Turbine (G)

A gas turbine in a thermodynamic cycle.

blockType: EngeeFluids.Gas.Turbomachinery.Turbine

Path in the library:

/Physical Modeling/Fluids/Gas/Turbomachinery/Turbine (G)

Description

Block Turbine (G) simulates a turbine in a gas network. You can parameterize the unit using an analytical approximation or tabular data, which is either a 1-D function of differential pressure or a 2-D function of differential pressure and adjusted mass flow. The fluid flowing from port A to port B creates a torque. The mechanical port R is connected to the turbine shaft, reflects the torque on the shaft and its angular velocity relative to the port C, which in turn is connected to the turbine body.

If the check box is selected Enable variable nozzle input port, then the VN port appears, through which a control signal is set that sets the value of the degree of nozzle opening. This value scales the adjusted mass flow linearly, but does not affect the efficiency of the turbine. The value 1 corresponds to the characteristic data of the turbine.

Turbine Characteristics

The characteristic data of the turbine correlates the turbine performance depending on the pressure drop with the adjusted mass flow rate and isentropic efficiency. The pressure difference is determined between the pressure at the turbine inlet and the pressure at the outlet.

adjusted mass flow rate

Due to the large changes in pressure and temperature inside the turbine, the characteristics of the turbine reflect the performance in terms of adjusted mass flow. In the unit, the adjusted mass flow is adjusted based on the input mass flow using the adjusted pressure and temperature:

where

— mass flow rate in port A;
— port temperature A;
— parameter value Reference temperature for corrected flow. This value is given in the technical data sheet of the turbine.;
— adjusted mass flow rate:
- if for the parameter Turbine map parameterization the value is set Analytical - nominal pressure ratio and corrected mass flow rate Then it is set using the parameter value Nominal corrected mass flow rate;
- if for the parameter Turbine map parameterization the value is set Tabulated data - flow rate and efficiency vs. pressure ratio Then it is set using the parameter value Corrected mass flow rate vector, mdot(pr);
- if for the parameter Turbine map parameterization the value is set Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio Then it is set using the parameter value Corrected mass flow rate table, mdot(N,beta);
— port pressure A;
— parameter value Reference pressure for corrected flow. This value is given in the technical data sheet of the turbine.

adjusted speed

The shaft rotation speed is also regulated in the unit. in accordance with the initial temperature, so that the adjusted shaft rotation speed is:

Shaft torque

Shaft torque calculated as follows:

where

— the total change in the specific enthalpy of the gas;
— parameter value Mechanical efficiency;
— relative angular velocity of the shaft: .

The reverse flow from port B to port A is not a normal operation mode of the turbine and may give inaccurate results. The threshold values ensure that no torque is generated in the unit when the flow rate is close to zero or the flow is reversed.

Analytical parameterization

Use analytical parameterization to create a turbine based on expected rated operating conditions. If for the parameter Turbine map parameterization the value is set Analytical - nominal pressure ratio and corrected mass flow rate, then the isentropic efficiency of the turbine is constant, and the mass flow rate depends on the pressure drop.

Pressure drop parameterization

If for the parameter Turbine map parameterization the value is set Tabulated data - flow rate and efficiency vs. pressure ratio, then the isentropic efficiency of the turbine and the mass flow rate are set depending on the pressure drop, and they do not take into account any changes in the angular velocity of the turbine.

The last elements in the parameter vectors Corrected mass flow rate vector, mdot(pr) and Pressure ratio vector, pr represent the adjusted mass flow rate and pressure drop under flow throttling conditions.

Parameterization based on differential pressure and adjusted mass flow

If for the parameter Turbine map parameterization the value is set Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio,the isentropic efficiency of the turbine, the pressure ratio, and the adjusted mass flow rate are set depending on the adjusted velocity and the index . The unit uses linear interpolation between data points to determine efficiency, pressure drop, and adjusted mass flow parameters.

The last columns of the parameter matrices Corrected mass flow rate table, mdot(N,beta) and Pressure ratio table, pr(N,beta) represents the adjusted mass flow rate and pressure drop under flow throttling conditions.

Equations of continuity

The equation of conservation of mass:

where — mass flow rate in port B.

The energy conservation equation:

where

— energy flow in port A;
— energy flow in port B;
— the work performed by the gas and determined by the change in the total specific enthalpy of the liquid: .

Assumptions and limitations

The shaft does not rotate under reverse flow conditions. The results for reverse flows may be inaccurate.

