3.1. THE CONCEPT OF SIMILITUDE
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a lengthy trial and error method that requires a significant knowledge of past prototype behavior. The calibration method is most useful for complex situations that have
a large number of variables, rendering it unfit for dimensional analysis. Similitude requirements for movable-bed
models are sometimes established by this method.
• Similitude by Differential Equations. If the differential equations governing a process are known, and if
the equations have been shown to be sufficiently accurate,
then similitude requirements can be determined directly
from the equations by casting them into a dimensionless
form. The dimensionless parameters in the equations provide the transfer relationships between the prototype and
model, and often the important parameters can be recognized from the equations . It is not necessary to solve the
equations for specific boundary conditions; this is the task
of the physical model. This method is sometimes referred
to as inspectional analysis.
2
• Similitude by Dimensional Analysis. Dimensional
analysis can be used in some cases to provide a complete set
of dimensionless products constructed from the pertinent
process variables. Similitude by dimensional analysis requires that the dimensionless products have the same value
in the prototype as in the model. When this is not possible,
those products thought to be most important must be kept
constant. As previously mentioned in Chapter 2, physical
insight into the process is essential in correctly determining
those products used to establish scaling requirements.
• Similitude by Scale Series. Several models constructed
at different scales can be operated to aid in establishing
similarity relationships and to identify scaling effects. This
method is useful when extensive prototype data are not
available, or when attempting to establish scaling criteria
for a complex physical process. Care must be taken when
analyzing model results, particularly when extrapolating
model results to prototype scale. Thoughtful analysis of
potential scale effects between model and prototype must
be performed.
2The same similarity principles extend to mathematical calculations. By determining
appropriate dimensionless products, the number of calculations can be reduced.
53
a lengthy trial and error method that requires a significant knowledge of past prototype behavior. The calibration method is most useful for complex situations that have
a large number of variables, rendering it unfit for dimensional analysis. Similitude requirements for movable-bed
models are sometimes established by this method.
• Similitude by Differential Equations. If the differential equations governing a process are known, and if
the equations have been shown to be sufficiently accurate,
then similitude requirements can be determined directly
from the equations by casting them into a dimensionless
form. The dimensionless parameters in the equations provide the transfer relationships between the prototype and
model, and often the important parameters can be recognized from the equations . It is not necessary to solve the
equations for specific boundary conditions; this is the task
of the physical model. This method is sometimes referred
to as inspectional analysis.
2
• Similitude by Dimensional Analysis. Dimensional
analysis can be used in some cases to provide a complete set
of dimensionless products constructed from the pertinent
process variables. Similitude by dimensional analysis requires that the dimensionless products have the same value
in the prototype as in the model. When this is not possible,
those products thought to be most important must be kept
constant. As previously mentioned in Chapter 2, physical
insight into the process is essential in correctly determining
those products used to establish scaling requirements.
• Similitude by Scale Series. Several models constructed
at different scales can be operated to aid in establishing
similarity relationships and to identify scaling effects. This
method is useful when extensive prototype data are not
available, or when attempting to establish scaling criteria
for a complex physical process. Care must be taken when
analyzing model results, particularly when extrapolating
model results to prototype scale. Thoughtful analysis of
potential scale effects between model and prototype must
be performed.
2The same similarity principles extend to mathematical calculations. By determining
appropriate dimensionless products, the number of calculations can be reduced.