to modelize particle trajectories. This page groups them for easy access.
    - Particle slip correction factor
      Understand how the flow solver corrects the particle traction force when the no-slip assumption cannot be used.
    - Initial conditions for injected particles
      Understand how the flow solver modelizes initial conditions for injected particles for transient and steady state solutions.
    - Boundary treatment
      Boundaries that represent a discontinuity in the equations of particle motion and particle position require a careful treatment. Learn how the flow solver represents these boundaries.
    - Wall boundaries
      The flow solver treats both slip or no-slip wall boundaries identically in the particle transport problem. However it applies different boundary treatments depending on the particle impact type.
    - Inlet and symmetry boundaries
      Learn how the flow solver modelizes the motion of particles for inlets or symmetry boundaries.
    - Periodic boundaries for particle tracking
      Understand how the flow solver relates the aproach and departure velocities for rotational and translational periodic boundaries.
  - 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.

Particle slip correction factor

Understand how the flow solver corrects the particle traction force when the no-slip assumption cannot be used.

The flow solver solves the Particle motion equations for a rigid sphere by imposing a no-slip assumption at the particle surface. This assumption breaks when the Knudsen number is high. This occurs when the particle size, given by its diameter d is the same order as the mean free path λ of the particle. Since the particle diameter d is usually fixed, it is the mean free path λ of the particle that dictates whether this assumption is valid or not.

When the no-slip assumption is no longer valid, the flow solver corrects the particle traction force by dividing it by the Cunningham correction factor C [34]:

where α, β, and γ are experimentally determined constants that are equal to 1.165, 0.483, and 0.997, respectively for ideal gases. The only unknown in the previous equation is the mean free path of the particle in the Knudsen number. The mean free path of the particle can be determined by evaluating the equation:

where:

T is the absolute temperature of the ideal gas.
P is the absolute pressure of the ideal gas.
S is the specified Sutherland constant for the viscosity of the gas.
T₀ is the specified reference temperature of the gas.
P₀ is the specified reference pressure of the gas.
λ₀ is the reference mean free path of the gas at temperature T₀ and pressure P₀, given by the following equation:
μ₀ is the reference viscosity of the ideal gas.
ρ₀ is the reference density of the ideal gas, which is calculated using ideal gas law.
k_B is the Boltzmann constant.
η is the Avogadro's number.
R is the universal gas constant.
R_g is the specific gas constant, which is obtained from the gas material properties.

The flow solver applies this correction factor to the net traction force acting on the particle surface in the following two ways:

The equations of motion for the particle trajectory is the corrected form given by:

Where is the uncorrected traction force

For detailed equations of these forces, see particle motion equations.