# Practical Steam Turbine Performance Calculations

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Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Practical Steam Turbine Performance Calculations

(using Flex Live’s Steam Flex routine or by manual methods)

A steam turbine’s power and/or efficiency can be quickly and accurately calculated using Flexware’s Steam Flex steam properties program. It will be necessary to obtain the following operating data from the field.

Inlet steam pressure Inlet steam temperature Inlet steam flow rate Extraction steam pressure (if extraction type) Extraction steam temperature (if extraction type) Extraction steam flow rate (if extraction type) Exhaust steam pressure Exhaust steam temperature (if the exhaust steam is dry & saturated or superheated) Shaft power (necessary for non-condensing or condensing turbines with wet exhaust steam) See Figure 1 for typical units used for the calculations.

Note the efficiency and/or power can also be calculated manually using a steam Mollier chart and steam tables such as Keenan and Keyes.

Go to Figure 1, page 12 for the descriptions of the various symbols used.

Basic calculations (manually or by Steam Flex).

Method 1 - Exhaust steam is dry & saturated or superheated. Can be used for non-condensing type turbines and the high-pressure section of an extraction steam turbine plus it may be possible to use for the noncondensing low-pressure section of an extraction turbine. See Figures 2, 3 or 4. Overall efficiency (η) = Actual enthalpy / Isentropic enthalpy. Actual enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2) Isentropic enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2i). Note – the exhaust enthalpy is calculated using the inlet entropy (s1) Overall efficiency (η) = (h1 – h2)/(h1 – h2i) Steam Power = (h1 – h2) x steam flow rate (M2)/C1 (for turbines with dry & saturated or superheated exhaust steam. Shaft power = Steam Power - mechanical losses (journal and thrust bearing losses).

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Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Method 2 - Exhaust steam is wet. Can be used for condensing steam turbines and for the low-pressure section of extraction steam turbines. See Figure 3 or 4. Shaft Power Known (generator, torque meter coupling or the driven unit’s power) Overall efficiency (η) = Actual enthalpy / Isentropic enthalpy Isentropic enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2i) - the exhaust enthalpy is calculated using the inlet entropy(s1) Steam power = Shaft power plus mechanical losses (journal and thrust bearing losses). (h1 – h2) = Steam power x C1/Steam flow rate (M2) Overall efficiency (η) = (h1 – h2)/(h1 – h2i)

Shaft Power Unknown Do a heat balance on the steam condenser to determine the turbine exhaust enthalpy. See Figure 5 h2 = hc + (hcw2 – hcw1) x Mcw /M2 If the cooling water flow rate is in volume flow (GPM or m3/hr), convert to mass flow cooling water mass flow (Mcw) = cooling water volume flow rate x C2 Overall efficiency (η) = (h1 – h2)/(h1 – h2i) Steam power = (h1 – h2) x Steam Flow Rate/C1 Shaft power = Steam power minus mechanical losses (journal and thrust bearings) Warning – the cooling water temperature rise is very low, so accurate temperature measures are critical for reliable results.

Special notes for extraction steam turbines High pressure section Use Method 1 for the inlet conditions Use the extraction steam pressure, temperature and enthalpy for the exhaust conditions. Use in the inlet steam flow rate (M1) for the steam flow. Low pressure section Use the extraction steam pressure, temperature and enthalpy for the inlet conditions. The steam flow is the inlet steam flow rate (M1) minus the extraction steam flow rate Mex). Use Method 1 or Method 2 for the exhaust depending on the exhaust steam conditions.

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Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Steam Turbine Performance Examples

Example 1 – Non-condensing steam turbine using Steam Flex

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Exhaust steam temperature Inlet steam flow rate

600 psia 700 oF

140 psia 430 oF

75,000 lb/hr

Results: Steam Power Overall efficiency

3,339 HP 76.6%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power. See Example 1 Steam Flex below for the summary of results

Revision 0

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3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 - Steam Flex Data Summary

Revision 0

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3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 – Non-condensing steam turbine using Mollier method and/or steam

tables

Input Data:

Inlet steam pressure Inlet steam temperature

600 psia 700 oF

Exhaust steam pressure Exhaust steam temperature

140 psia 430 oF

Inlet steam flow rate

75,000 lb/hr

From Steam Tables: inlet enthalpy (h1) Inlet entropy (s1)

1,351.1 BTU/lb 1.5875 BTU/lb oR

Read vertically down on Mollier chart to get the isentropic exhaust enthalpy

Isentropic exhaust enthalpy (h2i)

1202.5 BTU/lb. (Mollier chart)

This value can also be obtained from the steam tables by interpolation using the inlet entropy

Isentropic exhaust enthalpy (h2i)

1203.2 BTU/lb. (steam tables)

Actual exhaust enthalpy can be obtained from the steam tables

Exhaust enthalpy (h2)

1,237.8 BTU/lb

Efficiency: Efficiency (η) = (h1 – h2)/(h1 – h2i) Efficiency = (1,351.1 – 1,202.5)/(1,351.1 – 1,237.8) = 76.2% using Mollier chart Efficiency = (1,351.1 – 1,203.2)/(1,351.1 – 1,237.8) = 76.6% using steam tables

Steam Power: Steam Power = (h1 – h2) x steam flow rate (M2)/C1 Steam Power = (1,351.1 – 1,237.8) x 75,000/2,545 = 3,339 HP

Revision 0

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power Using the steam tables is generally more accurate than using a Mollier chart.

