- 上一篇：矫直力的计算体系创新英文文献和翻译
- 下一篇：多层住宅建筑给排水英文文献和中文翻译
29.2 to 154.8 Pa sn
. Although HEC aqueous solutions at the
selected concentrations exhibit shear-dependent viscoelastic
properties, their effect on the power consumption measure-
ments of the co-axial mixer was not investigated. It was
assumed to be negligible and have no significant influence
on the torquemeasurements in the laminar regime at rotational
speeds from 0 to 200 rpm. No Weissenberg effect (i.e., liquid
climbing up the rotating shaft) was observed during the
power curves measurements.
The viscosities of the CSweet Syrup and HEC solutions
were measured with the Viscosimeter V88 from Malvern
Instruments GmbH, whereas the viscosities of the glucose
syrup Glucomalt were measured with the rheometer Bohlin
CVO120 (Malvern Instruments) using a cone-plate configur-
ation. The measurement error with respect to viscosity is
below 5%.
Power draw measurement
For the torque measurement an error of +0.1 Nm is
expected and for the measurement of power consumption
the experimental error is estimated to be approximately
+5 W. Measurements with more than 5% error on torque
or power were eliminated.
Numerical Simulation
The commercial CFD software Fluent
w was employed to
calculate the three-dimensional velocity fields and energy
dissipation. The simulation approach used in this work for
calculating the liquid flow field is the transient ‘Moving
Mesh’ method implemented in the code Fluent 6. A more
simplified method is the multiple frame of reference (MFR),
but it can provide only a stationary solution of the flow field
for a given position of the impellers with respect to the proxi-
mity impeller. Tests using the MFR method with a co-axial
mixer demonstrated that the power consumption of the impel-
lers vary depending on the stationary position of the inner
impeller blades with respect to the anchor.
For the transient ‘Moving Mesh’ approach, a combination of
three rotating grid zones was used. The grid zone of the proxi-
mity impeller encapsulates two grid zones; one with the upper
and the other with the lower inner impeller. The size of the
rotating zones was kept constant for all cases studied. The
tank and impellers geometry was built in the software Gambit
w
(Fluent Inc., 2004) and then exported to ICEM CFD 5.0TM
(ANSYS Inc., 2005) for meshing. The three-dimensional tank
was entirely meshed with unstructured hexahedral elements.
The O-grid boundary meshes were used around the impellers.
The total number of grid cells was slightly over 1 000 000. The
size of the cells is in the range of 9.5 1025
and 8.3 1021
cm3
. The top surface of the tank was assumed to be flat and
a zero shear-stress boundary condition was set. All cases
were simulated in the laminar regime.
The torque for an impeller was computed by integrating the
cross product of the radius vector and the force vector at all
nodes on the impeller surface. The forces on the impeller
surface include both shear forces and normal forces. In the
laminar flows, the accuracy of the CFD sliding mesh
method depends strongly on the grid resolution. The cell den-
sity around the blades must be high enough to capture all
flow scales. The effect of the grid size was then investigated
by applying additional mesh refinements near the walls of the
impellers and on cells with a certain level of velocity gradient.
The torque values did not change significantly with further
scale reduction, which means that the solution is fairly grid
independent.
The accuracy of the sliding mesh method is also affected by
the time step size. This effect was studied and the time step