Report

ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Prediction of Performance of Simple Gas Turbine • From cycle calculations it is possible to determine the PRESSURE RATIO ( Rc ) which will give the best overall efficiency for a given Tmax. • MASS FLOW RATE (m)to give the most suitable desired power output. • After such preliminary calculations, the most suitable design data for a particular application can be chosen. • Then, it is possible to design individual components to give the required operation at the design point. • That is running at the design speed N*, mass flow rate m* and pressure ratio R*. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Prediction of Terformance of Simple Gas Turbine • Then the off-design performance has to be determined which is the divergence from the design point over the complete operating range of speed and power output. • The performance ¢ of the individual components may be estimated on the basis of the previous experience or actual experiments. When they are combined in an engine their operating range is considerably reduced. • The problem is to find the Operating point (OP) on each component ¢ when the engine is running at a steady speed (EQUILIBRIUM). • The plot of these OP's form the EQUILIBRIUM RUNNING LINE (ERL). Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Prediction of Performance of Simple Gas Turbine • For the whole range of operating speeds, it will generate the EQUILIBRIUM RUNNING DIAGRAM. • Determining the OP; the power output, thrust and the SFC can be obtained. • The Equilibrium Running Diagram indicates the margin of operation from the surge line (SL) . • This margin indicates a Margin of stability; indicates if there is enough margin to operate with adequate compressor efficiency. • If the surge line is crossed some action has to be taken to recover, not to give rise to a failure. • Ideally the engine should be operated within the region of maximum possible efficiencies. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Prediction of Performance of Simple Gas Turbine • Variation of SFC with reduction in power PART LOAD PERFORMANCE. This is important while running the GT at low power settings. • Poor sfc at part load is the biggest disadvantage of a GT, especially a vehicular one. • The effect of ambient conditions on maximum output is also important, i.e. high & low Ta and Pa. • Peak load energy generation: Europe: cold days in winter, America: hot days in Summer for airplanes: Runway length (safety) and pay load (economics) are affected. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-Design Performance of Simple GT • Here we will try to analyse a : a) Single shaft unit delivering shaft power. b) Free turbine engine - power turbine drives the load. c) Simple jet engine, where the useful output is from the propelling nozzle. • More complex arrangements - two spool engines, Turbofan & transient performance Chapter 9 • Flow characteristics of a free turbine and propelling nozzle are similar and impose the same restrictions on the Gas Generator. • As a result of this several jet engines have been converted to Free Turbine Power engine for peak load electric generation, and marine applications. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Component Characteristics ¢ • Axial compressor ¢ constant speed lines become vertical so ηc , Rc vs m is plotted. FIG.1 Compressor Characteristics Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Component Characteristics ¢ • Turbine ¢ do not show a significant variation in ND speed. Their operating range is usually severely restricted by another component downstream. FIG.2 Turbine Characteristics Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-Design Operation of The Single - Shaft GT • Since inlet and exhaust pressure losses are ignored; pressure ratio across the turbine is determined by the compressor pressure ratio and the pressure loss in the combustion chamber; ΔP034 = P012 - P032 • The mass flow through the turbine = mass flow through the compressor - Bleeds + fuel flow; m3 m1 -mbleed +mf Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point a) Select a constant speed line on the C¢ and choose an OP on this line thus . m T01 P01 ; ; c P01 P02 N/ T01 are selected. b) The corresponding point on the T¢ is obtained by the Compatibility of Speed and Flow. • COMPATIBILITY OF ROTATIONAL SPEED N = T03 Me 423 Spring 2006 N T01 T01 T03 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • COMPATIBILITY OF FLOW . . m 3 T03 = P03 . m1 T01 P01 * P01 P * 02 * P02 P03 T03 m * .3 T01 m1 • Here combustion chamber pressure loss P03/P02 = 1 - Pb/P02 . • . . m1 m 3 m assume . . m T03 P03 Me 423 Spring 2006 = m T01 P01 x P01 P T x 02 03 P02 P03 T01 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point . m T01 P01 and P02 P01 are fixed by the chosen OP on the C¢ P03 P02 is assumed to be constant. Neglecting inlet and exhaust pressure losses Pa = P01 = P04 . m T03 is a function of P03 Me 423 Spring 2006 P03 P04 P03 P03 P02 = . P04 P02 P01 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point Now in the flow compatibility the only unknown is T03 / T01 The rest can be obtained from C¢ and T¢. Thus, . m T03 P03 P P T 03 =( . ) . 