This is the model of a radial-inflow turbine. The following assumptions have been made in formulating this component type:
There are no heat losses.
| ST | PORTS_LIB.analog_signal | (n = 1) | OUT | Speed transmitter (Hz) | |
| Valve_in | PORTS_LIB.analog_signal | (n = 1) | IN | Position of Inlet valve (%) | |
| f_in | fluid | IN | |||
| f_out | fluid | OUT |
| D | REAL | 0.055 | Blade diameter | m | |
| M | REAL | 3 | Shaft mass | kg | |
| N_d | REAL | 2620 | Design speed | rps | |
| No | REAL | 2620 | Inital value of the shaft speed | rps | |
| P_in_d | REAL | 1 | Design inlet pressure | bar | |
| P_out_d | REAL | 1 | Design outlet pressure | bar | |
| Po | REAL | 1 | Initial pressure | bar | |
| T_in_d | REAL | 300 | Design inlet temperature | K | |
| To | REAL | 300 | Initial temperature | K | |
| eff_is_d | REAL | 0.73 | Design isentropic efficiency | - | |
| m_d | REAL | 0.111 | Design mass flow | kg/s | |
| mat | ENUM THERMAL.Material | SS_304 | Wall material | ||
| thw | REAL | 0.01 | Wall thickness | m |
| Aout | REAL | Area at the outlet | m^2 | ||
| E | REAL | Energy provided by the fluid | W | ||
| E_d | REAL | Design energy provided by the fluid | W | ||
| G | REAL | Mass flow per unit area for molecular flow | kg/(s�m^2) | ||
| Gd | REAL | Design mass flow per unit area for molecular flow | kg/(s�m^2) | ||
| I | REAL | Moment of inertia of the rotor | kg�m^2 | ||
| N | REAL | Shaft speed | Hz | ||
| cj | REAL | Jet velocity | m/s | ||
| cj_d | REAL | Design jet velocity | m/s | ||
| dP | REAL | ||||
| dP_lam | REAL | Pressure difference for laminar flow | bar | ||
| dP_loss | REAL | Pressure loss | Pa | ||
| eff_is | REAL | Isentropic efficiency | - | ||
| h_in | REAL | Inlet enthalpy | J/kg | ||
| h_in_d | REAL | Design inlet enthalpy | J/kg | ||
| h_out | REAL | Outlet enthalpy | J/kg | ||
| h_out_s | REAL | Outlet enthalpy in a isentropic process | J/kg | ||
| h_out_s_d | REAL | Design outlet enthalpy in an isentropic process | J/kg | ||
| ier | INTEGER | ||||
| m | REAL | Mass flow | kg/s | ||
| rho | REAL | Inlet density | kg/m^3 | ||
| rho_in_d | REAL | Design inlet density | kg/m^3 | ||
| s_in | REAL | Inlet entropy | J/kg | ||
| s_in_d | REAL | Design inlet entropy | J/kg | ||
| u1 | REAL | Blade velocity | m/s | ||
| u1_d | REAL | Design blade velocity | m/s | ||
| v | REAL | Blade-jet speed ratio | - | ||
| v_d | REAL | Design blade-jet speed ratio | - | ||
| vsound_d | REAL |
| Vol | Volume | |
| Jun | Valve |
| Jun.Cv | Aout / 2.4027e-005 | DATA | REAL | Valve flow coefficient for completely open position | "-" |
| Vol.D | D | DATA | REAL | Diameter | "m" |
| Vol.Po | Po | DATA | REAL | Initial pressure | "bar" |
| Vol.To | To | DATA | REAL | Initial temperature | "K" |
| Vol.mat | mat | DATA | ENUM Material | Wall material | "-" |
| Vol.thw | thw | DATA | REAL | Wall thickness | "m" |
This section gives a description of the model developed for simulating turbines at off-design conditions.
There are different ways of calculating the mass flow through a turbine. The mass flow has been calculated from the value of the design mass flow multiplied by the ratio between the isentropic mass flow per unit of area at working conditions and the isentropic mass flow per unit of area at design conditions.
where 
is the mass flow at working conditions, 
is the mass flow at the design condition,
and 
are the isentropic mass flow per unit of area at working conditions and at design conditions respectively.
G is calculated as in a junction:
The approach that has been used for calculating mass flow per unit of area through the turbine is to regard the stator blade section as an orifice.
The isentropic efficiency for a turbine is given by the equation:
where 
�is the outlet enthalpy for an
isentropic expansion, ho is the inlet enthalpy and h2 is the outlet enthalpy.
The isentropic efficiency of a turbine can be calculated by means of dimensionless parameters. The dimensionless parameter often used to calculate the radial-inflow turbine performance is the blade-jet speed ratio:
where 
�is the jet velocity and u1 is
the blade velocity.
The jet velocity is defined as the velocity corresponding to the ideal expansion through the turbine:
The blade velocity is given by the next equation:
where D is the rotor blade diameter and N is the shaft speed.
The variation of the efficiency for a
turbine can be approximated by a parabolic curve. The ratios 
�and 
�are used as parameters for
this parabolic equation,where hopt is the optimum efficiency and nopt is the corresponding optimum blade-jet speed ratio. It is
assumed that the turbines are designed to run at the optimum point. This means
that 
�and 
�where the subscript d denotes
the values used as design values. Thus, the parabolic equation to calculate the
isentropic efficiency is the following:
The rate of energy required to accelerate the speed of the shaft is a function of the rotational inertia of the impeller and the rotational speed:
where 
is the rotational inertia
If the inertial component is not considered, then the forth power of the speed is proportional to the energy flux provided by the fluid:
The equation to calculate the speed in off-design mode without the inertial component is as follows:
where 
is the energy flux provided by the fluid and 
�is the design energy flux
provided by the fluid.
where is the mass flow and the subscript d denotes the design values.
If the inertial component is considered, the equation used to calculate the speed will be the following:
The initial value of the dynamic variable 
�is obtained from the
initialization data 
:
Document generated automatically with EcosimPro Version: 5.4.14 Date: 2015:02:02 Time: 12:52:59