Page 5

3 March 2013

[email protected], www.flewareinc.com

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 - Mollier Chart Results

Revision 0

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Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 – Condensing steam turbine (Power Known) using Steam Flex

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Steam power Inlet steam flow rate

300 psia 500 oF 4 in Hg a 4,600 HP 45,000 lb/hr

Results: Overall efficiency Exhaust moisture

75.0% 11.6%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power. See Example 2 Steam Flex below for the summary of results

Revision 0

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3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 - Steam Flex Data Summary (Power Known)

Revision 0

Page 8 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 – Condensing steam turbine (Power Known) using Mollier method and steam tables

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Steam Power Inlet steam flow rate

300 psia 500 oF 4 in Hg a 4,600 HP 45,000 lb/hr

From Steam Tables: Inlet enthalpy (h1) Inlet entropy (s1)

1,257.6 BTU/lb 1.5701 BTU/lb oR

Read vertically down on Mollier chart to get the isentropic exhaust enthalpy. This value cannot be determined from the steam table because the exhaust is wet.

isentropic exhaust enthalpy (h2i)

910 BTU/lb

Exhaust Enthalpy: (h1 – h2) = Steam power x C1/Steam flow rate (M2) (h1 – h2) = 4,600 x 2,545/45,000 = 260.2 BTU/lb h2 = 1,257.6 – 260.2 = 997.4 BTU/lb

Efficiency: Efficiency (η) = (h1 – h2)/(h1 – h2i) Efficiency = 260.2/(1257.6 – 910) = 74.9%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power

Revision 0

Page 9 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 - Mollier Chart Results

Revision 0

Page 10 [email protected], www.flewareinc.com

3 March 2013

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Practical Steam Turbine Performance Calculations

(using Flex Live’s Steam Flex routine or by manual methods)

A steam turbine’s power and/or efficiency can be quickly and accurately calculated using Flexware’s Steam Flex steam properties program. It will be necessary to obtain the following operating data from the field.

Inlet steam pressure Inlet steam temperature Inlet steam flow rate Extraction steam pressure (if extraction type) Extraction steam temperature (if extraction type) Extraction steam flow rate (if extraction type) Exhaust steam pressure Exhaust steam temperature (if the exhaust steam is dry & saturated or superheated) Shaft power (necessary for non-condensing or condensing turbines with wet exhaust steam) See Figure 1 for typical units used for the calculations.

Note the efficiency and/or power can also be calculated manually using a steam Mollier chart and steam tables such as Keenan and Keyes.

Go to Figure 1, page 12 for the descriptions of the various symbols used.

Basic calculations (manually or by Steam Flex).

Method 1 - Exhaust steam is dry & saturated or superheated. Can be used for non-condensing type turbines and the high-pressure section of an extraction steam turbine plus it may be possible to use for the noncondensing low-pressure section of an extraction turbine. See Figures 2, 3 or 4. Overall efficiency (η) = Actual enthalpy / Isentropic enthalpy. Actual enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2) Isentropic enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2i). Note – the exhaust enthalpy is calculated using the inlet entropy (s1) Overall efficiency (η) = (h1 – h2)/(h1 – h2i) Steam Power = (h1 – h2) x steam flow rate (M2)/C1 (for turbines with dry & saturated or superheated exhaust steam. Shaft power = Steam Power - mechanical losses (journal and thrust bearing losses).

Revision 0

Page 1 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Method 2 - Exhaust steam is wet. Can be used for condensing steam turbines and for the low-pressure section of extraction steam turbines. See Figure 3 or 4. Shaft Power Known (generator, torque meter coupling or the driven unit’s power) Overall efficiency (η) = Actual enthalpy / Isentropic enthalpy Isentropic enthalpy = Inlet enthalpy (h1) – Exhaust enthalpy (h2i) - the exhaust enthalpy is calculated using the inlet entropy(s1) Steam power = Shaft power plus mechanical losses (journal and thrust bearing losses). (h1 – h2) = Steam power x C1/Steam flow rate (M2) Overall efficiency (η) = (h1 – h2)/(h1 – h2i)

Shaft Power Unknown Do a heat balance on the steam condenser to determine the turbine exhaust enthalpy. See Figure 5 h2 = hc + (hcw2 – hcw1) x Mcw /M2 If the cooling water flow rate is in volume flow (GPM or m3/hr), convert to mass flow cooling water mass flow (Mcw) = cooling water volume flow rate x C2 Overall efficiency (η) = (h1 – h2)/(h1 – h2i) Steam power = (h1 – h2) x Steam Flow Rate/C1 Shaft power = Steam power minus mechanical losses (journal and thrust bearings) Warning – the cooling water temperature rise is very low, so accurate temperature measures are critical for reliable results.

