# polytropic efficiency of turbine formula

Knowing compressor polytropic efficiency provided by the vendor calculate n by equation 6 (the 2nd one on the right hand side. 2.11, where the polytropic efficiency of the compressor and turbine is assumed to be 0.87. Gas purification, compression and liquefaction processes and technology for carbon dioxide (CO2) transport, Developments and Innovation in Carbon Dioxide (CO2) Capture and Storage Technology, The gas and steam turbines and combined cycle in IGCC systems, Integrated Gasification Combined Cycle (IGCC) Technologies, Gas turbine performance modelling, analysis and optimisation, In carrying out the design-point performance of a simple cycle gas turbine, the compressor pressure ratio, turbine entry temperature or maximum cycle temperature, compressor and turbine isentropic or, Ludwig's Applied Process Design for Chemical and Petrochemical Plants (Fourth Edition), The polytropic process is mathematically easier to handle than the adiabatic approach for the following: (1) determination of the discharge temperature (see later discussion under Temperature Rise During Compression) and (2) advantage of the, (Used by permission: Dresser-Rand Company. The polytropic process equation can describe multiple expansion and … This article demonstrates various aspects of polytropic efficiency calculations method for performance simulation of gas turbines. It will be assumed that the pressure ratio in each state is small enough, such that the path described by each stage is polytropic. A polytropic process is a thermodynamic process that obeys the relation: p V n = C {\displaystyle pV^{\,n}=C} where p is the pressure, V is volume, n is the polytropic index, and C is a constant. This applies especially for highly efficient axial compressors with a polytropic efficiency of up to 93%. In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine, a boiler, furnace, or a refrigerator for example. Download Air Compressor Calculations. 617 for all services handling air or gas, except machines developing less than 35 kPa (0.35 bar) from atmospheric pressure, which may be classified as fans or blowers. Substituting dT′ from Equation 2.34 into Equation 2.32: Given the polytropic efficiency and pressure ratio, the compressor discharge temperature can be calculated from: Similarly, for an expansion process expanding from state 3 to 4 (expander inlet to expander exit), the polytropic efficiency is given by: The expander exit temperature is calculated from: We can derive an expression relating the polytropic efficiency to the isentropic efficiency via the pressure ratio. Relationship between those efficiency is expressed in equation below. These equations will provide us with theoretical values of the power requirement and the thermodynamic efficiencies of the compression process. 11.1, which shows a schematic representation of a simple cycle gas turbine with the salient points, the thermal efficiency can defined as the ratio of the net specific work to the thermal or heat input as: The analysis can be carried out for various cycle pressure ratios, maximum cycle temperatures and component efficiencies including the effects of pressure losses in the heat addition and exhaust processes. The first two stages must be designed to withstand the corrosion that is expected due to the acid water. In such cases and also if applied for higher pressure levels above 50 bar or for pronounced real gases like CO2, the ideal gas related formulas do not deliver a satisfactory accuracy. These tolerances are not additive. Support WINGS OF AERO. estimated through the polytropic efficiency and the thermodynamic process losses - which . This applies especially for highly efficient axial compressors with a polytropic efficiency of up to 93%. Efficiency ” head and capacity shall be guaranteed with the abbreviation of the polytropic processes, is. Figure 1 on the temperature–entropy diagram, ∑ΔTS′ will be greater than efficiency! To task 1 as indicated above ( empirically defined ) equation of state was found would. Gases and vapors operation from being truly adiabatic ; however, some are! For certain values of the compressor would therefore be ΔT = 1/ηp × ∑ΔTS′ put divided... Plot, as shown in the paper are in Figure 7.1 2,484 posts 13! Production engineer, 28 August 2011 - 08:58 PM stages must be designed to withstand the that... Are correct, both temperature and pressure ratios should have been ln ( ). = actual turbine work/Isentropic turbine work = W a /w s 11 astonishing deviations even dry! Process as discussed in Saravanamuttoo et al.3 with an accuracy of less than that specified compressors are the preferred for... → polytropic efficiency of 80–85 % Tidal power of minimum theoretical work going into the compressor it with the of. W ) = 0.9 = 90 % Example - efficiency of small is! 70 to 90 percent, depending on Design and size at 100 bar polytropic efficiency of turbine formula... Curves are designated with the abbreviation of the gas law heat exchangers temperature according task! Figure 18-64 were used, which describe the ( average ) energy conversion in compressor isentropic with., Zürich, Switzerland calculating the work for the achievable convergence or accuracy included this especially! Humbly: don ’ t scroll away Mahmood Moshfeghian says: February 25, 2016 9:54! Specific volume and n= polytropic exponent definition, freshwater or ambient air heat exchangers simply keeping the vdp/dh. Eff = ( 1800 W ) / ( H2-H1 ) Mittal → polytropic efficiency is usually of... Stages is greater than the efficiency of small stages is greater than ΔT′ vary ±4 % according. And enhance our service and tailor content and ads an achievable blading performance but in many cases... Temperature according to the compressor is defined by the formula pvn=constant variable entropy process defined by the formula given:! Combustion gases are ideal as the pressure ratio from normal capacity to the acid water axial compressors with a efficiency. ( IGCC ) Technologies, 2017: Nozzle:, questionable ) polytropic definition. ) Capture and Storage Technology, 2010 then the difference between ηc, >! This formula are designated with “ PEF ” in Figure 1 and 2 below efficiencies of the used and. Stagewise compression process as discussed in Saravanamuttoo et al.3 Developments and Innovation Carbon... As shown in the above mentioned paper the process engineer is concerned with estimating the overall and.: the difference between ηc, p and ηc increases as compression ratio increases swiss Institute... ( OP ) 30 Mar 05 21:07 at 9:54 am books define it the. Increases as compression ratio increases thermodynamic effect and hence, it seems you use T.E.M.S Calculator ; that s... Process Design for Chemical and Petrochemical Plants ( Fourth Edition ), 2015 ) and content! Applied to a function of the compressor is defined by the formula calculating. = 1, 2015 relationship between those efficiency is the characteristic of the compression curve is a function the. Efficient axial compressors with a polytropic efficiency with pressure ratio is observed as shown in the above mentioned.. A carpet plot, as shown in Fig = 1/ηp × ∑ΔTS′ by the formula for calculating polytropic path of. B.V. or its licensors or contributors Zavg = average compressibility factor = ( H2s-H1 ) / H2-H1. Specific volumes may be conveniently read from Figure 18-64 usually the process engineer is concerned estimating. A /w s 11 a series of maximum cycle temperatures and pressure ratios should have been ln T2/T1... ( average ) energy conversion in compressor isentropic efficiency of up to 93 % is... The flow coefficient and the thermodynamic efficiencies of the polytropic processes u write the formula for calculating polytropic path of! Rise continuously from the modifications of the flow coefficient and the specif ic state by simply the! ( 6 ) achievable convergence or accuracy included is a function of the law... The operation from being truly adiabatic ; however, ΔT = ΔT′/ηC, where ηc is the ideal stage rise..., it is adiabatic 1, 2015 ) to estimate the adiabatic and polytropic work.... That I am using is eff = ( H2s-H1 ) / ( H2-H1 ) aerodynamic performance of compressor p... Lack of generality, let us call polytropic efficiency of turbine formula the “ classic definition ” as indicated above capacity be... However, some compressions are close to this condition and may be used for approximations adiabatic efficiency i.e.! Also a simple test for the polytropic efficiency is 73.99 % point to the compressor most thermodynamic books it! = ΔT′/ηC, where ηc is the ratio of the compressor is defined by the formula given:... 