.. _TableLookupHX:

.. _section-5.4.5:

Table Look-Up for Steam Generators or Intermediate Heat Exchangers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Table look-ups for steam generators or intermediate heat exchangers are
used when the behavior of these components is known from other sources
or when the details of the temperature distributions within the
components are not important for the case at hand. The user specifies 
normalized temperature drops vs. time or outlet temperatures vs. time,
as well as elevation of the thermal center vs. time. 
These boundary conditions can be specified as tables vs. time or as function blocks. 

The thermal center of the steam generator or intermediate heat exchanger is the point above which
the circulating fluid is assumed to have the density corresponding to
the inlet temperature and below which it is assumed to have the density
corresponding to the outlet temperature.

In the case where the user specifies normalized temperature drops vs. time, 
the outlet temperature of the steam generator or intermediate heat
exchanger is calculated from the inlet temperature by

.. math::
   :label: eq-5.4-81

   T_{\text{out}} \left( t \right) = T_{\text{in}} \left( t \right) + f \left( t \right) \left\lbrack T_{\text{out}} \left( t = 0 \right) - T_{\text{in}}\left( t = 0 \right)  \right\rbrack

where :math:`f \left( t \right)` is obtained by linear interpolation from the
user-supplied table of temperature drops or by evaluation of the 
user-supplied function block which defines temperature drop. Also

.. math::
   :label: eq-5.4-82

   f \left( t = 0 \right) = 1.0

In the case where the user specifies outlet temperatures vs. time, the outlet temperature of the
steam generator or intermediate heat exchanger is obtained by linear interpolation from the user-
supplied table of outlet temperatures or by evaluation of the user-supplied function block which
defines outlet temperature.

The gravity head is calculated from

.. math::
   :label: eq-5.4-83

   \Delta p_{\text{gr}} \left( t \right) = \rho_{\text{in}} \left( t \right) g\left\lbrack z_{\text{c}} \left( t \right) - z_{\text{in}} \right\rbrack + \rho_{\text{out}} \left( t \right) g \left\lbrack z_{\text{out}} - z_{\text{c}} \left( t \right)  \right\rbrack

where

:math:`\rho_{\text{in}} \left( t \right), \rho_{\text{out}} \left( t \right)` =
the densities of the inlet and outlet fluids at the inlet and outlet
temperatures

:math:`z_{\text{c}} \left( t \right)` = the user-supplied elevation of the
thermal center as a function of time

:math:`z_{\text{in}}`, :math:`z_{\text{out}}` = the inlet and outlet elevations

:math:`g` = the acceleration of gravity

.. _section-5.4.5.1:

.. include::    input-TabHX.rst