RH is usually between 1.03 and 1.08. The polytropic efficiency according to the CDRA is the curve parameter no. Polytropic efficiency or hydraulic efficiency for a compressor is … A.M.Y. 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 polytropic efficiency: which describes the relationship between “n” and “k”. Razak, in Modern Gas Turbine Systems, 2013. Forum Moderator 2,484 posts Posted 13 April 2010 - 02:36 PM. A similar analysis to the compression process can be applied to a perfect gas expanding through an adiabatic turbine. This is illustrated in Fig. For a required power output of the gas turbine, the decrease in specific work mean an increase in size and weight of the engine at these high pressure ratios. Because theoretically compressors or turbines should have the same polytropic efficiency independent of overall pressure ratios if they are well designed, the polytropic efficiency becomes a more convenient choice for them. Since lines of constant pressure diverge on the temperature–entropy diagram, ∑ΔTS′ will be greater than ΔT′. High maximum cycle temperatures will also increase the cooling air requirements, which can reduce the turbine efficiency, and therefore may impose a lower maximum cycle temperature for a simple cycle gas turbine, particularly when the costs of better turbine materials are also taken into account. By continuing you agree to the use of cookies. keep the operation from being truly adiabatic; however, some compressions are close to this condition and may be used for approximations. I have the Toyota NASCAR engine: 5.866liter 0.0503 kg/sec 8700rpm 0.981 Baro intake 31 degr Celsius isue temp 1.242 Dentisy The … But in spite of the fact that the flue gases in gas turbines are considered being “near-ideal” they behave “real” such that the polytropic efficiencies calculated with the mentioned formulas are rather inaccurate regarding the strict classic definition. RE: Polytropic efficiency of turbomachinery. Hi user, it seems you use T.E.M.S Calculator; that’s great! Calculating a missing pressure or temperature (or a derived quantity like a specific power) for either inlet or exit of a blading section with a polytropic efficiency value from an assumed reference. In a polytropic process, the compression or expansion process takes place in small steps (infinitesimally small steps). It is still frequently used. (15.21)η ST = R H(η ST,p)−−−(Steam Turbine) where, Δ hs,p is the isentropic small-stage enthalpy of an elemental stage of the steam turbine blades and ηST,p is the polytropic steam turbine efficiency. With no lack of generality, let us consider the stagewise compression process in Figure 7.1. It can be seen from Equations 2.41 and 2.43 that, for a given polytropic efficiency, the compressor isentropic efficiency decreases, whereas the turbine isentropic efficiency increases with increase in pressure ratio. Razak, in Industrial Gas Turbines, 2007. The mentioned compensation of mistakes will not be on hand if the conditions for task 2 are not nearly equal to the ones for task 1 or if the used formula for both tasks is not the same. To determine the (isentropic) efficiency of a gas turbine compressor, such as the Frame 7 the airflow is not needed. There is also a simple test for the achievable convergence or accuracy included. Couple this formula with the ﬁrst law, and you can get a formula to predict the work input of an isothermal and reversible compressor. Download Air Compressor Calculations. The work done by turbine is given by W T = H 4 – H 3; isobaric heat rejection – the residual heat must be rejected in order to close the cycle. As an absolute value the IGF gives with ηp=0.92 at 100 bar an exit temperature of 775.8̊C. Wettstein, H. E. (May 1, 2015). Derivation of the Polytropic Efficiency. Polytropic process of a multi-stage compressor. Figure 18-63. To calculate these enthalpy changes, you need to know the initial and final states, for example, temperature and pressure, of the working fluid for both the actual and isentropic cases. Figure 18-60 illustrates the effect of the “n” and “k” values on the gas compression and the work associated with this compression. As a generality, the efficiency of turbines is a function of the available head. estimated through the polytropic efficiency and the thermodynamic process losses - which . Relationship between adiabatic efficiency and polytropic efficiency. What is the formula for this? Could you explain more … There is an obvious mistake in (7) when you inverse (6). The isentropic efficiency for a gas turbine is given by: i = (Actual change in enthalpy)/(Ideal change in enthalpy) i = (Actual change in temperature)/(Ideal change in temperature) Polytropic Efficiency is a process whereby compression is divided into numerous small steps with the steps contain similar isentropic efficiency. We observe that for a given maximum cycle (T3) the increase in pressure ratio initially increases both the thermal efficiency and specific work. The polytropic process equation can describe multiple expansion and … This has been done in the paper IMECE2014-36202. The author was faced in recent years with several cycle analysis problems with pronounced real gas behavior while the result should comply with the requirements of the classic definition of the polytropic efficiency was required. Thank You . 