Special notes for extraction steam turbines High pressure section Use Method 1 for the inlet conditions Use the extraction steam pressure, temperature and enthalpy for the exhaust conditions. Use in the inlet steam flow rate (M1) for the steam flow. Low pressure section Use the extraction steam pressure, temperature and enthalpy for the inlet conditions. The steam flow is the inlet steam flow rate (M1) minus the extraction steam flow rate Mex). Use Method 1 or Method 2 for the exhaust depending on the exhaust steam conditions.

Revision 0

Page 2 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Steam Turbine Performance Examples

Example 1 – Non-condensing steam turbine using Steam Flex

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Exhaust steam temperature Inlet steam flow rate

600 psia 700 oF

140 psia 430 oF

75,000 lb/hr

Results: Steam Power Overall efficiency

3,339 HP 76.6%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power. See Example 1 Steam Flex below for the summary of results

Revision 0

Page 3 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 - Steam Flex Data Summary

Revision 0

Page 4 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 – Non-condensing steam turbine using Mollier method and/or steam

tables

Input Data:

Inlet steam pressure Inlet steam temperature

600 psia 700 oF

Exhaust steam pressure Exhaust steam temperature

140 psia 430 oF

Inlet steam flow rate

75,000 lb/hr

From Steam Tables: inlet enthalpy (h1) Inlet entropy (s1)

1,351.1 BTU/lb 1.5875 BTU/lb oR

Read vertically down on Mollier chart to get the isentropic exhaust enthalpy

Isentropic exhaust enthalpy (h2i)

1202.5 BTU/lb. (Mollier chart)

This value can also be obtained from the steam tables by interpolation using the inlet entropy

Isentropic exhaust enthalpy (h2i)

1203.2 BTU/lb. (steam tables)

Actual exhaust enthalpy can be obtained from the steam tables

Exhaust enthalpy (h2)

1,237.8 BTU/lb

Efficiency: Efficiency (η) = (h1 – h2)/(h1 – h2i) Efficiency = (1,351.1 – 1,202.5)/(1,351.1 – 1,237.8) = 76.2% using Mollier chart Efficiency = (1,351.1 – 1,203.2)/(1,351.1 – 1,237.8) = 76.6% using steam tables

Steam Power: Steam Power = (h1 – h2) x steam flow rate (M2)/C1 Steam Power = (1,351.1 – 1,237.8) x 75,000/2,545 = 3,339 HP

Revision 0

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power Using the steam tables is generally more accurate than using a Mollier chart.

Page 5

3 March 2013

[email protected], www.flewareinc.com

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 1 - Mollier Chart Results

Revision 0

Page 6 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 – Condensing steam turbine (Power Known) using Steam Flex

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Steam power Inlet steam flow rate

300 psia 500 oF 4 in Hg a 4,600 HP 45,000 lb/hr

Results: Overall efficiency Exhaust moisture

75.0% 11.6%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power. See Example 2 Steam Flex below for the summary of results

Revision 0

Page 7 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 - Steam Flex Data Summary (Power Known)

Revision 0

Page 8 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 – Condensing steam turbine (Power Known) using Mollier method and steam tables

Input Data: Inlet steam pressure Inlet steam temperature Exhaust steam pressure Steam Power Inlet steam flow rate

300 psia 500 oF 4 in Hg a 4,600 HP 45,000 lb/hr

From Steam Tables: Inlet enthalpy (h1) Inlet entropy (s1)

1,257.6 BTU/lb 1.5701 BTU/lb oR

Read vertically down on Mollier chart to get the isentropic exhaust enthalpy. This value cannot be determined from the steam table because the exhaust is wet.

isentropic exhaust enthalpy (h2i)

910 BTU/lb

Exhaust Enthalpy: (h1 – h2) = Steam power x C1/Steam flow rate (M2) (h1 – h2) = 4,600 x 2,545/45,000 = 260.2 BTU/lb h2 = 1,257.6 – 260.2 = 997.4 BTU/lb

Efficiency: Efficiency (η) = (h1 – h2)/(h1 – h2i) Efficiency = 260.2/(1257.6 – 910) = 74.9%

Notes: Inlet steam flow is used. If the steam leakage for the seals is known, it can be deducted to

give a more accurate result. Shaft power can be determined by subtracting the Mechanical Losses (if known) from the

Steam Power

Revision 0

Page 9 [email protected], www.flewareinc.com

3 March 2013

Flexware®

Turbomachinery Engineers ® ® A Veteran & Employee Owned Company

Example 2 - Mollier Chart Results

Revision 0

Page 10 [email protected], www.flewareinc.com

3 March 2013

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