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]) "Medium state at default properties"; 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;

model IndirectTankHeatExchanger "Heat exchanger typically submerged in a fluid with a second fluid circulating through it" replaceable package MediumHex = Modelica.Media.Interfaces.PartialMedium "Heat transfer fluid flowing through the heat exchanger"; replaceable package MediumTan = Modelica.Media.Interfaces.PartialMedium "Heat transfer fluid inside the tank"; extends Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters; extends Buildings.Fluid.Interfaces.LumpedVolumeDeclarations( redeclare final package Medium = MediumHex); extends Buildings.Fluid.Interfaces.PartialTwoPortInterface( redeclare final package Medium = MediumHex, final show_T=false); parameter Integer nSeg(min=2) "Number of segments in the heat exchanger"; parameter Modelica.SIunits.HeatCapacity CHex "Capacitance of the heat exchanger"; parameter Modelica.SIunits.Volume volHexFlu "Volume of heat transfer fluid in the heat exchanger"; parameter Modelica.SIunits.HeatFlowRate Q_flow_nominal "Heat transfer at nominal conditions"; final parameter Modelica.SIunits.ThermalConductance UA_nominal= abs(Q_flow_nominal/(THex_nominal-TTan_nominal)) "Nominal UA value for the heat exchanger"; parameter Modelica.SIunits.Temperature TTan_nominal "Temperature of fluid inside the tank at UA_nominal"; parameter Modelica.SIunits.Temperature THex_nominal "Temperature of fluid inside the heat exchanger at UA_nominal"; parameter Real r_nominal(min=0, max=1)=0.5 "Ratio between coil inside and outside convective heat transfer"; parameter Modelica.SIunits.Diameter dExtHex "Exterior diameter of the heat exchanger pipe"; parameter Modelica.Fluid.Types.Dynamics energyDynamics=Modelica.Fluid.Types.Dynamics.DynamicFreeInitial "Formulation of energy balance for heat exchanger internal fluid mass"; parameter Modelica.Fluid.Types.Dynamics energyDynamicsSolid=energyDynamics "Formulation of energy balance for heat exchanger solid mass"; parameter Modelica.Fluid.Types.Dynamics massDynamics=energyDynamics "Formulation of mass balance for heat exchanger"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; parameter Boolean hA_flowDependent = true "Set to false to make the convective heat coefficient calculation of the fluid inside the coil independent of mass flow rate"; parameter Boolean hA_temperatureDependent = true "Set to false to make the convective heat coefficient calculation of the fluid inside the coil independent of temperature"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a port[nSeg] "Heat port connected to water inside the tank"; Buildings.Fluid.FixedResistances.PressureDrop res( redeclare final package Medium = MediumHex, final dp_nominal=dp_nominal, final m_flow_nominal=m_flow_nominal, final allowFlowReversal=allowFlowReversal, final homotopyInitialization=homotopyInitialization, final show_T=show_T, final from_dp=from_dp, final linearized=linearizeFlowResistance) "Calculates the flow resistance and pressure drop through the heat exchanger"; MixingVolumes.MixingVolume vol[nSeg](each nPorts=2, each m_flow_nominal=m_flow_nominal, redeclare each package Medium = MediumHex, each V=volHexFlu/nSeg, each energyDynamics=energyDynamics, each massDynamics=massDynamics, each p_start=p_start, each T_start=T_start, each X_start=X_start, each C_start=C_start, each C_nominal=C_nominal, each final prescribedHeatFlowRate = false, each final allowFlowReversal=allowFlowReversal) "Heat exchanger fluid"; Modelica.Thermal.HeatTransfer.Components.HeatCapacitor cap[nSeg]( each C=CHex/nSeg, T(each start=T_start, each fixed=(energyDynamicsSolid == Modelica.Fluid.Types.Dynamics.FixedInitial)), der_T( each fixed=(energyDynamicsSolid == Modelica.Fluid.Types.Dynamics.SteadyStateInitial))) if not energyDynamicsSolid == Modelica.Fluid.Types.Dynamics.SteadyState "Thermal mass of the heat exchanger"; protected Sensors.MassFlowRate senMasFlo( redeclare package Medium = MediumHex, allowFlowReversal=allowFlowReversal) "Mass flow rate of the heat transfer fluid"; Modelica.Thermal.HeatTransfer.Components.Convection htfToHex[nSeg] "Convection coefficient between the heat transfer fluid and heat exchanger"; Modelica.Thermal.HeatTransfer.Components.Convection HexToTan[nSeg] "Convection coefficient between the heat exchanger and the surrounding medium"; Modelica.Thermal.HeatTransfer.Sensors.TemperatureSensor temSenHex[nSeg] "Temperature of the heat transfer fluid"; Modelica.Thermal.HeatTransfer.Sensors.TemperatureSensor temSenWat[nSeg] "Temperature sensor of the fluid surrounding the heat exchanger"; Modelica.Blocks.Routing.Replicator rep(nout=nSeg) "Replicates senMasFlo signal from 1 seg to nSeg"; HeatExchangers.BaseClasses.HACoilInside hAPipIns[nSeg]( each m_flow_nominal=m_flow_nominal, each hA_nominal=UA_nominal/nSeg*(r_nominal + 1)/r_nominal, each T_nominal=THex_nominal, each final flowDependent=hA_flowDependent, each final temperatureDependent=hA_temperatureDependent) "Computation of convection coefficients inside the coil"; HeatExchangers.BaseClasses.HANaturalCylinder hANatCyl[nSeg]( redeclare each final package Medium = Medium, each final ChaLen=dExtHex, each final hA_nominal=UA_nominal/nSeg*(1 + r_nominal), each final TFlu_nominal=TTan_nominal, each final TSur_nominal=TTan_nominal-(r_nominal/(1+r_nominal))*(TTan_nominal-THex_nominal)) "Calculates an hA value for each side of the heat exchanger"; Modelica.Thermal.HeatTransfer.Sensors.TemperatureSensor temSenSur[nSeg] "Temperature at the external surface of the heat exchanger"; equation for i in 1:(nSeg - 1) loop connect(vol[i].ports[2], vol[i + 1].ports[1]); end for; connect(rep.u,senMasFlo. m_flow); connect(port,HexToTan. fluid); connect(vol[1].ports[1],senMasFlo.port_b); connect(cap.port,HexToTan.solid); connect(vol.heatPort,htfToHex. fluid); connect(htfToHex.solid,HexToTan. solid); connect(temSenHex.T, hAPipIns.T); connect(hAPipIns.hA, htfToHex.Gc); connect(HexToTan.solid,temSenSur. port); connect(temSenWat.port, port); connect(temSenSur.T, hANatCyl.TSur); connect(hANatCyl.TFlu, temSenWat.T); connect(port_a, senMasFlo.port_a); connect(vol[nSeg].ports[2], res.port_a); connect(res.port_b, port_b); connect(temSenHex.port, vol.heatPort); connect(rep.y, hAPipIns.m_flow); connect(hANatCyl.hA,HexToTan. Gc); end IndirectTankHeatExchanger;

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;