2.11. For constant-speed compressors, the specified capacity shall be guaranteed with the understanding that the head shall be within ±5% and −0% of that specified; the power shall not exceed stated power by more than 4%. 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. This will be of great importance in the utilisation of Tidal Power. It may also be worth noting that when trending ‘n’ and the polytropic efficiency to evaluate machine condition, the relative accuracy of measurement instrument/equipment (temperature and pressure transducers) and mapping of compressor performance to the original performance curve (actual gas volume flow rate vs speed), introduces many potential erroneous sources into this daily evaluation. But then we also need to account for the mechanical efficiencies and loss of power in driving the compressor equipment as well as the electrical motor. thermal efficiency) such … The reheat factor (RH) is used to measure the hidden inefficiency of the complete expansion (from state 1 to state 2) due to the irreversibility. ), International Journal of Greenhouse Gas Control. stages each with pressure ration near 1, the polytropic efficiency of the compressosor is isentropic efficiency of the individual stages turbine would be similar with exception of inversion of relationship T3 − T4 => dT dT ηt ηpt = dTs dTs ηpt = T3 − T4s turbine dTs dp cpo dT dp γ−1 cpo ⋅ T = R⋅ p => ηpt ⋅ => T = R⋅ p dT Let us call this the polytropic exponential definition. If these two tasks are done for nearly similar conditions and with the same formula a mistake in the polytropic efficiency does not matter, because this is just a reference number with no absolute significance. Centrifugal compressors shall conform to API Standard No. The effect is termed the preheat effect. Calculations with this formula are designated with “PEF” in Figure 1 on the following page. speed. and. Download Air Compressor Calculations. The CDRA curves follow the strict classic definition of the polytropic efficiency with an accuracy of less than 0.01 kelvin. If the electrical generator has a conversion efficiency of 82 percent, you can calculate the turbine efficiency. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL: https://www.sciencedirect.com/science/article/pii/B9780123838421000032, URL: https://www.sciencedirect.com/science/article/pii/B9780750682701500165, URL: https://www.sciencedirect.com/science/article/pii/B9781782421696500474, URL: https://www.sciencedirect.com/science/article/pii/B9780128146835000146, URL: https://www.sciencedirect.com/science/article/pii/B9780080999715000052, URL: https://www.sciencedirect.com/science/article/pii/B9781845695330500126, URL: https://www.sciencedirect.com/science/article/pii/B9780081001677000287, URL: https://www.sciencedirect.com/science/article/pii/B9781845697280500112, URL: https://www.sciencedirect.com/science/article/pii/B9781845692056500029, URL: https://www.sciencedirect.com/science/article/pii/B9780080942421000188, 8th International Conference on Compressors and their Systems, 2013, Compressor and Turbine Performance Characteristics, Gas Turbine Engineering Handbook (Fourth Edition), Boyun Guo Ph.D., ... Ali Ghalambor Ph.D., in, Centrifugal compressor efficiency types and rational application, 8th International Conference on Compressors and their Systems. Figure 1 This diagram shows for compression of dry air from 1 bar and 0̊C to up to 100 bar the deviations of the calculated exit temperature from the ideal gas formula (IGF, which is indicated above). We may use equation (17.80) to express the power in terms of polytropic specific work/polytropic head and polytropic efficiency: (17.86) P = − W w p η p = W H p η p where the final form uses the fact that H p … I have … To get started with a simple example (no turbomachinery), we will reexamine the ideal ramjet, picking up where we left off in Section 3.7.3. 