02 . 03 T 01 P01 P02 m T01 P01 Thus, knowing T01, T03 can be calculated. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • Having determined T03 , the SPEED COMPATIBILITY : N = T03 by N T03 N x T01 T01 T03 and and P03 P04 with T ¢ t • The compressor & turbine temperature changes can be determined. T012 T034 Me 423 Spring 2006 T01 P02 ( 1)/ (( ) 1) c P01 1 t T03 (1 ( ) 1/ ) P03 / P04 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point And the NET POWER corresponding to selected OP is : . m CpG T034 1 m . m Cpa T012 m could be calculated knowing P01 , T01 c) Having matched the C¢ & T¢ it is necessary to ascertain whether the work output corresponding to the OP is compatible with that required by the driven load. For this; variation of power with speed "P(N)" should be known. This will indicate whether the OP selected represents a valid solution (Equilibrium). Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point Examples: • If the engine were run on a test bed, Coupled to an electric/or hydraulic dynamometer, the load could be set independent of speed. Then, it is possible to operate at any point on C¢ within safety limits (T03 , N). • With a Propeller load - Power absorbed varies with as N3 of propeller. Knowing ṁ and gear ratio, the load characteristics in terms of Pout turbine vs Nturbine can be plotted which corresponds to a single Poutput per constant speed curve N / T01 i.e single point on a fixed C¢. • Only at this point the required output is given. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point FIG.3 Load Characteristics Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • Then the single point on each constant speed line of the C¢ has to be found. • This is done by trial error, taking several OP on the C¢ and establishing the power output for each OP. • If the power output by turbine is not equal to power required by propeller then the engine will not be in equilibrium but accelerate or decelerate. • Finding the equilibrium points on a series of constant speed lines, and joining them the equilibrium running line is obtained. • The most common type of load used with a single shaft GT is the ELECTRIC GENERATOR which runs at constant N with the electrical load varying . Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • Then the single point on each constant speed line of the C¢ has to be found. • This is done by trial error, taking several OP on the C¢ and establishing the power output for each OP. • If the power output by turbine is not equal to power required by propeller then the engine will not be in equilibrium but accelerate or decelerate. • Finding the equilibrium points on a series of constant speed lines, and joining them the equilibrium running line is obtained. • The most common type of load used with a single shaft GT is the ELECTRIC GENERATOR which runs at constant N with the electrical load varying . Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point FIG.4 Equiblirium Running Lines Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • The equilibrium running line for a generator set would correspond to a particular line of constant N / T01 • Each point on the line would represent a different value of T03 and Pout. • At each speed it is possible to find by trial error the compressor OP corresponding to zero net output and connecting the No-Load Running Line for a Generator Set is obtained. • Looking at the C¢ and propeller equilibrium line, the operation is generally at a high ηc. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Procedure of Obtaining an Equilibrium Running Point • Generator load results in a rapid drop in ηc as the load is reduced. • The location of equilibrium running line w.r.t. surge line indicates whether it could be brought to full power without any complications. • If ERL and SL intersects a blow-off valve around the compressor rear is employed. No such problem for bringing up an electric generator (No load condition). • With the above findings T032 and hence from Combustion curves, f could be determined for an assumed b then, sfc can be calculated. