enable_surface_heating command

Purpose

Modelling frictional heating between solid particles in contact.

Syntax

enable_surface_heating keyword value

Keywords:

Keyword	Description
id	user-assigned name for the command call
track_heating	`yes` or `no`; do / do not track the surface heating default: `no`

Associated material properties

Material properties

electricalResistivity ( $\rho$ ): electric resistivity of the material [ $\Omega m$ ]
thermalConductivity ( $\lambda$ ): thermal conductivity of the material [ $W/m K$ ]

Description

Note

This command enables the general capability to compute surface heating, but heating due to normal or tangential contact still needs to be enabled via the appropriate settings in particle_contact_model and wall_contact_model. An example would be

particle_contact_model normal hertz tangential history settings heating_normal_hertz on heating_tangential_history on

A list of the contact models capable of computing surface heating can be found below

This command reproduces the frictional heating generated by solid particles in contact. The power dissipated (energy per unit of time) by the normal contact between two particles is equal to:

$P_n = F_{n,d} v_n$

where $F_{n,d}$ is the normal damping force and $v_n$ is the normal relative velocity at the contact point. The same applies to a tangential contact, i.e.

$P_t = F_{t,d} v_t$

where $F_{t,d}$ is the tangential damping force and $v_t$ is the tangential relative velocity at the contact point.

For tangential interaction, there is also a second mode of energy dissipation, which is the dissipation of energy when the surfaces slip over each other when the Coulomb friction limit is reached:

$P_t = \mu F_n v_t$

where $\mu$ is the static coefficient of friction and $F_n$ is the total normal force.

The power dissipated is divided among the two particles in contact (or between the particle and wall) as proposed by Nguyen et al.. The partition coefficient of generated heat $\beta_{ij}$ reads as follows:

$\beta_{ij} = \frac{1}{2} \left( \frac{\rho_i} {\rho_i + \rho_j} + \frac{\lambda_i} {\lambda_i+\lambda_j} \right )$

where $i$ and $j$ refer to the two material’s in contact.

The energy dissipated by the particle-wall friction generates heat that is transfered to both particle and wall, therefore increasing their temperatures. This happens even when the wall temperature is not tracked by a mesh_module heattransfer command i.e. walls are not adiabatic when the enable_surface_heating is used.

Currently, the following models can contribute to surface heating: model hertz, model hooke, tangential history. Each one of these contact models must have explicitly switched on the surface heating contribution (e.g., for model hertz, the keyword/value pair heating_normal_hertz on must be used).

This model also requires the enable_heat_transfer command, which automatically calculates the appropriate heat flux contribution for each particle.

Output information

If track_heating yes, the command additionally registers a per-particle property with ID ‘surfaceHeating’, which stores the following values for post-processing for each particle:

id_surfaceHeating[1]: energy dissipated by normal particle-particle contact damping
id_surfaceHeating[2]: energy dissipated by tangential particle-particle contact damping
id_surfaceHeating[3]: energy dissipated by tangential particle-particle contact slip
id_surfaceHeating[4]: energy dissipated by normal particle-wall contact damping
id_surfaceHeating[5]: energy dissipated by tangential particle-wall contact damping
id_surfaceHeating[6]: energy dissipated by tangential particle-wall contact slip

These can be accessed by various output commands.

For example, in a system with three spherical particles, the energy dissipated by normal particle-particle contact damping for each particle can be obtained in the following way:

variable dissipation_pp_normal_damping atom  id_surfaceHeating[1]
variable dissipation_particle_1        equal v_dissipation_pp_normal_damping[1]
variable dissipation_particle_2        equal v_dissipation_pp_normal_damping[2]
variable dissipation_particle_3        equal v_dissipation_pp_normal_damping[3]
status_style all {time, v_dissipation_particle_1, v_dissipation_particle_2, v_dissipation_particle_3}

Restrictions

Currently, only the following models contribute to surface heating:

Normal Models: model hertz, model hertz fragmentation bruchmueller, model hertz time dependent, model hertz vel dependent, model hooke,

Tangential Models: tangential history, tangential history powder, tangential history time dependent, tangential history tempdep, tangential history attrition,

Coarse-graining information: Using coarsegraining in combination with this command might lead to different dynamics or system state and thus to inconsistencies.

Literature

[1] Nguyen, Viet, et al. “Thermomechanical modelling of friction effects in granular flows using the discrete element method.” Journal of Mechanics of Materials and Structures 4.2 (2009): 413-426.