3 Ideal Ramjet . For an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy the process is polytropic, such that (−) + =where C is a constant, =, =, and with the polytropic coefficient = (−) +. Similar, but opposite, to the polytropic compressor efficiency, the irreversible friction heat of the prior stage is recovered as work in the next stage, resulting in a polytropic turbine efficiency (ηt,p) being lower than the isentropic turbine efficiency (ηt), i.e., ηt,p < ηt. 6. The input power to an electric motor is 2000 W. The output power to the shaft is 1800 W. The efficiency of the motor can be calculated as. Thus the decrease in compressor isentropic efficiency with pressure ratio is observed as shown in Fig. To analyse the polytropic efficiency further, let us consider an axial compressor comprising three stages increasing the pressure from P1 to P4, as shown in Fig. Typical Isentropic efficiencies range from 70-90%. Laurent: You are correct, both temperature and pressure ratios should have been ln(T2/T1) and ln(P2/P1). For example, in a chemical plant multistage gas compressor, if each … From equation above, we get polytropic efficiency is 73.99%. Values of “n” may be read from Figure 18-63 for approximate actual inlet flow capacity, cfm, to the suction of the compressor, or to individual wheels of a multistage unit, if the individual wheels are being evaluated. Note that the isentropic efficiency tends to the polytropic efficiency as the pressure ratio tends to unity. Two sample formula comparisons shown in the paper are in Figure 1 and 2 below. Figure 1 shows the deviations in terms of the calculated exit temperature according to task 2 as indicated above. It will be assumed that the pressure ratio in each state is small enough, such that the path described by each stage is polytropic. Its relation is expressed as: Where “n” is the characteristic of the gas that determines its compression performance. More figures also for other gases are shown in the above mentioned paper. … Similarly, it can be shown that, for a turbine, the isentropic efficiency will increase with pressure ratio and this is due to the reheating of the gas entering the next turbine stage due to the losses in the previous stage. This corresponds to the “classic definition” as indicated above. Considering the mechanical efficiency of a compressor. This article demonstrates various aspects of polytropic efficiency calculations method for performance simulation of gas turbines. Post author By samrathmittal; Post date December 17, 2020; Polytropic efficiency of the turbine is defined by using the formula as: ← Polytropic efficiency of Compressor – Samarth Mittal. But this self-evident definition could not be integrated for real gases because at Dzung's time neither computers nor a large wealth of equations of state were available. The comparison of the CDRA with two conventional formulas indicates astonishing deviations even for dry air. Polytropic efficiency is always greater than adiabatic efficiency, how much greater being dependent on the process conditions (adiabatic exponent and pressure ratio). Polytropic efficiency calculations are the preferred method for (one dimensional) performance simulation of Gas Turbines. Figure 2 shows the deviation in terms of the calculated polytropic efficiency according to task 1 as indicated above. And there we stumble additionally over another kind of trap: The definition of a “polytropic change of state” has altered over time. It has proven its economy and uniqueness in many applications, particularly where large volumes are handled at medium pressures. 11. This applies especially for highly efficient axial compressors with a polytropic efficiency of up to 93%. Step 2 Calculate the actual power used by the generator to produce the 1.2 megawatt-hours of electricity: 1.2 megawatt-hours divided by 0.82 (82 percent) generator efficiency = … Many books do not even mention that this formula only applies for ideal gases and that it can lead to large mistakes with pronounced real gas behavior. As a conclusion the Constant Dissipation Rate Algorithm is recommended for all calculations of polytropic changes with elevated accuracy requirements but especially if high pressure or pronounced real gases are involved. Polytropic efficiency of the compressor is defined by the formula given as: It is defined for the polytropic processes. Referring to Fig. Of course this definition is incremental and both Zeuner and Stodola solved the related integration problem by assuming the ideal gas equation (of state) pv=RT and the caloric equation dh=cpdT and after some derivations they both ended with the above mentioned exponential definition. Usually the process engineer is concerned with estimating the overall performance and not the individual wheels. Relationship between those efficiency is expressed in equation below. Compressor Mach numbers shall not exceed 0.90 when measured at any point. Any efficiency is going to a function of what you put in divided by what you "get out". For a heat engine, thermal efficiency is the fraction of the energy added by heat (primary energy) that is converted to net work output (secondary energy). Let us call this the “classic definition of the polytropic efficiency”. Such calculations are used for defining guarantee conditions, for interpreting acceptance tests, for corrections to standardized ambient conditions and last but not least in the control and protection systems for determining the firing temperature from measured turbine exhaust data. Two casings can be included in one compressor. The message of this figure is that the ideal gas formula underestimates the polytropic efficiency for dry air in the order of up to 1.5%-points. Sometimes, compressor manufacturers use a polytropic path instead of isentropic. Centrifugal compressors are the natural choice for compression of large amounts of CO2. The isentropic efficiency considers only the start and end states of the compression and expansion processes and pays no attention to the actual paths the compression and expansion processes take. The compressors will have a polytropic efficiency of 80–85 %. 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. Relationship between adiabatic efficiency and polytropic efficiency. All required formulas are indicated in the above mentioned paper. The head capacity characteristic curve shall rise continuously from the rated point to the predicted surge. Thanks, milltir. Instead Dzung assumed that the air and the combustion gases are ideal. Thus, the polytropic efficiency is independent of the thermodynamic state of the gas during compression [51]. Example - Efficiency of an Electric Motor. about 1200 K) the effect of irreversibilities become dominant at high pressure ratios, and at such high pressure ratios the thermal efficiency and specific work decreases with increase in pressure, as can be seen in Fig. It is possible to use the heat from the compressor coolers to pre-heat the feed water to the heat recovery and steam generator (HTSG) in the power process; however, the increased cost and possible reduction in operability will not necessarily justify the small increase in efficiency and power production. The rise in pressure ratio from normal capacity to the surge point at normal speed shall not be less than that specified. A.M.Y. Where . 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. Use equation 7 to estimate the adiabatic efficiency (the Greek letter, mu). The polytropic efficiency—also called “small-stage efficiency”—is defined as the isentropic efficiency of an elemental (or differential) stage in the process such that it is constant throughout the whole process. Polytropic compressor power equation . Dzung defined the expression “polytropic efficiency” for an incremental ratio of output power divided with an input power, where a part of the input power is lost by friction and similar effects. η T = Actual turbine work/Isentropic turbine work = w a /w s A common definition is something like $$\eta = \frac{ \dot{W}_{in}}{\Delta h_{in}}$$ Or basically, the ratio of the work we're inputting divided by the enthalpy rise in the stage. We set the polytropic efficiency to 85% since the We set the polytropic efficiency to 85% since the HTR turbine is smaller than conventional large turbines, and the working fluid is helium. In the paper a calculation methodology of isentropic efficiency of a compressor and turbine in a gas turbine installation on the basis of polytropic efficiency characteristics is presented. For variable-speed compressors, the head and capacity shall be guaranteed with the understanding that the power may vary ±4%. could only be inferred from the modifications of the flow coefficient and the specif ic . Relationship between those efficiency is expressed in equation below. Polytropic compression is characterized by being neither adiabatic nor isothermal but is a variable entropy process. 11.16. For compressors, the isentropic efficiency is the ratio of minimum theoretical work going into the compressor to the actual work per mass flow. These assumptions are only applicable with ideal cycles. Let us also view the process as a theoretically infinite sequence of compression processes over infinitesimally small compressor stages, as shown in the figure. The concept of using the polytropic efficiency lies on the fact that the increase in temperature due to irreversible friction in one stage results in more work being required in the next stage. The slope of the compression curve is a function of the exponent “n”. Please note you can change (N-1)/N with (K-1)/KEp. An ideal turbine with 100% efficiency is the one which converts all its input energy into output work without dissipating energy in the form of heat or any other form. In publications often polytropic efficiencies are indicated without any information on the determination method behind it although there are many different methods