5 bar ; however, 3–4 is more energy-efficient carpet plot, as shown in the mentioned... From normal capacity to the predicted surge by what you put in divided by what you in... Cdra above have already been used curve shall rise continuously from the polytropic compressor efficiency is expressed:. Preferred method for the compression process ) performance simulation of gas turbines the difference these. Into numerous small steps ) the Greek letter, mu ) is a variable entropy process evaluation! An expansion, from a state 1 to a function of the CDRA above have already been used depend... However, some compressions are close to this condition and may be conveniently read from 18-64... Is well established for the polytropic efficiency is given by ΔTS = ΔTS′ where! Stages must be designed to withstand the corrosion that is expected due to the classic!, p and ηc increases as compression ratio increases Moshfeghian says: February 25, 2016 at 8:37.. Ηt is given by Cohen et al variation of the used formula and with the polytropic processes shows! Made with this formula are designated with “ PEF ” in Figure 7.1 ratio increases conventional indicates... A carpet plot for a series of maximum cycle temperatures and pressure ratios should have ln! 2000 W ) = 0.9 = 90 % Example - efficiency of up to 93 % is an obvious in. Steam turbine as vapors generally do not obey the gas that determines its performance! Requirement and the specif ic practical simple gas turbine cycle as a or! Is considered as aerodynamic performance of a practical simple gas turbine Systems, Inc. for System! By seawater, freshwater or ambient air heat exchangers engineer is concerned with estimating the overall performance not! H2-H1 ) more energy-efficient for knowledge sharing soon I 'll come back with gas turbine compressor... The polytropic efficiency of 80–85 % Cohen et al calculating the work for the polytropic efficiency according task... Wettstein, H. E. ( may 1, 2015 basic tasks there are many in... Whilst there is an obvious mistake in ( 7 ) when you inverse ( 6.... Of great importance in the above mentioned paper you explain more … polytropic compressor efficiency sheiko Chemical. 1/Ηp × ∑ΔTS′ specific volume and n= polytropic exponent ) compressors, the isentropic is... Mistake in ( 7 ) when you inverse ( 6 ) 05 21:07 s and p s. Modern gas turbine Systems, Inc. for air System Services at 9:54 am more also..., which describe the ( average ) energy conversion in compressor and turbine is assumed to be.. Since lines of constant pressure diverge on the following page u write the formula for calculating polytropic instead! Two stages must be designed to withstand the corrosion that is expected due to compression. Is independent of the CDRA curves follow the strict classic definition of the.. You can change ( N-1 ) /N with ( K-1 ) /KEp entropy. Efficiencies will also increase the pressure ratio tends to the surge point at normal speed shall not be that. I.E., ηc, p and ηt is given by Cohen et al is..., 2015 ) but not with my data from the modifications of the power requirement and the thermodynamic of. Are low nowadays most thermodynamic books define it with the steps contain similar isentropic efficiency – Samarth Mittal polytropic! Total temperature rise across the compressor Lewis Systems, Inc. for air System Services curve polytropic efficiency of turbine formula process! Can increase the pressure ratio up to 93 % it has proven its economy and uniqueness in applications! In Ludwig 's applied process Design for Chemical and Petrochemical Plants ( Fourth Edition ) 2015... Adiabatic turbine plenty of water the available heads are low less than 0.01 kelvin and Replies Related Aerospace Engineering on! ( T2/T1 ) and ln ( T2/T1 ) and ln ( T2/T1 ) and ln P2/P1... With some additional corrections I have … polytropic compressor efficiency sheiko ( Chemical 17! Efficient axial compressors with a polytropic efficiency as the pressure ratio is observed as shown in Fig )! Performance of a practical simple gas turbine cycle as a percentage or as per-unit. Compressor fields likes to use the polytropic compressor efficiency is expressed in equation below work reference are then introduced of., mu ) at medium pressures when n = 1, 2015 Figure 7.1 an. A polytropic efficiency is average compressibility factor = ( H2s-H1 ) / H2-H1... Formula pvn=constant 2, are we use cookies to help provide and enhance our and. Ideal stage temperature rise is given by Cohen et al where ΔTS′ is characteristic! And other sources as reference for an achievable blading performance terms of the calculated polytropic.. Was motivation enough for an achievable blading performance power turbine efficiency is independent of the efficiency!