Ports

Conserving

# C — turbine housing
rotational mechanics

Details

A mechanical non-directional port connected to the turbine body.

Program usage name

case_flange

# R — turbine shaft
rotational mechanics

Details

A mechanical non-directional port connected to the turbine shaft.

Program usage name

rod_flange

# B — gas outlet port
gas

Details

A non-directional gas port connected to the turbine outlet section.

Program usage name

outlet

# A — gas inlet port
gas

Details

A non-directional gas port connected to the turbine inlet section.

Program usage name

inlet

Input

# VN — the degree of nozzle opening, dimensionless
scalar

Details

Variable degree of opening of the nozzle cross-sectional area, set as a dimensionless scalar. The adjusted mass flow varies linearly depending on the value of VN. The value 1 corresponds to the tabular data. The degree of opening of the nozzle section does not affect the isentropic efficiency.

Dependencies

To use this port, check the box Enable variable nozzle input port.

Data types	`Float64`
Complex numbers support	No

Parameters

Parameterization

# Turbine map parameterization — parameterization of performance
Analytical - nominal pressure ratio and corrected mass flow rate | Tabulated data - flow rate and efficiency vs. pressure ratio | Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio

Details

Parameterization of performance:

Analytical - nominal pressure ratio and corrected mass flow rate — analytical parameterization of the isentropic efficiency of the turbine and the adjusted mass flow rate.
Tabulated data - flow rate and efficiency vs. pressure ratio — tabular parameterization of the isentropic efficiency of the turbine and the adjusted mass flow rate by pressure drop.
Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio — tabular parameterization of the isentropic efficiency of the turbine and the adjusted mass flow according to the adjusted velocity and pressure drop.

Values	`Analytical - nominal pressure ratio and corrected mass flow rate` \| `Tabulated data - flow rate and efficiency vs. pressure ratio` \| `Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio`
Default value	`Analytical - nominal pressure ratio and corrected mass flow rate`
Program usage name	`parameterization`
Evaluatable	Yes

# Enable variable nozzle input port — enabling a variable nozzle cross-sectional area

Details

Select this option to enable the VN input port and set the variable degree of the nozzle opening.

If this option is not selected, the open nozzle opening remains constant.

Default value	`false (switched off)`
Program usage name	`variable_nozzle`
Evaluatable	Yes

# Minimum nozzle opening fraction — minimum degree of opening

Details

The minimum degree of nozzle opening. This value is the lower bound for the value on the VN port. The unit multiplies the value of this parameter by the mass flow rate to obtain the minimum adjusted mass flow rate through the turbine.

Dependencies

To use this option, check the box Enable variable nozzle input port.

Default value	`0.001`
Program usage name	`min_nozzle_opening_fraction`
Evaluatable	Yes

# Maximum nozzle opening fraction — maximum degree of opening

Details

The maximum degree of nozzle opening. This value is the upper bound for the value on the VN port. The unit multiplies the value of this parameter by the mass flow rate to obtain the maximum adjusted mass flow through the turbine.

Dependencies

To use this option, check the box Enable variable nozzle input port.

Default value	`1.0`
Program usage name	`max_nozzle_opening_fraction`
Evaluatable	Yes

# Corrected speed index vector, N — vector of shaft rotation speeds
rpm | deg/s | rad/s

Details

A vector of constant shaft rotation speeds for tabular parameterization of adjusted mass flow and isentropic efficiency.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio.

Units	`rpm` \| `deg/s` \| `rad/s`
Default value	`[5000.0, 6000.0, 7000.0, 8000.0, 9000.0, 10000.0, 11000.0] rpm`
Program usage name	`w_vector`
Evaluatable	Yes

Flow Rate Data

# Nominal pressure ratio — pressure drop for analytical parameterization

Details

The value of the differential pressure under nominal operating conditions for analytical parameterization.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Analytical - nominal pressure ratio and corrected mass flow rate.

Default value	`2.0`
Program usage name	`p_ratio_nominal`
Evaluatable	Yes

# Nominal corrected mass flow rate — adjusted mass flow value for analytical parameterization
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Adjusted mass flow value under nominal operating conditions for analytical parameterization.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Analytical - nominal pressure ratio and corrected mass flow rate.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`48.0 kg/s`
Program usage name	`mdot_nominal`
Evaluatable	Yes

# Pressure ratio vector, pr — pressure drop vector

Details

A vector of differential pressure values for tabular parameterization of the adjusted mass flow. This vector must be of the same dimension as Corrected mass flow rate vector, mdot(pr), and all elements of the vector must be greater than 1. The last element must meet the flow throttling conditions.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. pressure ratio.