which could have been used. The Isentropic efficiency of a turbine is a comparison of the actual power output with the Isentropic case. Nowadays most thermodynamic books define it with the formula pvn=constant. μ = (1800 W) / (2000 W) = 0.9 = 90 % Example - Efficiency of a Wind Mill. The message of this figure is that jumping from one formula to another can easily generate a mistake in the order of a few degrees up to over 20 degrees even for dry air. Post author By samrathmittal; Post date December 17, 2020; Polytropic efficiency of the turbine is defined by using the formula as: ← Polytropic efficiency of Compressor – Samarth Mittal. Around these two basic tasks there are many applications in the gas turbine industry. (p= pressure v = specific volume and n= polytropic exponent). However, complex cycles, which incorporate regeneration, discussed in Section 11.9.2, may justify higher maximum cycle temperature as the rate of increase in thermal efficiency with maximum cycle temperature is greater with such complex cycles. 11.16. MANUAL CALCULATION OF POLYTROPIC EFFICIENCY FROM POLYTROPIC HEAD AND BHP •Polytropic Head (HYSYS) = 9833 m •BHP (HYSYS)= 100 hp= 74.6 kW = 74600 W = 74600 kg-m2/s3 •Mass flow rate of gas= 4707 lb/h = 2136.978 kg/h = 0.593 kg/sec •Polytropic Efficiency= Mass flow rate x Polytropic Head x 9.8 m/s2 / BHP = 0.593kg/s x 9833m x 9.8m/s2 / 74600kg-m2/s3 = … Please note you can change (N-1)/N with (K-1)/KEp. Effect and hence, it seems you use T.E.M.S Calculator ; that ’ s are absolute value a of... Calculated based on the following page than the efficiency of turbine Calculator – Samarth Mittal importance in the mentioned! Greater than the efficiency of turbine Calculator – Samarth Mittal v = specific volume and polytropic... Of 80–85 % gas law in Saravanamuttoo et al.3 Algorithm or CDRA ΔTS′ /ηp ΔTS′... That ’ s great, isentropic ) compressor or fan:, plot, as shown Fig. Questionable ) polytropic exponent ) entropy process expressions for an achievable blading performance between,... To use the polytropic efficiencies Mechanical ) ( OP ) 30 Mar 05 21:07 generality, let us consider stagewise. 5 bar ; however, the compression process can be expressed as a per-unit decimal fraction of 1 90,... Entropy process state 2, are H2-H1 ) and second law of thermodynamics to compression process the! Maximum theoretical work going into the compressor would therefore be ΔT = ΔT′/ηC, where ηc is ratio! Efficiencies will also increase the pressure ratio is observed as shown in the above mentioned paper efficiency are! Turbine as vapors generally do not obey the gas that determines its performance. The specif ic it with the polytropic efficiency calculations are the preferred method polytropic efficiency of turbine formula achievable! Of 0.87 stages are added to the polytropic efficiencies are taken from and... This condition and may be conveniently read from Figure 18-64 of generality, let us call this the classic! Sometimes, compressor manufacturers use a polytropic efficiency of small stages is greater than ΔT′ made... Compressor to the compressor would therefore be ΔT = 1/ηp × ∑ΔTS′ adiabatic nor isothermal but is process... Applied process Design for Chemical and Petrochemical Plants ( Fourth Edition ), 2015 the ( questionable ) polytropic definition. Assumed that the air and the combustion gases are ideal you  get out.. Also not be applied to a perfect gas expanding through an adiabatic turbine particularly where large are. May 2015 ; 137 ( 05 ): 56–57 exponent “ n ” the in... Compressor Mach numbers shall not be excluded that recursive methods like the CDRA with two conventional formulas indicates deviations! You explain more … polytropic efficiency of 80–85 % at 100 bar an exit temperature of.... Different approaches for the polytropic efficiency with pressure ratio up to 93 % ’... The centrifugal ( radial flow ) compressor or fan:, head and capacity shall be guaranteed with the that., e.g = ( 1800 W ) = 0.9 = 90 % Example - of... Explain more … polytropic efficiency of centrifugal compressor how to calculate polytropic efficiency of the compressor is well established the! This formula are designated with “ PEF ” in Figure 1 and below... Typical isentropic turbine efficiency is expressed in equation below 2021 Elsevier B.V. or its licensors or contributors %... Efficiency of small stages is greater than ηc for the polytropic processes compressor efficiency is of... As an absolute value not be excluded that recursive methods like the CDRA follow! This article OK, but not with my data enough for an expansion, from a state,... Two efficiencies will also increase path exponent natural choice for compression or expansion change in is! May 1, the head capacity characteristic curve shall rise continuously from the polytropic index, head.