1 Process Modeling for Dynamic Disperse Particle Separation …
7
charge density. This corresponds to a fluctuation in fluid acceleration close to the
electrode and higher velocities appear, producing turbulence. The model presented
here does not properly resolve the time scales of this process and thus the additional
turbulence production is neglected. The iteration limit is 200, but the solution was
observed to converge after 2–3 iterations, allowing a convergence tolerance of 10
−5 .
Linear upwind and cell limited least square schemes discretize the divergences and
gradients, respectively.
2.3 Numerical Grid and Mesh Setup
Three numerical mesh configurations approximate different ESP geometries. These
configurations govern the principle particle transport and electric wind influence on
flow structure for the ESP geometries. Regions close to the spraying electrodes are
refined. The rectangular cells align with the inlet mean flow direction. The area from
electrode to wall is slightly altered to fit the electric field. Reasons for adjustments
in mesh cell direction are the fluid cell Courant number
CFL i = u i
t
x
(7)
and the electric Courant number
CFL el = b|E|
t
x
(8)
where u i is continuous phase cell velocity magnitude, b is the ion mobility, E the
electric field, x is characteristic cell length and t is the time step. These numbers
determine the solver stability criterion. The cell limited upwind scheme is more
accurate, if cells are in direction of the flow. This direction is perpendicular for the
ion flux (in direction of the electric field) and the fluid flow (in direction of the
channel length). The cell direction increases the accuracy of both field solutions.
The two meshes for spiked wire electrode setups are developed based on the wireelectrode mesh and highly refined close to the electrode tips. For all cases, the wall
distance was adjusted to fit the specific turbulence model needs. The criterion was
checked after each successful run. Further cell reduction was achieved coarsening
the inlet and outlet regions. For the studies of particle transport inside the spiked-wire
precipitators, the volume is discretized using a maximum of about 3 Mio cells in case
of asymmetric and symmetric spikes.
For the wire-electrode mesh, a simplified 2D structure is extrapolated into the
third dimension using hex-cells. The near wall region is resolved while electrode
regions are captured just roughly to reduce the number of cells. The mesh coarsens
in intermediate regions using a cell growth function. A mesh independency study
allowed reduction in the total number of cells from more than 8,000,000 to just
366,060.
7
charge density. This corresponds to a fluctuation in fluid acceleration close to the
electrode and higher velocities appear, producing turbulence. The model presented
here does not properly resolve the time scales of this process and thus the additional
turbulence production is neglected. The iteration limit is 200, but the solution was
observed to converge after 2–3 iterations, allowing a convergence tolerance of 10
−5 .
Linear upwind and cell limited least square schemes discretize the divergences and
gradients, respectively.
2.3 Numerical Grid and Mesh Setup
Three numerical mesh configurations approximate different ESP geometries. These
configurations govern the principle particle transport and electric wind influence on
flow structure for the ESP geometries. Regions close to the spraying electrodes are
refined. The rectangular cells align with the inlet mean flow direction. The area from
electrode to wall is slightly altered to fit the electric field. Reasons for adjustments
in mesh cell direction are the fluid cell Courant number
CFL i = u i
t
x
(7)
and the electric Courant number
CFL el = b|E|
t
x
(8)
where u i is continuous phase cell velocity magnitude, b is the ion mobility, E the
electric field, x is characteristic cell length and t is the time step. These numbers
determine the solver stability criterion. The cell limited upwind scheme is more
accurate, if cells are in direction of the flow. This direction is perpendicular for the
ion flux (in direction of the electric field) and the fluid flow (in direction of the
channel length). The cell direction increases the accuracy of both field solutions.
The two meshes for spiked wire electrode setups are developed based on the wireelectrode mesh and highly refined close to the electrode tips. For all cases, the wall
distance was adjusted to fit the specific turbulence model needs. The criterion was
checked after each successful run. Further cell reduction was achieved coarsening
the inlet and outlet regions. For the studies of particle transport inside the spiked-wire
precipitators, the volume is discretized using a maximum of about 3 Mio cells in case
of asymmetric and symmetric spikes.
For the wire-electrode mesh, a simplified 2D structure is extrapolated into the
third dimension using hex-cells. The near wall region is resolved while electrode
regions are captured just roughly to reduce the number of cells. The mesh coarsens
in intermediate regions using a cell growth function. A mesh independency study
allowed reduction in the total number of cells from more than 8,000,000 to just
366,060.