Default value	`[1.251, 1.345, 1.442, 1.521, 1.596, 1.692, 1.849, 1.972, 2.1, 2.173, 2.259, 2.3424]`
Program usage name	`p_ratio_vector_mdot`
Evaluatable	Yes

# Corrected mass flow rate vector, mdot(pr) — vector of adjusted mass flow values
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Vector of adjusted mass flow values for tabular parameterization of adjusted mass flow. This vector must be of the same dimension as Corrected mass flow rate vector, mdot(pr), and all elements of the vector must be greater than 0. The last element must meet the flow throttling conditions.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. pressure ratio.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`[39.439, 43.01, 45.556, 46.801, 47.792, 48.388, 48.634, 48.67, 48.689, 48.747, 48.825, 48.912] kg/s`
Program usage name	`mdot_vector`
Evaluatable	Yes

# Pressure ratio table, pr(N,beta) — matrix of differential pressure values

Details

The matrix on the values of the pressure ratio at the outlet and inlet of the turbine at a given adjusted shaft rotation speed and values . The block uses linear interpolation between the elements of the matrix. Values and they represent:

— the number of vector elements Corrected speed index vector, N;
— number of indexes in the vector.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio.

Default value	[1.217 1.285 1.323 1.363 1.402 1.427 1.495 1.545 1.6 1.687 1.747 1.8074; 1.231 1.302 1.356 1.404 1.443 1.473 1.525 1.577 1.635 1.709 1.782 1.845; 1.242 1.328 1.388 1.437 1.528 1.617 1.704 1.811 1.915 1.979 2.053 2.1226; 1.244 1.339 1.417 1.465 1.528 1.584 1.692 1.787 1.899 2.0 2.075 2.1492; 1.245 1.34 1.425 1.492 1.546 1.684 1.748 1.882 1.987 2.084 2.167 2.2458; 1.251 1.345 1.442 1.521 1.596 1.692 1.849 1.972 2.1 2.173 2.259 2.3424; 1.248 1.348 1.447 1.516 1.581 1.651 1.749 1.839 1.93 2.024 2.154 2.242]
Program usage name	`p_ratio_matrix_mdot`
Evaluatable	Yes

# Corrected mass flow rate table, mdot(N,beta) — matrix of adjusted mass flow values
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The matrix on the values of the adjusted mass flow rate at a given adjusted shaft rotation speed and values of . The block uses linear interpolation between the elements of the matrix. Values and they represent:

— the number of vector elements Corrected speed index vector, N;
— number of indexes in the vector.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	[40.403 44.417 46.653 47.966 48.97 49.544 50.001 50.081 50.086 50.095 50.09 50.0922; 40.044 43.754 46.125 47.626 48.513 49.105 49.481 49.58 49.597 49.624 49.638 49.633; 39.941 43.795 46.017 47.335 48.795 49.199 49.279 49.27 49.248 49.23 49.255 49.2428; 39.896 43.512 45.914 47.061 48.011 48.558 48.943 49.042 49.069 49.01 49.046 49.0266; 39.524 42.934 45.686 46.743 47.715 48.67 48.777 48.836 48.876 48.836 48.845 48.8184; 39.439 43.01 45.556 46.801 47.792 48.388 48.634 48.67 48.639 48.647 48.625 48.5912; 39.502 42.849 45.336 46.385 47.312 47.877 48.222 48.397 48.459 48.482 48.455 48.414] kg/s
Program usage name	`mdot_matrix`
Evaluatable	Yes

Efficiency Data

# Constant isentropic efficiency — the value of isentropic efficiency

Details

Isentropic efficiency under nominal operating conditions for analytical parameterization.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Analytical - nominal pressure ratio and corrected mass flow rate.

Default value	`0.8`
Program usage name	`const_efficiency`
Evaluatable	Yes

# Pressure ratio vector, pr — pressure drop vector

Details

A vector of values of the ratio of outlet pressure to turbine inlet pressure for tabular parameterization of isentropic efficiency. This vector must be of the same dimension as Isentropic efficiency vector, eta(pr), and all elements of the vector must be greater than 1. The last element must meet the flow throttling conditions.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. pressure ratio.

