Drag Force
Use the Drag Force node to exert a drag force on particles in a fluid.
Supported formulations:
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Newtonian,
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Newtonian, first order, and
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Newtonian, ignore inertial terms.
For Newtonian, ignore inertial terms the Drag Force is required in all domains in the selection of the physics interface.
Drag Force
Select a Drag law: Stokes (the default), Schiller-Naumann, Haider-Levenspiel, Oseen correction, Hadamard-Rybczinski, or Standard drag correlations.
For Newtonian, ignore inertial terms the Drag law list is not shown. The Stokes drag law is always used.
Stokes drag and the Oseen correction are applicable for particles that have a relative Reynolds number much less than one. If the particle Reynolds number is greater than one, then select Schiller-Naumann. If, in addition, the particles are nonspherical, select Haider-Levenspiel. If the particles are very pure gas bubbles or liquid droplets, select Hadamard-Rybczinski. The Standard drag correlations are a set of piecewise-continuous functions that are applicable over a wide range of relative Reynolds numbers.
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For all choices, enter coordinates for the Velocity field u (SI unit: m/s) based on space dimension. If another physics interface is present which computes the velocity field then this can be selected from the list.
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For all choices, the Dynamic viscosity μ (SI unit: Pa·s) is taken From material. For User defined enter another value or expression.
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For all choices, the fluid Density ρ (SI unit: kg/m3) is taken From material. For User defined enter another value or expression.
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For the Stokes drag law, the Include wall corrections check box is shown. This check box is cleared by default. Select it to apply corrections to the drag force for particles in a wall-bounded flow. If the Include wall corrections check box is selected, the Wall Corrections section will be shown (see below).
Selecting the Include wall corrections check box can cause a significant increase in computation time in 3D models with a fine boundary mesh.
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For Haider-Levenspiel enter a value or expression for the particle Sphericity Sp (dimensionless). The default is 1.
Particle Motion in a Fluid in Theory for the Particle Tracing for Fluid Flow Interface.
Rarefaction Effects
This section is only available if the Include rarefaction effects check box is selected in the physics interface Particle Release and Propagation section. It defines a correction factor that is multiplied by the drag force to account for a large particle Knudsen numbers.
Select an option from the Rarefaction effects list: Basset, Epstein, Phillips, Cunningham-Millikan-Davies (the default), or User defined.
The Basset model is appropriate for relative Knudsen numbers much less than one, while the Epstein model is appropriate for free molecular flows. The Phillips model is usable at intermediate values of the relative Knudsen number and shares the same asymptotic behavior as the Epstein and Basset numbers at very large and small Knudsen numbers, respectively. The Cunningham-Millikan-Davies model includes three tunable parameters that can be used to fit the drag force correction factor to empirical data.
Select an option from the Mean free path calculation list: Ideal gas, hard sphere collisions (the default) or User defined correction. For User defined correction enter a Mean free path correction λ’/λ (dimensionless). The default value is 1.
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If Basset, Epstein, or Phillips is selected from the Rarefaction effects list, enter an Accommodation coefficient σR (dimensionless). The default value is 1. The accommodation coefficient may be interpreted as the fraction of gas molecules that undergo diffuse reflection at the particle surface.
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If Cunningham-Millikan-Davies is selected from the Rarefaction effects list, enter the three dimensionless coefficients C1, C2, and C3. The default values are 2.514, 0.8, and 0.55, respectively. When entering a set of Cunningham coefficients, note that the COMSOL implementation of the Cunningham correction factor defines the relative Knudsen number using particle diameter, not radius.
Enter a value or expression for the Pressure p (SI unit: Pa). If a physics interface is present that computes the pressure, it can be selected directly from the list.
Drag Force in a Rarefied Flow in Theory for the Particle Tracing for Fluid Flow Interface.
Turbulent Dispersion
If particles are moving in a turbulent flow, this section can be used to apply random perturbations to the drag force to account for the turbulence.
Select an option from the Turbulent dispersion model list: None (the default), Discrete random walk, or Continuous random walk.
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If None is selected, no turbulent dispersion term is applied.
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If Discrete random walk is selected, a random term is added to the background fluid velocity when computing the drag force at every time step taken by the solver. The random perturbation term is held constant for a time interval equal to the interaction time of the particle with an eddy in the flow.
