Buildings.Fluid.Storage.BaseClasses

Information

This package contains base classes that are used to construct the models in Buildings.Fluid.Storage.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
Buoyancy	Model to add buoyancy if there is a temperature inversion in the tank
ThirdOrderStratifier	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.

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
replaceable package Medium		Modelica.Media.Interfaces.Pa...	Medium model
Volume	V		Volume [m3]
Integer	nSeg	2	Number of volume segments
Time	tau		Time constant for mixing [s]

Connectors

Type	Name	Description
replaceable package Medium		Medium model
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 sta_default = Medium.setState_pTX(T=Medium.T_default,
         p=Medium.p_default, X=Medium.X_default[1:Medium.nXi]);
   parameter Modelica.SIunits.Density rho_default=Medium.density(sta_default) 
    "Density, used to compute fluid mass";
   parameter Modelica.SIunits.SpecificHeatCapacity cp_default=Medium.specificHeatCapacityCp(sta_default) 
    "Specific heat capacity";
   parameter Real k(unit="W/K") = V*rho_default*cp_default/tau/nSeg 
    "Proportionality constant, since we use dT instead of dH";
   Modelica.SIunits.TemperatureDifference dT[nSeg-1] 
    "Temperature difference between adjoining volumes";
equation 
  for i in 1:nSeg-1 loop
    dT[i] = heatPort[i+1].T-heatPort[i].T;
    Q_flow[i] = k*noEvent(smooth(1, if dT[i]>0 then dT[i]^2 else 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.ThirdOrderStratifier

Information

This model reduces the numerical dissipation that is introduced by the standard first-order upwind discretization scheme which is created when connecting fluid volumes in series.

The model is used in conjunction with Modelica.Fluid.Storage.Stratified. It computes a heat flux that needs to be added to each volume of Modelica.Fluid.Storage.Stratified in order to give the results that a third-order upwind discretization scheme (QUICK) would give.

The QUICK method can cause oscillations in the tank temperatures since the high order method introduces numerical dispersion. There are two ways to reduce the oscillations:

• To use an under-relaxation coefficient alpha when adding the heat flux into the volume.
• To use the first-order upwind for hOut[2] and hOut[nSeg]. Note: Using it requires nSeg>=4.

Both approaches are implemented in the model.

The model is used by Buildings.Fluid.Storage.StratifiedEnhanced.

Limitations

The model requires at least 4 fluid segments. Hence, set nSeg to 4 or higher.

Extends from Buildings.BaseClasses.BaseIcon (Base icon).

Parameters

Type	Name	Default	Description
replaceable package Medium		Modelica.Media.Interfaces.Pa...	Medium model
MassFlowRate	m_flow_small		Small mass flow rate for regularization of zero flow [kg/s]
Integer	nSeg		Number of volume segments
Real	alpha	0.5	Under-relaxation coefficient (1: QUICK; 0: 1st order upwind)

Connectors

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

  parameter Modelica.SIunits.MassFlowRate m_flow_small(min=0) 
    "Small mass flow rate for regularization of zero flow";
  parameter Integer nSeg(min=4) "Number of volume segments";

  parameter Real alpha(
    min=0,
    max=1) = 0.5 "Under-relaxation coefficient (1: QUICK; 0: 1st order upwind)";

  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.Fluid.Interfaces.FluidPort_a[nSeg + 2] fluidPort(redeclare each 
      package Medium = Medium) 
    "Fluid port, needed to get pressure, temperature and species concentration";

protected 
  Modelica.SIunits.SpecificEnthalpy[nSeg + 1] hOut 
    "Extended vector with new outlet enthalpies to reduce numerical dissipation (at the boundary between two volumes)";
  Modelica.SIunits.SpecificEnthalpy[nSeg + 2] h 
    "Extended vector with port enthalpies, needed to simplify loop";
  Modelica.SIunits.HeatFlowRate Q_flow[nSeg] 
    "Heat exchange computed using upwind third order discretization scheme";
  //    Modelica.SIunits.HeatFlowRate Q_flow_upWind
  //     "Heat exchange computed using upwind third order discretization scheme"; //Used to test the energy conservation
  Real sig 
    "Sign used to implement the third order upwind scheme without triggering a state event";
  Real comSig 
    "Sign used to implement the third order upwind scheme without triggering a state event";

equation 
  assert(nSeg >= 4, "
Number of segments of the enhanced stratified tank should be no less than 4 (nSeg>=4).");

  // 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;

  // Value that transitions between 0 and 1 as the flow reverses.
  sig = Modelica.Fluid.Utilities.regStep(
    m_flow,
    1,
    0,
    m_flow_small);
             // at surface between port_a and vol1

  comSig = 1 - sig;

  // at surface between port_a and vol1
  hOut[1] = sig*h[1] + comSig*h[2];
  // at surface between vol[nSeg] and port_b
  hOut[nSeg + 1] = sig*h[nSeg + 1] + comSig*h[nSeg + 2];

  // Pros: These two equations can further reduce the temperature overshoot by using the upwind
  // Cons: The minimum of nSeg hase to be 4 instead of 2.
  hOut[2] = sig*h[2] + comSig*h[3];
  // at surface between vol1 and vol2
  hOut[nSeg] = sig*h[nSeg] + comSig*h[nSeg + 1];
  // at surface between vol[nSeg-1] and vol[nSeg]

  for i in 3:nSeg - 1 loop
    // at surface between vol[i-1] and vol[i]
    // QUICK method
    hOut[i] = 0.5*(h[i] + h[i + 1]) - comSig*0.125*(h[i + 2] + h[i] - 2*h[i + 1])
       - sig*0.125*(h[i - 1] + h[i + 1] - 2*h[i]);
    //     hOut[i] = 0.5*(h[i]+h[i+1]); // Central difference method
  end for;

  for i in 1:nSeg loop
    // difference between QUICK and UPWIND; index of H_flow is same as hOut
    Q_flow[i] = m_flow*(hOut[i + 1] - hOut[i]) - (H_flow[i + 1] - H_flow[i]);
  end for;

  //   Q_flow_upWind = sum(Q_flow[i] for i in 1:nSeg); //Used to test the energy conservation

  for i in 1:nSeg loop
    // Add the difference back to the volume as heat flow. An under-relaxation is needed to reduce
    // oscillations caused by high order method
    heatPort[i].Q_flow = Q_flow[i]*alpha;
  end for;
end ThirdOrderStratifier;