Solids model

Solids settings

Enabling the SOLIDS solver and specifying options common to both DEM and PIC models. The following inputs must be preceded by the “solids.” root

	Description	Type	Default
types	Specified name(s) of the SOLIDS types or None to disable the SOLIDS solver. The user defined names are used to specify DEM and/or PIC model inputs.	String	None
molecular_weight	Value of constant solid molecular weight	Real	0
specific_heat	Specify which specific heat model to use for solid. Available options include: ‘constant’ for constant specific heat model	String	None
specific_heat.constant	Value of species molecular weight. [required if fluid.specific_heat = ‘constant’].	Real	0
reference_temperature	Value of the reference temperature used for specific enthalpy	Real	0
species	Specify which species can constitute the fluid phase [defined species must be a subset of the species.solve arguments].	String	None
newton_solver.absolute_tol	Define absolute tolerance for Damped-Newton solver	Real	1.e-6
newton_solver.relative_tol	Define relative tolerance for Damped-Newton solver	Real	1.e-6
newton_solver.max_iterations	Define max number of iterations for Damped-Newton solver	int	100

Below is an example for specifying the solids solver model options.

solids.types = my_solid0  my_solid1

solids.reference_temperature = 298.15

solids.specific_heat = mixture

solids.species = Fe2O3  FeO

DEM model settings

Enabling the DEM solver and specifying model options.

	Description	Type	Default
dem.solve	Specified name(s) of the DEM types or None to disable the DEM solver. The user defined names are used to specify DEM model inputs.	String	None
dem.friction_coeff.pp	Friction coefficient :: particle to particle collisions [required]	Real	0
dem.friction_coeff.pw	Friction coefficient :: particle to wall collisions [required]	Real	0
dem.spring_const.pp	Normal spring constant :: particle to particle collisions [required]	Real	0
dem.spring_const.pw	Normal spring constant :: particle to wall collisions [required]	Real	0
dem.spring_tang_fac.pp	Tangential-to-normal spring constant factor :: particle to particle collisions	Real	0.2857
dem.spring_tang_fac.pw	Tangential-to-normal spring constant factor :: particle to wall collisions	Real	0.2857
dem.damping_tang_fac.pp	Factor relating the tangential damping coefficient to the normal damping coefficient :: particle to particle collisions	Real	0.5
dem.damping_tang_fac.pw	Factor relating the tangential damping coefficient to the normal damping coefficient :: particle to wall collisions	Real	0.5
dem.implicit_drag	Apply fluid-particle drag force by implicit velocity update.	int	0

The following inputs use the DEM type names specified using the dem.solve input to define restitution coefficients and are proceeded with dem.restitution_coeff. These must be defined for all solid-solid and solid-wall combinations.

	Description	Type	Default
[solid0].[solid1]	Specifies the restitution coefficient between solid0 and solid1. Here the order is not important and could be defined as [solid1].[solid0]	Real	0
[solid0].wall	Specifies the restitution coefficient between solid0 and the wall. Order is not important and this could be defined as wall.[solid0]	Real	0

Below is an example for specifying the inputs for two DEM solids.

dem.solve = sand  char

dem.friction_coeff.pp     =     0.25
dem.friction_coeff.pw     =     0.15

dem.spring_const.pp       =   100.0
dem.spring_const.pw       =   100.0

dem.spring_tang_fac.pp    =     0.2857
dem.spring_tang_fac.pw    =     0.2857

dem.damping_tang_fac.pp   =     0.5
dem.damping_tang_fac.pw   =     0.5

dem.restitution_coeff.sand.sand =  0.85
dem.restitution_coeff.sand.char =  0.88
dem.restitution_coeff.char.char =  0.90

dem.restitution_coeff.sand.wall =  0.85
dem.restitution_coeff.char.wall =  0.89

Implicit drag

By default, the fluid-particle drag force is applied explicitly to particles,

\[u_p^{n^{\prime}+1} = u_p^{n^\prime} + dt_{\mathrm{DEM}}\left(\beta^n (u_f^{n+1} - u_p^{n}) + \mathcal{F}_p^{n^\prime}\right)/m_p\]

where \(u_p\) is the p-th particle velocity at the indicated time level, \(\beta^n\) is the drag coefficient, \(u_f^{n+1}\) is the fluid velocity, \(\mathcal{F}_p\) are all non-drag forces (e.g., gravitational, buoyancy, collision etc.), and \(m_p\) is particle mass. Terms exist at different time levels due in part to how the fluid and particle models are coupled and partly because particles typically sub-step in time. Specifically, a time step advances the fluid from \(t^n\) to \(t^{n+1}\), then particles take multiple smaller time steps to traverse the same total time. In the above equation, prime markers differentiate quantities updated at each DEM sub-step.

The updated particle velocity, \(u_p^{n^{\prime}+1}\), is substituted into the drag expression when implicit drag is enabled.

\[u_p^{n^{\prime}+1} = \frac{u_p^{n^\prime} + dt_{\mathrm{DEM}}\left( \beta^n u_f^{n+1} + \mathcal{F}_p^{n^\prime} \right)/m_p}{1 + dt_{\mathrm{DEM}} \beta^n / m_p}\]

By using the updated velocity, the drag force computed for the fluid and particles is inconsistent, and interphase momentum is not conserved. However, implicit drag may be needed for numerical stability when the particle density is much less than the fluid (such as bubbles).

Solids model

Solids settings

DEM model settings

Implicit drag

PIC model settings