Buildings.Fluid.Storage.BaseClasses

Information

Extends from Modelica.Fluid.Icons.BaseClassLibrary (Icon for library).

Package Content

Name	Description
Buoyancy	Model to add buoyancy if there is a temperature inversion in the tank
Stratifier	Model to reduce the numerical dissipation in a tank

Buildings.Fluid.Storage.BaseClasses.Buoyancy

Information

This model outputs a heat flow rate that can be added to fluid volumes in order to emulate buoyancy during a temperature inversion. For simplicity, this model does not compute a buoyancy induced mass flow rate, but rather a heat flow that has the same magnitude as the enthalpy flow associated with the buoyancy induced mass flow rate.

Parameters

Type	Name	Default	Description
Volume	V		Volume [m3]
Integer	nSeg	2	Number of volume segments
Time	tau		Time constant for mixing [s]

Connectors

Type	Name	Description
HeatPort_a	heatPort[nSeg]	Heat input into the volumes

Modelica definition

model Buoyancy 
  "Model to add buoyancy if there is a temperature inversion in the tank"
  extends Buildings.BaseClasses.BaseIcon;
  replaceable package Medium = 
    Modelica.Media.Interfaces.PartialMedium "Medium model";
  parameter Modelica.SIunits.Volume V "Volume";
  parameter Integer nSeg(min=2) = 2 "Number of volume segments";
  parameter Modelica.SIunits.Time tau(min=0) "Time constant for mixing";

  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a[nSeg] heatPort 
    "Heat input into the volumes";

  Modelica.SIunits.HeatFlowRate[nSeg-1] Q_flow 
    "Heat flow rate from segment i+1 to i";
protected 
   parameter Medium.ThermodynamicState sta0 = Medium.setState_pTX(T=Medium.T_default,
         p=Medium.p_default, X=Medium.X_default[1:Medium.nXi]);
   parameter Modelica.SIunits.Density rho_nominal=Medium.density(sta0) 
    "Density, used to compute fluid mass";
   parameter Modelica.SIunits.SpecificHeatCapacity cp0=Medium.specificHeatCapacityCp(sta0) 
    "Specific heat capacity";
   parameter Real k(unit="W/K") = V*rho_nominal*cp0/tau/nSeg 
    "Proportionality constant, since we use dT instead of dH";
equation 
  for i in 1:nSeg-1 loop
    Q_flow[i] = k*max(heatPort[i+1].T-heatPort[i].T, 0);
  end for;

  heatPort[1].Q_flow = -Q_flow[1];
  for i in 2:nSeg-1 loop
       heatPort[i].Q_flow = -Q_flow[i]+Q_flow[i-1];
  end for;
  heatPort[nSeg].Q_flow = Q_flow[nSeg-1];
end Buoyancy;

Buildings.Fluid.Storage.BaseClasses.Stratifier

Information

This model reduces the numerical dissipation that is introduced by the standard upwind discretization scheme. The model is described by Wischhusen (2006). Since we use this model in conjunction with Modelica.Fluid, we compute a heat flux that need to be added to each volume in order to give the results published in the above paper. The model is used by Buildings.Fluid.Storage.StratifiedEnhanced.

References

Wischhusen Stefan, An Enhanced Discretization Method for Storage Tank Models within Energy Systems, Modelica Conference, Vienna, Austria, September 2006.

