Type206: Stratified Fluid Storage Tank with Internal Heat Exchanger
by R. Kubler and F. Muller
	As with the TRNSYS Type4, this tank is assumed to consist of NS
fully-mixed equal volume segments and is discharged directly.  The heat 
exchanger consists of NF equal volume segments each of which is coupled to a 
storage node according to the following rules:
 NF must be less than or equal to NS. The number of nodes below the heat 
exchanger, NDEAD, allows the user to model a dead volume in which heat only 
penetrates slowly by conduction.  The lowermost heat exchanger node is always 
in contact with the lowermost 'active' storage node, i.e. with node no. NS-DEAD.
	Special features of the model are:
- The charge flow always enters from the top of heat exchanger and flows 
  downward. (except if NF = 1)
- The load flow always enters the storage in the bottom (Node NS) and 
  leaves the storage at the top (Node 1).
- The heat exchanger fluid heat capacity is taken into account in the model,
  so that heat exchangers with large fluid content can be modeled accurately.
  There is no restriction on the heat exchanger fluid content.
- The heat transfer capacity rate of the heat exchanger (UA)f,s is assumed
  to be constant and equally distributed over the NF nodes, the option for
  flow and temperature dependent (UA)f,s will be included in a future version.
- No inversion layers are allowed in the storage, a mixing routine eliminates
  them after each time step.  
- The subroutine TYPE74 chooses its own optimum time step, depending on the
  operating conditions, which is less than or equal to the time step chosen
  for the simulation.  Therefore the results delivered by the storage model
  are not sensitive to simulation time step size and the user need not bother
  about it as when using the other storage models TYPE4 and TYPE38.
- The differential equations are solved inside the subroutine without using
  the TRNSYS module DIFFEQ, therefore no derivatives are specified.
- The internal heater receives the heating power as input and is not 
  equipped with a controller.  During a storage test the heating power is
  always measured, therefore validation requires the heating power as input.
  A thermostat control can be simulated with TRNSYS with the help of the heater
  TYPE6 and the on-off controller TYPE2.  The on-off controller receives
  the temperature from the layer in which the thermostat is placed
  (Output no. 10+ NT), campares it with the set value and turns the auxiliary
  heater on and off.  The auxiliary heater supplies its power output to 
  the auxiliary input of the storage TYPE74.

  The heat balance for each storage node is represented by this equation:

  M[s] * C[p,s]    dT[s,j]
 -------------- * --------- = dM[s] * C[p,s] * (T[s,j+1] - T[s,j])
       NS           dT
                                      (UA)[f,s]
                            + eps1 * ----------- * (T[f,k] - T[s,j])
                                         NS
                                                    d    dT[s,j]
                            + eps2 * (UA)ss      * ---( ---------)
                                                    dx    dx
                              (UA)[s,a]
                            - ---------- * (T[s,j] - T[a])
                                 NS

 eps1 = 1 if the storage node is in contact with the heat exchanger node
 eps2 = 1 if the dM[s] = 0 and dM[f] = 0
 eps2 = 0 if dM[s] > 0 or dM[f] > 0

  The heat exchanger equation looks similar;

  M[f] * C[p,f]     dT[f,k] 
---------------- * --------- = dM[f] * C[p,f] * (T[f,k-1] - T[f,k])
       NF              dT
                                 (UA)[f,s]
                               + ---------- * (T[s,j] - T[f,k])
                                     NF

                                 (UA)[f,a]
                               - ---------- * (T[f,k] - T[a])
                                    NF

	An important point is the difference in the definition between 
(UA)[f,s] as is used in TYPE74, and (UA)[f,s] as is commonly used in heat
exchanger theory.  (UA)[f,s] is based on the temperature difference 
between the exit temperature of a heat exchanger node and the corresponding
storage temperature, while commonly (UA)[f,s] is based on the log-mean
temperature difference.  The relation between (UA)[f,s] and (UA)[f,s] is
described by this equation.

    NF      (UA)[f,s]
SUMMATION( ----------- * (T[f,k] - T[s,j]))  
   k=1         NF

                               (T[f,i] - T[s,j1]) - (T[f,NF] - T[s,j2])
                 = (UA)[f,s] * ----------------------------------------
                                           T[f,i] - T[f,j1]
                                     ln ( ------------------ )
                                           T[f,0] - T[f,j2]

  where j  = NS-NDEAD-NF+K
        j1 = NS-NDEAD-NF+1
        j2 = NS-NDEAD

REf: Model 4PORT for TRNSYS  by R. Kubler, F. Muller  July 1991
     Univ. of Stuttgart  FAX: 685 3242