Domain

• thermal storage

Intended application (including scale and resolution)

Intended to be used for return-supply connections in, e.g., district heating networks and possibly in combination with a heater unit. The temporal resolution is minutes to hours.

Modelling of spatial aspects

• discretized (single device)

The model represents a stratified storage tank. The tank uses several volumes to model the stratification. The tank has a fixed volume. Thus, the same mass flow injected at the top of the tank leaves the tank at the bottom and vice versa.

Model dynamics

• dynamic

Heat conduction is modelled between the volumes through the fluid, and between the volumes and the ambient. Effects modelled include buoyancy, heat transfer between layers as a result of heat conduction and mass flow as well as heat transfer of each layer to the ambient. The model is able to capture flow reversals and zero flow.

Model of computation

• time-continuous
• The model avoids the use of events if possible (see, e.g., the noEvent- or smooth-operator described in the Modelica standard).

Functional representation

• explicit
• other, please specify: acausal modelling. The fluid ports (port_a and port_b) use Modelica’s acausal modelling paradigm. Thus, no strict classification of input/output variables is possible. Instead a design flow direction from port_a to port_b is used for this classification. An additional note is added to these variables for clarification. Moreover, Modelica ports are not restricted to single variables. The fluid ports used here define a mix of multiple variables, i.e., enthalpy (stream), mass flow (flow) and pressure (potential). For more details see the Modelica Specification and the respective fluid port model Modelica.Fluid.Interfaces.FluidPort.

Input variables (name, type, unit, description)

• Modelica.Fluid.Interfaces.FluidPort port_a (acausal): fluid port at return side

Output variables (name, type, unit, description)

•  Real T_i: temperature of layer I [K]
• Modelica.Fluid.Interfaces.FluidPort port_b (acausal): fluid port at supply side

Parameters (name, type, unit, description)

• Real m_flow_nominal: nominal mass flow through component [kg/s]
• Real VTan: tank volume [m3]
• Real hTan: height of tank (without insulation) [m]
• Real dIns: thickness of insulation [m]
• Real kIns: specific heat conductivity of insulation [W/m*K]
• Integer nSeg: number of volume segments/stratifi-cation layers [-]
• Real TemAmb: ambient temperature (to calculate losses) [K]

Internal variables (name, type, unit, description)

See Modelica models:

• Tank: IBPSA.Fluid.Storage.StratifiedEnhanced

Internal constants (name, type, unit, description)

See Modelica models:

• Tank: IBPSA.Fluid.Storage.StratifiedEnhanced

Model equations

Governing equations

See Modelica models:

• Tank: IBPSA.Fluid.Storage.StratifiedEnhanced

Constitutive equations

See Modelica models:

• Medium: IBPSA.Media.Water

Initial conditions

• Real T_init_i: initial temperature of medium of layer i [K]

Boundary conditions

Optional: graphical representation (schematic diagram, state transition diagram, etc.)

Model Validation

Narrative

Test system configuration

Inputs and parameters

Model parameters:

• m_flow_nominal = 1 kg/s
• VTan = 5 m3
• hTan = 2 m
• dIns = 0.2 m
• kIns = 0.04 W/m*K
• nSeg = 10
• TAmb = 20 °C

• port_a: connected to fluid boundary with a fixed temperature of 70 °C and prescribed mass flow according to control function

• port_b: connected to fluid boundary

Control function (optional)

Initial system state

• T_init_i = 20 °C ∀ i ∈ [1, nSeg]

Temporal resolution

Evolution of system state

The system starts in thermal equilibrium. The tank and the ambient are at the same temperature and, thus, do not exchange heat (no losses). No mass flow is running through the tank. Once a mass flow with hot water enters the tank at the top, the temperature of the tank starts to increase from top to bottom. Cold water from the bottom of the tank is leaving the tank. As the water at the bottom of the tank is becoming warmer, also the water leaving the tank is becoming warmer. This temperature reaches nearly (losses) the supply temperature once the tank is full.

Results

Sensitivity analysis (optional)

Narrative

The storage volume is varied. The sensitivity of the state of charge and the heat losses on tank volume is assessed.

Test system configuration

Simulation runs for 6 hours. Rest is same as in model validation.

Source of uncertainty

The tank volume VTan is varied in the range of 1 m3 to 10 m3 with a step size of 1 m3.

Inputs and parameters

Control function (optional)

Initial system state

Temporal resolution

 Same as in model validation.

Evolution of system state

With higher tank volumes the tank will need more time to get fully charged. Also heat losses are expected to rise due to the higher surface area of the tank.

Results

Results for the SOC show that the higher the tank volume, the later it is fully charged. This is not surprising as the mass flow into the tank is the same for all cases. A tank that is 1 m3 bigger takes around 22 minutes longer to fully charge. The heat losses of the storage tank increase with larger tank volumes. This is mainly due to the higher surface area.

Model harmonization

Narrative

Test system configuration

Source of uncertainty

Inputs and parameters

Control function (optional)

Initial system state

Temporal resolution

Evolution of system state

Results

State of charge of the tank:

                                   ???= number of layers with temperature>????

Where ???? is the minimum temperature at which a layer is counted to be fully charged.

Total heat losses during simulation:

Where ????? is the heat loss.