Parameters

Type	Name	Default	Description
Integer	nSeg	2	Number of volume segments
Real	a	1E-4	Tuning factor. a=0 is equivalent to not using this model
TemperatureDifference	delta	1	Temperature difference for which which exp(-|x|) will be approximated [K]

Connectors

Type	Name	Description
HeatPort_a	heatPort[nSeg]	Heat input into the volumes
input RealInput	m_flow	Mass flow rate from port a to port b
input RealInput	H_flow[nSeg + 1]	Enthalpy flow between the volumes
FluidPort_a	fluidPort[nSeg + 2]	Fluid port, needed to get pressure, temperature and species concentration

Modelica definition

model Stratifier 
  "Model to reduce the numerical dissipation in a tank"
  extends Buildings.BaseClasses.BaseIcon;
  replaceable package Medium = 
    Modelica.Media.Interfaces.PartialMedium "Medium model";

  parameter Integer nSeg(min=2) = 2 "Number of volume segments";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a[nSeg] heatPort 
    "Heat input into the volumes";

  Modelica.Blocks.Interfaces.RealInput m_flow 
    "Mass flow rate from port a to port b";

  Modelica.Blocks.Interfaces.RealInput[nSeg+1] H_flow 
    "Enthalpy flow between the volumes";
  Modelica.SIunits.Enthalpy[nSeg+2] hOut 
    "Extended vector with new outlet enthalpies to reduce numerical dissipation";
  Modelica.SIunits.Enthalpy[nSeg+2] h 
    "Extended vector with port enthalpies, needed to simplify loop";

  parameter Real a(min=0)= 1E-4 
    "Tuning factor. a=0 is equivalent to not using this model";
  parameter Modelica.SIunits.TemperatureDifference delta = 1 
    "Temperature difference for which which exp(-|x|) will be approximated";

  Modelica.Fluid.Interfaces.FluidPort_a[nSeg+2] fluidPort(
      redeclare each package Medium = Medium) 
    "Fluid port, needed to get pressure, temperature and species concentration";
protected 
  Integer s(min=-1, max=1) "Index shift to pick up or down volume";
   parameter Medium.ThermodynamicState sta0 = Medium.setState_pTX(T=Medium.T_default,
         p=Medium.p_default, X=Medium.X_default[1:Medium.nXi]);
   parameter Modelica.SIunits.SpecificHeatCapacity cp0=Medium.specificHeatCapacityCp(sta0) 
    "Density, used to compute fluid volume";
  Real[nSeg] intArg "Argument for interpolation function";
  parameter Real intDel=a*cp0*delta 
    "Scaling argument delta for interpolation function";
  Real[nSeg] ex "Output of smooth exponential function";
equation 
  // assign zero flow conditions at port
  fluidPort[:].m_flow = zeros(nSeg+2);
  fluidPort[:].h_outflow = zeros(nSeg+2);
  fluidPort[:].Xi_outflow = zeros(nSeg+2, Medium.nXi);
  fluidPort[:].C_outflow  = zeros(nSeg+2, Medium.nC);

  // assign extended enthalpy vectors
  for i in 1:nSeg+2 loop
    h[i] = inStream(fluidPort[i].h_outflow);
  end for;
  // in loop, i+1-s is the "down" volume, i+1+s is the "up" volume
  s = if m_flow > 0 then 1 else -1;
  hOut[1] = h[1];
  hOut[nSeg+2] = h[nSeg+2];
  for i in 1:nSeg loop
     /*
     // original implementation that causes chattering
     intArg[i-1] = -a * abs(h[i-s]-h[i]);
     hOut[i] = (h[i]-h[i+s]) * exp(intArg[i-1])   + h[i+s];
     */
     // approximation that is once continuously differentiable
     // and does not cause chattering
     intArg[i] = a * (h[i-s+1]-h[i+1]);
     ex[i] = Buildings.Utilities.Math.Functions.smoothExponential(
                                                         intArg[i], intDel);
     hOut[i+1] = (h[i+1]-h[i+s+1]) * ex[i]   + h[i+s+1];
     if s > 0 then
       heatPort[i].Q_flow = -m_flow * (hOut[i]-hOut[i+1])   +H_flow[i] -H_flow[i+1];
     else
       heatPort[i].Q_flow = +m_flow * (hOut[i+2]-hOut[i+1]) -H_flow[i] +H_flow[i+1];
     end if;
  end for;
end Stratifier;