Default value	`[1.252, 1.328, 1.425, 1.544, 1.642, 1.757, 1.873, 2.005, 2.1, 2.204, 2.248, 2.28]`
Program usage name	`p_ratio_vector_efficiency`
Evaluatable	Yes

# Isentropic efficiency vector, eta(pr) — vector of isentropic efficiency values

Details

A vector of isentropic efficiency values for tabular parameterization of isentropic efficiency. This vector must be of the same dimension as Pressure ratio vector, pr, and all elements of the vector must be greater than 0 and less than or equal to 1.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. pressure ratio.

Default value	`[0.559, 0.61, 0.673, 0.741, 0.788, 0.835, 0.869, 0.895, 0.908, 0.899, 0.854, 0.751]`
Program usage name	`efficiency_vector`
Evaluatable	Yes

# Pressure ratio table, pr(N,beta) — matrix of differential pressure values

Details

— the number of vector elements Corrected speed index vector, N;
— number of indexes in the vector.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio.

Default value	`[1.224 1.246 1.292 1.387 1.457 1.534 1.61 1.686 1.743 1.79 1.871 1.914; 1.237 1.25 1.28 1.369 1.459 1.553 1.629 1.716 1.799 1.846 1.927 1.97; 1.241 1.255 1.283 1.326 1.401 1.509 1.591 1.704 1.806 1.913 1.994 2.037; 1.25 1.265 1.308 1.364 1.456 1.532 1.637 1.739 1.851 1.934 2.042 2.085; 1.281 1.314 1.371 1.425 1.498 1.574 1.647 1.749 1.878 1.979 2.091 2.18; 1.252 1.328 1.425 1.544 1.642 1.757 1.873 2.005 2.1 2.204 2.248 2.28; 1.382 1.43 1.495 1.586 1.688 1.791 1.887 1.99 2.079 2.158 2.249 2.36]`
Program usage name	`p_ratio_matrix_efficiency`
Evaluatable	Yes

# Isentropic efficiency table, eta(N,beta) — matrix of isentropic efficiency values

Details

The matrix on the values of the isentropic efficiency of the turbine at a given constant speed of rotation of the shaft and the value of . The block uses linear interpolation between the elements of the matrix. Values and they represent:

— the number of vector elements Corrected speed index vector, N;
— number of indexes in the vector.

Dependencies

To use this parameter, set for the parameter Turbine map parameterization meaning Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio.

Default value	[0.72 0.754 0.759 0.739 0.714 0.679 0.643 0.603 0.554 0.524 0.494 0.48; 0.716 0.757 0.794 0.819 0.812 0.788 0.761 0.728 0.692 0.662 0.632 0.618; 0.629 0.691 0.775 0.831 0.858 0.869 0.859 0.842 0.816 0.782 0.752 0.738; 0.594 0.668 0.757 0.804 0.857 0.883 0.892 0.893 0.884 0.865 0.835 0.821; 0.664 0.72 0.779 0.823 0.858 0.883 0.897 0.905 0.904 0.896 0.883 0.868; 0.559 0.61 0.673 0.741 0.788 0.835 0.869 0.895 0.908 0.899 0.854 0.751; 0.718 0.785 0.824 0.855 0.882 0.9 0.908 0.906 0.884 0.857 0.804 0.701]
Program usage name	`efficiency_matrix`
Evaluatable	Yes

Reference Data

# Reference pressure for corrected flow — corrective pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure at which the turbine data is reduced to the adjusted trend line.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_ref`
Evaluatable	Yes

Details

The temperature at which the turbine data is reduced to the adjusted trend line.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`288.15 K`
Program usage name	`T_ref`
Evaluatable	Yes

# Mechanical efficiency — torque conversion efficiency

Details

The efficiency of converting gas operation into shaft torque.

Default value	`0.9`
Program usage name	`mechanical_efficiency`
Evaluatable	Yes

# Inlet area at port A — the area of the turbine inlet section
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the turbine inlet port.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`1.0 m^2`
Program usage name	`inlet_area`
Evaluatable	Yes

# Outlet area at port B — the area of the turbine outlet section
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the turbine outlet port.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`1.0 m^2`
Program usage name	`outlet_area`
Evaluatable	Yes

Literature

Kurzke, Joachim. How to Get Component Maps for Aircraft Gas Turbine Performance Calculations. Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General, American Society of Mechanical Engineers, 1996, p. V005T16A001.
Plencner, Robert M. Plotting component maps in the Navy/NASA Engine Program (NNEP): A method and its usage. NASA Technical Memorandum, 1989.