In optimization, the fields used in the calculation of an objective or constraint
function must be in the form of a single scalar value. However, the fields computed
by Ansys Polyflow rarely meet this criteria. For this reason, you must define
"extractors", that is, a set of functions that reduces a field in a given domain to
a single scalar value (which is then referred to as an "extracted value"). An
example of such an extracted value is the minimum of the temperature on wall
, where 
is a sub-part of the domain definition of the temperature field.
Another example of an extracted value is the average of the velocity norm along the
line 
, where 
is a sub-part of the domain definition of the velocity field.
An extractor operates on the values of a field 
in a domain 
. The set of values of 
in the domain 
are noted as 
. Note that though the tensor type of field can be either a scalar
or a vector, for the sake of simplicity it will always be denoted as 
.
Typically, the extraction of a value has the following steps:
Reduce a non-scalar field on a given domain to a scalar field on the same domain.
If the field
is not a scalar, you have to use a restriction function
to reduce the non-scalar field to a scalar one on the
domain 
. This resulting scalar field is called the restricted
field and noted 
. For example, you can reduce a velocity field by
calculating the norm at every node. Extract a single value from the scalar field.
If the restricted field
is not a single value, you must use a function
(which can also be noted as 
). This function either selects a value of interest from
the restricted field, or combines all the values into a single one.
Thus, the extracted value 
that results from the extractor can be written as follows:
 | (36–25) |
The following examples illustrate the previous definitions:
For the extracted value "
": The field
is the temperature on the wall 
: 
. The restriction function
is a simple equality, since the temperature is
already a scalar field: 
The function
is the minimum: 
.
For the extracted value "
": The field
is the velocity on the line 
: 
. The restriction function
is the norm: 
. The function
is the average: 
.
Extractors are automatically generated for the amplitude of displacement defined in a mesh deformation preprocessor, as well as for fields that are already a single scalar value. Otherwise, you must define suitable extractors for the fields used in your optimization functions (see Problem Setup for further details).
The available fields 
for the extractors include:
output fields of the main task
coordinates
velocity
pressure
temperature
displacement
species
output fields of postprocessors
flow rate (see Flow Rate
flow balance (see Quantification of Die Balancing for details)
fields in a problem with a constrained free jet
force applied on the free jet
torque applied on the free jet
flow rate at the die exit (when a single fluid is extruded)
flow balance at the die exit (when a single fluid is extruded)
tangential velocity in the die exit (when a single fluid is extruded)
(in Cartesian coordinates), where 
is the unit vector perpendicular to the die exit
section.
The available restriction functions 
include:
the current value
(36–26)
This function consists of the current values of
and is only applied when the field 
is a scalar field (for example, pressure, temperature).
This is selected automatically, since scalar values are detected. the norm of a vector
(36–27)
This function computes the norm of a vector
of 
components. This is the default selection for a vector
field. the
component of a vector 
(36–28)
This function extracts the
component of a vector.
The available functions 
include:
the minimum
(36–29)
This function computes the minimum of the restricted field
. This function must be used with care, because the
location of the minimum can change when the geometry is reconfigured during
the optimization process. Such a jump in the location of the minimum may
lead to convergence trouble during the optimization. the maximum
(36–30)
This function computes the maximum of the restricted field
. This function must be used with care, because the
location of the maximum can change when the geometry is reconfigured during
the optimization process. Such a jump in the location of the maximum may
lead to convergence trouble during the optimization. the average
(36–31)
This function computes the average of the restricted field
. This average is based on the nodal values
(
): the sum of nodal values divided by the number of nodal
values (
). the value at the closest node (in deformed configuration)
(36–32)
This function extracts the value of restricted field
at node 
, which is whatever node is closest to the coordinates
at a given optimization step. Note that if the point
is located in an area that is subject to mesh deformation,
the node closest to the coordinates may change. Such a jump in the location
of the closest node may lead to convergence trouble during the optimization.
the value at the closest node (in the initial configuration)
(36–33)
This function extracts the value of restricted field
at node 
, which is the node that is initially closest to the
coordinates 
at the first step of optimization. Even if the point
is located in an area that is subject to mesh deformation,
will not change during the remaining steps (although the
value of 
may change). the weighted average
(36–34)
This function computes the weighted average of the restricted field
. This weighted average is obtained from the ratio of the
integral of 
over the domain 
and the integral of 1 over the domain 
(that is, the length, area, or volume). the integral
(36–35)
This function computes the integral of the restricted field
over the domain 
.
In addition to the functions listed previously, there are special functions for the coordinates. These functions compute the length, area, or volume of a domain that has 1, 2, or 3 dimensions, respectively. This function is only available if the coordinates have been selected for the field.
Note that the function 
is ignored for fields that have only one value. This is the case
for fields whose interpolation type is constant over the domain (for example, flow
rate, flow balance), or if the domain from which the value is extracted is a
point.
Table 36.1: Extracted Values lists the extracted values by combining
the functions 
and 
.
Table 36.1: Extracted Values
| Restriction Functions | ||||
|
|
| ||
| Functions for Obtaining the Extracted Value | Minimum |
|
|
|
| Maximum |
|
|
| |
| Average |
|
|
| |
| Value at Closest Obtaining the Node (Deformed) |
|
|
| |
| Value at Closest Node (Initially) |
|
|
| |
| Weighted Average |
|
|
| |
| Integral |
|
|
| |
| Coordinate Functions | Length | |||
| Area | ||||
| Volume | ||||
The next sections explain how the extracted values can be used when calculating the objective function and constraints.