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If Continuous random walk is selected, a random perturbation is applied to each particle by integrating a Langevin equation. Unlike Discrete random walk, the perturbation of the background velocity that is applied to each particle depends on the time history of all previously applied perturbations.
If Discrete random walk or Continuous random walk is selected, enter values or expressions for the following:
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The Turbulent kinetic energy k (SI unit: m2/s2) determines the magnitude of the turbulent dispersion term. If a physics interface is present that computes the turbulent kinetic energy, it can be selected directly from the list.
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The Turbulent dissipation rate ε (SI unit: m2/s3) is related to the lifetime of eddy currents in the flow. If a physics interface is present that computes the turbulent dissipation rate, it can be selected directly from the list.
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The Lagrangian time scale coefficient CL (dimensionless) is used to compute the Lagrangian time scale of the particle-eddy interactions. The default value is 0.2.
The Continuous random walk model also supports corrections for anisotropic turbulence, which is prevalent in wall-bounded flows. Select the Include anisotropic turbulence in boundary layers check box to compute different random contributions to the fluid velocity field based on the streamwise, spanwise, and wall normal directions in the flow, which are computed using the fluid velocity direction and the direction to the nearest point on an adjacent wall. When searching for the nearest wall, boundaries using the Symmetry, Inlet, and Outlet features are ignored.
Selecting the Include anisotropic turbulence in boundary layers check box can cause a significant increase in computation time in 3D models with a fine boundary mesh. See the Wall Corrections section.
Particle Motion in a Turbulent Flow in Theory for the Particle Tracing for Fluid Flow Interface.
After selecting the Include anisotropic turbulence in boundary layers check box, enter a value or expression for the Friction velocity u∗ (SI unit: m/s). The friction velocity is used to define the wall distance in viscous units, which determines the width of the region in which anisotropic turbulence should apply. The default is 0.11775 m/s.
Additional Terms
The Include virtual mass and pressure gradient forces check box is cleared by default. Select this check box to exert additional forces on particles called the virtual mass (or added mass) force and the pressure gradient force. The virtual mass force is exerted on a particle moving through a fluid, as fluid must be displaced to fill the empty space the particle leaves behind.
The virtual mass and pressure gradient forces are most significant when the density of the surrounding fluid is of a similar order of magnitude to (or greater order of magnitude than) the particle density. Therefore they are often neglected when modeling solid particles in a gas, but can be very significant when modeling solid particles in a liquid. These forces also depend on the temporal and spatial derivatives of the fluid velocity components. Consider increasing the discretization order of the degrees of freedom for fluid velocity when modeling the fluid flow.
Virtual Mass Force and Pressure Gradient Force in Theory for the Particle Tracing for Fluid Flow Interface.
Wall Corrections
This section is only available if Stokes is selected as the Drag law in the Drag Force section. It is also shown if Continuous random walk is selected from the Turbulent dispersion model list and the Include anisotropic turbulence in boundary layers check box is selected in the Turbulent Dispersion section. This section controls the search algorithm that is used to locate the nearest point on a wall for each particle. The particle displacement from the nearest wall is used to define wall corrections for the drag force and to define fluid velocity perturbations from anisotropic turbulent dispersion.
Select a Mesh search method: Use tolerance, Closest point (the default), or Walk in connected component. For either Use tolerance or Walk in connected component, enter a value or expression for the Search radius r (SI unit: m). The default is 2 cm. The search radius can depend on global parameters but not on other variables.
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Use tolerance is a balanced option with better performance than Closest point, especially in finely meshed 3D geometries. As long as the Search radius is sufficiently large, this is a good option for channels or pipes with a large aspect ratio.
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Closest point is the most robust option, but also the slowest. Because it is not limited by a search radius, it is a fair choice when the model geometry includes both narrow channels and wide-open regions.
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Walk in connected component should only be used when the coordinates of the nearest point on a wall changes continuously over time for each particle, rather than jumping between different boundaries.
Wall Corrections in Theory for the Particle Tracing for Fluid Flow Interface.
Advanced Settings
Use the Particles to affect list to apply the force to specific particles. The available settings are the same as for the Force node.
If any option except None is selected from the Turbulent dispersion model list, the Drag Force feature creates random numbers. If, in addition, the Arguments for random number generation setting is User defined in the physics interface Advanced Settings section, enter the Additional input argument to random number generator. The default value is 1.