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on single shaft gas turbine • The following data refer to a SSGT operating at design speed: Ambient conditions:Pa=1.013 bar, Ta=288 K, m=98% (Neglect all pressure losses!) Calculate: T03 for Power=3800 kW 1) Establish the T03 for each point given on the CC 2) Establish (T02 - T01), (T03 - T04) and find Pout 3) Plot T03 vs Pout to find the T03 for Pout =3800 kW • Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on single shaft gas turbine . T03 m T03 T01 P03 1) m T01 P02 P03 T 139 5 03 2.11 P01 P01 P02 T01 329 . / 1 T034 0.87 1285 1 1/ 4 370K 5 288 (5)1/ 3.5 1 200.5K 0.84 T012 T03 1285K . . m m T01 P01 . Pa 19.6kg / s Ta m Cp G T034 Me 423 Spring 2006 1 m . (m Cp a T012 ) 4305kW Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator • The GG performs the same function for both the jet engine and free turbine engine. • It generates continuous flow of gas at high pressure and temperature, to be expanded to lower pressure to produce either shaft work or a high velocity propulsive jet. • The compatibility of speed and flow are the same as the single shaft engine. Thus; T N N T03 = T01 . 01 T03 . m T03 P03 Me 423 Spring 2006 x = m T01 P01 * P01 P * 02 P02 P03 T03 T01 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator • However, the pressure ratio of the turbine is not known. • It must be determined by equating the turbine work to the compressor work. • The work requirement; m Cpg T034 = Cpa T012 T034 T012 T01 Cpa 1 or = * * . T03 T01 T03 Cpg m • These equations are linked by (T03/T01) and a trial-anderror procedure is necessary to determine T03 for any arbitrary point on C¢ Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator . a) Select a comp. OP b) Calculate N / T01 P02 m T01 , , , c P01 P01 1 T01 P02 1 (( ) ) T012 from T012 = T01 c P01 . c) Guess a value of P03/P01 & calculate m T03 P03 from T¢ d) Find T03 / T01 from FLOW compatibility e) Using T03 / T01 COMPATIBILITY Me 423 Spring 2006 calculate N / T03 from SPEED Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator f) With N / T03 g)Calculate and P03 / P04 find c from T¢ T034 ( ) from T03 T034 1 = t (1- ( ) 1/ ) T03 P03 / P04 h) Calculate (T03/T01 ) using (T034/T03) and POWER COMPATIBILITY i) Check T03/T01 with the "one" from flow compatibility (Step d) j) If different modify P03/P04 and repeat the steps c to i until obtaining the correct T03/T01 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator k) The agreement of T03/T01 indicates that the turbine OP is compatible with the compressor OP for the temperature increase in CC satisfying T03/T01. It is not necessary to calculate this for a series of points because the downstream components impose limits on the operating zone of the C¢. This could be repeated for a series of points and points of constant T03/T01 could be joined up, but unnecessary since the flow compatibility with the downstream components (power turbine/or/ propelling nozzle restricts the operating zone on the C¢. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Equilibrium Running of a Gas Generator • The matching procedure outlined here has been developed on the assumption that turbine ¢ do not exhibit a variation of m T03 / P03 with N / T03 This is true if the flow correspond to choked mass flows. • If not choked; before guessing P03 / P04 *Guess T03/T01 calculate N / T03 from speed compatibility *calculate m T03 / P03 from flow compatibility *Then P03 / P04 and ηt can be obtained from T¢ *T034/T03 can be calculated compatibility T03/T01 and the GG work *Compare T03/T01 with the initial guess. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine The matching is done by select a point on C¢. i) Flow compatibility i.e mass flow of GG = mass flow FT . . m T04 m T03 P03 = x * P04 P03 P04 T04 = T03 1 - T034 and T03 T04 T03 T034 1 = t (1- ( ) 1/ ) T03 P03 / P04 where ii) The pressure ratio available is fixed by the compressor and GGT press ratios. P04 P02 P03 P04 = x x Pa P01 P02 P03 Inlet and exit duct losses ignored. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine iii) Having found the pressure ratio across the power Turbine, the value of m T04 / P04 can be found from the FT¢. iv) If m T04 / P04 from (i) and (iii) do not match; a new point on the constant speed C¢ has to be selected and this procedure has to be repeated until the flow compatibility between 2 turbines is satisfied. • For each N / T01 line on the C¢ there will be only one point which will satisfy both the requirement of the GG and the flow compatibility of the FT. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine • Equilibrium running line can be produced for different N / T01 on C¢. The running line for the FT engine is independent of the load and determined by the swallowing capacity (ṁ) of the PT. • FT engine has quite a different load performance than the single shaft GT. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine FIG.5 Equilirium Running Line for Free Turbine Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of 2 TURBINES IN SERIES • The iterative procedure of a FT/GG matching can be simplified if the 2-Turbines in series are considered. • The variation of t at any pressure ratio is not large, particularly in the restricted range of operation. As a result the change in t does not affect T03 / T04 so has a little effect on m T04 / P04 • Therefore, a mean value of ηt is taken at any given pressure ratio. Then,. . m T04 / P04 f (m T03 / P03 , P03 / P04 , t ) Now the GG turbine exit conditions can be mapped on the GGT¢. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine FIG.6 Operation of Turbines in Series Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine • The flow compatibility between the 2 turbines places a major restriction on the OP of GGT. • As long as the PT is choked, the GGT will operate at a fixed ND point at all choked OP. • With the PT unchoked the GG will operate at a fixed pressure ratio for each PT pressure ratio (i.e. fixed OP) • Thus the maximum pressure ratio across the GGT is controlled by choking PT. (i.e the SWALLOWING capacity the GT). • The turbine pressure ratios can be expressed in terms of the Rc as: P03 P03 P02 Pa = . x P04 P02 P01 P04 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off-design Operation of Free Turbine Engine FIG. 7 Compressor Pressure Ratio vs GGT Pressure Ratio • For any value of the compressor pressure ratio, GGT pressure ratio can be obtained. Thus m T03 / P03 and T034 /T03 are fixed for GG flow compatibility & GG power compatibility. Thus for the GG, pressure ratio iteration is not necessary to find the correct equilibrium point. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Power Output & Sfc with Output Speed of a Free Turbine Engine • Power output of a FT engine = ṁ Cpg T045 where T045 = tp T04 (1 ( 1 ) P04 / Pa 1 ) FIG.8 Variation of Power Output with Output Speed Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation Of Power Output & sfc with Output Speed of a Free Turbine Engine • power output for each equilibrium running point (one for each compressor speed); i) P04 /Pa will be known ii) T04 can be calculated from T04 = T03 - T034 knowing Pa, Ta ; m can be found from m T01 / P01 P04 N PT tp from PT ¢ but tp = f ( , ) Pa T04 • Free turbines are used to drive a variety of loads each of which are different (pump, propeller, electric generator), each with different vs Npt ¢ .These curves are quite flat in the higher Npt region where pt is fairly constant. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation Of Power Output & sfc with Output Speed of a Free Turbine Engine FIG.9 Variation of sfc With Power Output • sfc increases as power is reduced, since as fuel flow decreases; Nc decreases, T03 decreases; but as T03 decreases cycle decreases. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Power Output & sfc with Output Speed of a Free Turbine Engine • Fuel consumption can be calculated similar to the single shaft units since the fuel consumption depends only on GG parameters. There will be one value for each N1 / as Pout T01 . sfc however, is a function of both Nc and Npt • The off-design performance can be expressed by plotting sfc vs Pout for different Npt. This shows the performance of the unit when coupled to different types of loads. • Although for convenience Ncomp is chosen as the independent variable; in practice the fuel flow is the independent variable. A chosen value of fuel flow and (T03) determines Ncomp and therefore Pout. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Torque Characteristics • In case of a GT delivering shaft power, the variation of torque with output speed at a given power determines its suitability for different applications (e.g. high starting torque for traction). a) For the single shaft engine the compressor is constrained to turn at some multiple of load speed. Load speed decrease = Compressor speed decrease unsuitable for traction (since m decrease out decrease) b) Normal curve of Internal Combustion Engine is flat. c) Free power turbine has a favourable torque ¢ over a wide load-speed range for a fixed Nc. This is because the compressor can supply an essentially constant flow at a given compressor speed irrespective of the FT speed. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Torque Characteristics • Therefore, at constant Pout as Npt decrease t increase. • The torque might stall at high t or very low Npt. With a reduction in Npt quite a large increase in obtained efficiently. t can be • But at least a speed gear box have to be used for traction (usually 5-6 speed automatic transmission is used in heavy load vehicles) Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Torque Characteristics FIG.10 Torque Characteristics Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine Given: m 30kg / s Rc 6 T03 1200 K t 0.87 m 0.99 Pa 1.01bar Calculate: c 0.84 P032 0.2bar Ta 288K . . m T03 m T04 , • Power developed and the turbine ND flows P03 P04 • If the engine is running at same mechanical speed at ambient temp. of 268 K, calculate T03, P03 / P04 and Pout assuming the following: a)Combustion pressure loss remains constant. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on Gas Turbine with Free Power Turbine . . b)Both turbines are choking with values of m T03 and m T04 as P04 P03 calculated above. No change in t c)At 268 K and the same N, the N / T01 line on the C¢ is a vertical line with ND flow 5% greater than the design value. d)Variation of compressor efficiency with pressure ratio at the relevant value of N / T is: 01 P02 / P01 c Me 423 Spring 2006 6.0 6.2 6.4 6.6 0.873 0.843 0.845 0.840 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine Solution: • Design Point Calculation: . OP on CC: m T01 P01 T 03 1200 T 01 288 . 30 288 504.1 1.01 P02 6.0 P01 P03 P02 P03 0.2 1 1 0.967 P02 P02 6 1.01 . m T03 m T01 P01 P02 T03 1 1200 504.1 1.034 177.3 P03 P01 P02 P03 T01 6 288 T012 ( 1) 288 T01 P02 (6)1/ 3.5 1 229.2 K 1 ( ) c P01 0.84 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on Gas Turbine with Free Power Turbine GG T034 T012 P04 1 T034 1 P03 t T03 Cpa 1 1005 1 =229.2 =202.9 CpG m 1147 99 1/ 4 1 203 = 1 0.42 0.87 1200 P03 P02 0.2 6 1.01 0.2 5.86bar T 04 1200 203 997 K Power Turbine: P04 P04 P02 P03 P04 6 0.967 0.42 2.445 P05 Pa Pa P02 P03 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on Gas Turbine with Free Power Turbine P04 2.445 1.01 2.47bar T045 1 1 1/ 4 1/ t 1 ( ) 0.87 1 ( ) 0.174 T04 P04 / P05 2.445 T045 0.174 997 173.7 K . out m CpG T045 m 30 1.147 173.7 0.99 5918kW . m T03 P03 . 177.3 Me 423 Spring 2006 m T04 P04 30 997 383.5 2.47 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine OFF DESIGN At Ta= T01 =268K . m T01 P01 1.05 504.1 529.5 T01 T01 0.931 0.965 288 288 • If the PT remains choked, the GGT will be constrained to operate at a fixed ND point and thus the value of T034 203/1200 0.169 as for the design condition T03 The Work Compatibility: T012 T034 T03 Cpg T03 T03 1147 m =0.169 0.99 =0.191 T01 T03 T01 Cpa 1005 T01 T01 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine hence T03 T012 =5.23 A T01 T01 Flow Compatibility . . m T03 m T01 P01 T03 P03 P01 P03 T01 T03 P 0.335 03 B T01 P01 Now the problem is to find the OP that satisfies A and B simultaneously for T03 / T01 With the variation in efficiency; . m T03 c f P03 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine ( 1) T012 1 P02 1 ( ) T01 c P01 P02 P01 With the constant value of CC loss P03 P01 P02 /P03 Iterations Tabulated : Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine ( 1) T012 1 P02 ) 1 ( T01 c P01 With the constant value of CC loss P03 P02 P01 P01 P02 /P03 Iterations Tabulated: Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine • Solving Graphically the required pressure ratio : P02 / P01 = 6.41 with T03 / T01 = 4.34 • Therefore; To3 = 4.34*268=1163K • P developed can be calculated; • since the GGT still operates at the same ND point T034 0.169 T03 P03 2.373 P04 T034 1163 0.169 197.2K T045 1 1 1/ 4 1/ t 1 ( ) ) 0.174 0.87 1 ( T04 P04 / P05 2.445 . m T01 P01 . 529.5 m Me 423 Spring 2006 529.5 1.01 32.7kg / s 268 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Example on gas turbine with Free Power Turbine • Power output P = 32.7kg/s* 1.147J/kg.K*179,6K*0,99= 6680kW • Thus on a cold day a decrease of Tamb to To1=268K results in a decrease of max. cycle temperature from 1200K to 1163K. • T03/T01 increases from 4.17 to 4.34 due to the increased N / T01 • Power increases from 5910 to 6680 kW. This is due to increase of mass flow rate and compressor pressure ratio. • The beneficial effect of low Ta on GT is evident also the adverse effect of increase of Ta. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Off Design Operation Of The Jet Engine Propelling Nozzle Characteristics •The propelling nozzle area is determined from the design point calculations. •A fixed nozzle area has a major influence on the off-design operation. •The nozzle ¢ in terms of ND variables is given in terms of m T04 / P04 and P04/Pa . m T04 T04 V5 A5 P5 T04 = V5 A5 5 = . . . P04 P04 T04 R P04 T5 V52 1 = 2 Cp j (1- ( ) 1/ ) T04 P04 / P5 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Propelling Nozzle Characteristics T5 T T 1 = 1 - 04 5 = 1 - j (1- ( ) 1/ ) T04 T04 P04 / P5 • For a nozzle of given area and j . m T04 / P04 = f (P04 / P5 ) • These are valid up to the critical point. The CRITICAL point of the nozzle is when P04 1 - 1 /( 1) = 1 / (1( )) Pc j + 1 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Propelling Nozzle Characteristics FIG.11 Propelling Nozzle Characteristics Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Propelling Nozzle Characteristics • for P04/Pa > P04/Pc , the nozzle is choked P5 = Pc > Pa and m T04 / P04 = const (not a function of P04/Pa ). • The similarity between this and the turbine ¢ is evident. • When the nozzle is choked Tc 2 = ; V5 = a5 = T04 +1 RT5 i.e (M5 1) • Generally V = T0 M R V52 V52 2 R for choked nozzle = = -1 2 T04 T05 +1 1+ M 2 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of GG with Nozzle • The Nozzle will exert the same restriction on the operation of the GG as the FT, at STATIC conditions, • The equilibrium running line can be determined as for FT. Here the effect of forward speed (Va) on the equilibrium running line has to be considered. FORWARD SPEED RAM PRESSURE RATIO = f(Ma, ηi) RAM P02 increase P04 increase P04/P5 increase when choked m T04 / P04 maximum and independent of P04/P45 thus Va . Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of GG with Nozzle • Then the Turbine OP will be unchanged because of the compatibility of flow between turbine & nozzle. • That is; As long as the nozzle is choked, the equilibrium running line is uniquely determined by the fixed Turbine OP and independent of flight speed. • Practically ALL JET ENGINES during take off, climb and cruise operate with Choked Nozzle. • The nozzle may be unchoked when preparing to land or taxying. • Since the running line is close to surge line at low ,the effect of Va on ERL has to be N / T01 considered. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of GG with Nozzle • Nozzle pressure ratio and Ram pressure ratio can be related as: P04 P04 P03 P02 P01 = * * Pa P03 P02 P01 Pa • The ram pressure ratio is: P01 - 1 2 / 1 = (1 + i ( ) Ma ) Pa 2 • Therefore, for a given intake efficiency i ; P04/Pa = f (GG parameters and flight Mach Number). • *The same procedure as for the FPT can be followed to obtain the equilibrium running point. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of GG with Nozzle FIG. 12 Jet Engine Running Lines Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Matching of GG with Nozzle • For each compressor speed N / T01 the calculation is repeated for several Ma to cover the desired range of flight speed. • The result A fan of Equilibrium RL of constant Ma. • These merge to a single RL at higher N / the nozzle is choked. T01 , where • Increasing Ma pushes the equilibrium RL away from SL at low compressor speeds. • Therefore, the Ram pressure rise allows the Rc decrease for the required flow. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Thrust With Rotational-speed; Forward-speed; Altitude • The Net Thrust of the jet is; F = m (V5-Va) + (P5-Pa) A5 • Fnet over the complete range of inlet conditions (Va, N / T01 ) is determined by ND quantities as: . m T01 P01 F V5 T04 T03 = . ( . Pa P01 Pa T04 T03 T01 • Since: Va = T01 Me 423 Spring 2006 Va = T0a Va P5 ) + ( -1) A5 T01 Pa M a R 1 2 1 Ma 2 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Thrust With Rotational-speed; Forward-speed; Altitude • When the Nozzle is UNCHOKED; 1 = 2 Cp j (1- ( ) 1/ ) P04 / P5 V5 / T04 • with P5 = Pa and the pressure thrust is 0 since P5 / Pa = 1 • When the Nozzle is CHOKED; V / T = ( 2 R ) 5 04 +1 P5 P04 Pc P04 and P5 Pa = P04 . P02 = P04 . Pa where the critical pressureratio, Pc / P04: 1 - 1 / 1 Pc / P04 = (1 ( )) j + 1 Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Thrust With Rotational-speed; Forward-speed; Altitude FIG.13 Variation of Thrust (F/ Pa ) with engine speed (N/T01) and flight speed (Ma) Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation of Thrust With Rotational-speed; Forward-speed; Altitude • There; N = Ta N . T01 T01 T01 -1 2 and = ( 1+ Ma ) Ta Ta 2 • The thrust for a given N/T01= f (Ma) ; although for choked flow there is a UNIQUE ERL. • Increasing flight speed Va, m*Va= momentum drag increases P02 increases (i.e RAM increases ) • At low N/T01, momentum drag increase predominates thus Ma increases Fn decreases . • At high N/T01, Ram pressure rise predominates Thus Ma increases Fn increases Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT ENGINE SPEED • Although performance is expressed in terms of ND speed, N/T01 , the actual mechanical speed N imposes a limit due to turbine stresses, and controlled. • If the speed is kept well below this limit, the take-off thrust is substantially reduced. • If N exceeds the correct limit: i) The centrifugal stresses increase with the square of speed N2 ii) A rapid increase in Turbine Inlet Temperature T03 (2% in N may cause 50K in T03) Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT ENGINE SPEED • Since the blade life is determined by CREEP, the time which the high speeds are permitted must be controlled. Take-off rating t < 5 min 100% Nmax Climb rating - reduction in fuel flow t < 30 min at 98 % Nmax Cruise rating - further reduction in fuel and rotor speed at 95 % Nmax Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Effect of Ambient Conditions on the take off rating Ta: With Engine running at max speed, Ta ,N/ Ta hence N/T01 , along the equilibrium running line ; . m T01 P decrease 02 decrease P01 Pa • Therefore, Ta Fn ( loss of thrust) T03 T03 = ( T03 / T01 )*T01 • On a hot day T03 > T03max N is required, thus Fn Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Effect of Ambient Conditions on the take off rating Pa: Fn and Pa in direct proportion (since (F / Pa) ...) Altitude , Pa and Ta ( up to 11000 m) since as Pa Fn but as Ta Fn Then Fn • Therefore ; thrust decreases with increase in altitude. • Airports at high altitudes, especially around tropical zones are critical (Mexico-City, Nairobi ) suffer from this problem. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude • Fuel consumption and fuel capacity of the aircraft determine the range • sfc(fuel flow /per unit thrust) indicates economy Both are functions of N/T01 and Ma. • With combustion efficiency b assumed, fuel consumption can be determined from : m, f/a curves, with ΔT032 . Therefore; fuel flow = f ( N/Ta ,Ma, Pa, Ta) Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude • Dependence of fuel flow on Ambient conditions can be eliminated by ND fuel flow m f Pa T a • The fuel parameter slightly depends on Ma when based on T01 and P01. They merge to a single line, for the choked nozzle conditions. sfc with ( altitude ) since Ta but since sfc f(Pa) this is not as marked Fn . * sfc with Ma . Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude FIG. 14 S.f.c. Curves Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Methods of Displacing the Equilibrium Running Line • If the Equilibrium Running Line (ERL) intersects the Surge Line (SL), it is not possible to bring the engine up to full power directly. • The compressor may surge when the engine accelerates even ERL is not cutting the SL. • Many high performance compressors have a kink in the SL. • A running line intersecting SL at low N/T01 and at the kink is shown in Figure 15. To overcome ERL is lowered down in dangerous regions. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Methods of Displacing the equilibrium running line • BLOW-OFF is a method to achieve this. • Air is bled from some intermediate compressor stage. Some turbine work is wasted. blow-off valve only operates when it is essential. • Variable Area Propelling Nozzle; an alternative method to blow-off. • Either method will produce a reduction in P02/P01 at a given N/T01, hence lower the ERL. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Methods of Displacing the equilibrium running line FIG. 15 Effect of Blow-off and Increased Nozzle Area Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Methods of Displacing the equilibrium running line FIG. 16 Effect of Variable Area Propelling Nozzle Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP Prediction of Performance for GT Methods of Displacing the equilibrium running line • In a variable area nozzle as nozzle area increases, A5 increases (P03/P04 ↑ ,so ΔP034/T03 ↑). If N/T01 is held constant P02/P01 ↓. Therefore, RL will be moved away from SL. To keep N/T01 constant fuel flow to be reduced. P02 T03 P01 T01 T03 1 T01 T034 / T03 P02 1 P01 T034 / T03 • for N/T01 held constant and A5↑ ; P03 T034 P02 as increase increase decrease P04 T03 P01 ERL will be removed away from SL. Me 423 Spring 2006 Prof. Dr. O. Cahit ERALP