Turbine (TPF)#

The Turbine (TPF) block simulates turbine operation in a two-phase hydraulic network. The pressure drop and mass flow rate are calculated based on the provided data, relative to the nominal operating mode.

Law of Conservation of Mass (1) :

(1)#\[\dot m_A + \dot m_B=0\]

where:

\(\dot m_A\) – mass flow rate at the input, [kg/s];

\(\dot m_B\) – mass flow rate at the outlet, [kg/s].

Law of conservation of energy (2), (3) :

(2)#\[\phi_A + \phi_B - P_ж= 0\]

where:

\(\phi_A\) - energy flow at the input, [W];

&emsp\(\phi_B\) - energy flow at the output, [W].;

\(P_ж=\dot m_A \cdot (h_{tA}-h_{tB})\) – power transmitted by the flow of the medium, [W];

\(h_{tA}, h_{tB}\) - total enthalpies at the input and output, [J/kg].

(3)#\[h=u+p \cdot v + \frac{v \cdot \dot m^2}{2 \cdot F^2}\]

where:

\(v\) – specific volume, [m\(^3\)/kg];

\(u\) – specific internal energy, [J/kg];

\(p\) – pressure, [Pa];

\(F\) – flow cross-sectional area, [m\(^2\)].

Shaft torque (4) :

(4)#\[\tau=\frac{\eta_M\cdot \dot m \cdot \Delta h_t}{\omega}\]

where:

\(\eta_M\) - mechanical Efficiency;

\(\omega\) - angular velocity of the shaft, [rad/s];

\(\Delta h_t=\eta_{isen} \cdot (h_{tA}-h_{tB}^{isen})\)

\(h_{tB}^{isen}\) - total enthalpy at the outlet for an isentropic process, [J/kg];

\(\eta_{isen}\) – isentropic Efficiency.

Pressure drop

The pressure drop is determined according to the following formula (5) :

(5)#\[\frac{\dot m^2}{\dot m^2_{ном}}\cdot \frac{v_{вх}}{v_{вх}^{ном}}\cdot \frac{p_{вх}^{ном}}{p_{вх}}=\frac{1-(\frac{p_{вых}}{p_{вх}})^{\frac{\eta_n+1}{\eta_n}}}{1-(\frac{p_{вых}^{ном}}{p_{вх}^{ном}})^{\frac{\eta_n+1}{\eta_n}}}\]

where:

\(\dot m_{nom}\) – nominal mass flow rate of the medium, [kg/s];

\(p_{output}\) - output pressure, [Pa];

\(p_{output}^{nom}\) - nominal pressure at the output, [Pa];

\(p_{in}\) - input pressure, [Pa];

\(p_{in}^{nom}\) - nominal pressure at the input, [Pa];

\(\eta_n\) - polytropic Efficiency;

\(v_{in}^{nom}\) - nominal specific volume at the inlet, [m\(^3\)/kg];

\(v_{in}\) - specific volume at the inlet, [m\(^3\)/kg].

Note

The reverse flow of coolant is not modeled.

1. Properties#

Property	Default Value	Description	Units of measurement
Nominal inlet pressure	3.5	-	MPa
Nominal outlet pressure	1.0	-	MPa
Nominal mass flow rate	1.5	-	kg/s
Nominal specific volume	0.085	-	m\(^3\)/kg
Isentropic efficiency	0.9	-	-
Mechanical efficiency	0.9	-	-
Inlet fluid flow area	0.01	-	m\(^2\)
Outlet fluid flow area	0.02	-	m\(^2\)
Laminar flow pressure ratio	0.999	-	-
Polytropic efficiency	0.9	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Two-phase fluid
Mechanical port	Input	-	-	Rotational motion
Output	Output	-	-	Two-phase fluid

In order to see the connection capabilities of the block, you need to go to page Description of block ports