6.7. Heat boundary¶

Supplier type

Type label	Description	Active
Heat BoundPT	Defines pressure and temperature (constant or time varying)	Yes
Heat BoundMT	Defines mass flow and temperature (constant or time varying)	Yes
Heat BoundT(PM)	Defines temperature and pressure or mass flow (constant or time varying)	Yes

The model is undefined and no (valid) solution can be found without boundary conditions applied at the extremities of the pipeline system. In a well defined model enough core variables (i.e., pressure, temperature and mass flow) must be defined to find a solution for the entire system.

Only one variable can be activated via the control lines (or action table). The first letter of the type name of the component (i.e., P, M or T) indicates which variable can be controlled by the action table or control signal line. The second letter indicates which variable can be controlled by a secondary time-table. In the case of BountT, the user needs to specify whether mass flow or pressure is controlled by the secondary time-table.

6.7.1. Mathematical model¶

Each boundary condition in WANDA Heat prescribes a combination of mass flow or pressure and temperature. The variables are prescribed using an (action) table or control signal line. Each boundary condition therefore contains one of the two following functions:

(6.7.1)¶\[\dot{m} = f\left( t \right)\]

(6.7.2)¶\[p = f\left( t \right)\]

Additionally, the following equation is required:

(6.7.3)¶\[T = f\left( t \right)\]

Sign convention:

positive flow is into the system
negative flow is out of the system.

Reservoirs with a positive flow also pre-describe their temperature for the system.

6.7.2. Heat BoundPT¶

Pressure-temperature boundary

The Heat BoundPT prescribes the pressure and temperature in a certain point of the system: the pressure can be changed with an action table or control signal line, the temperature can be changed with a secondary time-table of the component.

6.7.2.1. Hydraulic specifications¶

Description	Input	SI-units	Remarks
Pressure at t = 0 [s]	real	[N/m²]
Temperature	Constant time varying
Constant temperature	real	[°C]	Only if Temperature = constant
Temperature time table	table		Only if Temperature = time varying

6.7.2.2. Actions¶

In unsteady state both the pressure and the temperature can vary in time. The time variation of the pressure can be defined via a specified table or can be set through control components. An example action table is given below:

BoundPT Action table

Time [s]	Pressure [kPa]
0.0	10.0
0.99	10.0
1.0	20.0
1.99	20.0
2.00	0.0
2.99	0.0
3.00	20.0
10.00	25.0

In this example, the pressure remains at the steady state value until 0.99 s. At t = 1.0 s the pressure suddenly rises to 20.0 kPa and keeps that value until 1.99 s. At t = 2.00 s the pressure falls stepwise to 0 kPa, etc.

The temperature variation must be specified via a user defined table. Linear interpolation will be performed between two values in the table. No extrapolation will be done; the last function value will be held if the actual time is outside the last table value.

6.7.3. Heat BoundMT¶

Mass flow-temperature boundary

The Heat BoundMT prescribes the mass flow and temperature in a certain point of the system: the mass flow can be changed with an action table or control signal line, the temperature can be changed with a secondary time table of the component.

Positive mass flows represent flow into the system. Negative flow represents flow from the system

6.7.3.1. Hydraulic specifications¶

Description	Input	SI-units	Remarks
Mass flow at t= 0 [s]	real	[kg/s]
Temperature	Constant Time varying
Constant temperature	real	[°C]	If Temperature = Constant
Temperature time table	table		If Temperature = time varying

6.7.3.2. Actions¶

In unsteady state the mass flow can vary in time. The time variation must be defined in the action table or through a control signal line. An example is given below:

BoundMT Action table

Time [s]	Mass flow [kg/s]
0.0	0.0
1.00	200.0
10.00	20.0

In the example the mass flow is zero at steady state. It rises linearly in 1 s to 200 kg/s. After 1 s the mass flow decreases linearly in 9 s to 20 kg/s.

The temperature variation must be specified via a user defined table. Linear interpolation will be performed between two values in the table. No extrapolation will be done; the last function value will be held if the actual time is outside the last table value.

6.7.4. Heat BoundT(PM)¶

Temperature (mass flow/pressure) boundary condition

The Heat BoundT(PM) prescribes the temperature and either the pressure or mass flow in a certain point of the system: Temperature can be changed with action table or control signal line pressure or mass flow can be changed with a secondary time table of the component.

Positive mass flows represent flow into the system, negative mass flows represent flow from the sytem.

6.7.4.1. Hydraulic specifications¶

Description	Input	SI-units	Remarks
Temperature at t = 0 [s]	real	[°C]
Prescribed	pressure mass flow
Pressure	constant time varying		Only if Prescribed = pressure
Constant pressure	real	[N/m²]	If Pressure = constant
Pressure time table	table		If Pressure = time varying
Mass flow	constant time varying		Only if Prescribed = mass flow
Constant mass flow	real	[kg/s]	If Mass flow = constant
Mass flow time table	table		If Mass flow = time varying

6.7.4.2. Actions¶

In unsteady state the temperature can vary in time. The time variation must be defined in the action table or through a Control signal line. An example table is given below:

BOUNT(MP) Action table

Time [s]	Temperature [°C]
0.0	0.0
1.00	20.0
10.00	15.0

In the example the temperature is zero at steady state. It rises linearly in 1 s to 20 °C. After 1 s the flow decreases linearly in 9 s to 15 °C.

The pressure or mass flow variation must be specified via a user defined table. Linear interpolation will be performed between two values in the table. No extrapolation will be done; the last function value will be held if the actual time is outside the last table value.