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ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES Prof. Dr. O. Cahit ERALP Slide 2 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP From cycle calculations it is possible to determine the PRESSURE RATIO ( R c ) which will give the best overall efficiency for a given T max.From cycle calculations it is possible to determine the PRESSURE RATIO ( R c ) which will give the best overall efficiency for a given T max. MASS FLOW RATE to give the most suitable desired power output.MASS FLOW RATE to give the most suitable desired power output. After such preliminary calculations, the most suitable design data for a particular application can be chosen.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.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*.That is running at the design speed N*, mass flow rate m* and pressure ratio R*. Prediction of Performance of Simple Gas Turbine Slide 3 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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.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 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 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).The plot of these OP's form the EQUILIBRIUM RUNNING LINE (ERL). Prediction of Terformance of Simple Gas Turbine Slide 4 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP For the whole range of operating speeds, it will generate the EQUILIBRIUM RUNNING DIAGRAM.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.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).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. 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.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.Ideally the engine should be operated within the region of maximum possible efficiencies. Prediction of Performance of Simple Gas Turbine Slide 5 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation of SFC with reduction in power PART LOAD PERFORMANCE. This is important while running the GT at low power settings.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.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 T a and P a.The effect of ambient conditions on maximum output is also important, i.e. high & low T a and P a. Peak load energy generation:Peak load energy generation: Europe: cold days in winter, America: hot days in Summer for airplanes: Runway length (safety) and for airplanes: Runway length (safety) and pay load (economics) are affected. pay load (economics) are affected. Prediction of Performance of Simple Gas Turbine Slide 6 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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.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 9More 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.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.As a result of this several jet engines have been converted to Free Turbine Power engine for peak load electric generation, and marine applications. Slide 7 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Component Characteristics FIG.1 Compressor Characteristics Axial compressor constant speed lines become vertical so c, R c vs is plotted.Axial compressor constant speed lines become vertical so c, R c vs is plotted. Slide 8 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Component Characteristics FIG.2 Turbine Characteristics Turbine do not show a significant variation in ND speed. Their operating range is usually severely restricted by another component downstream. Turbine do not show a significant variation in ND speed. Their operating range is usually severely restricted by another component downstream. Slide 9 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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;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; P 034 = P 012 - P 032 The mass flow through the turbine = mass flow through the compressor - Bleeds + fuel flow;The mass flow through the turbine = mass flow through the compressor - Bleeds + fuel flow; Off-Design Operation of The Single - Shaft GT Slide 10 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP a) Select a constant speed line on the C and choose an OP on this line thus N/ T 01 are selected. N/ T 01 are selected. b) The corresponding point on the T is obtained by the Compatibility of Speed and Flow. COMPATIBILITY OF ROTATIONAL SPEEDCOMPATIBILITY OF ROTATIONAL SPEED Procedure of Obtaining an Equilibrium Running Point Slide 11 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP COMPATIBILITY OF FLOWCOMPATIBILITY OF FLOW Here combustion chamber pressure lossHere combustion chamber pressure loss P 03 /P 02 = 1 - P b /P 02 P 03 /P 02 = 1 - P b /P 02 assume assume Procedure of Obtaining an Equilibrium Running Point Slide 12 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point are fixed by the chosen OP on the is assumed to be constant. Neglecting inlet and exhaust pressure losses P a = P 01 = P 04 is a function of is a function of and Slide 13 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point Now in the flow compatibility the only unknown is The rest can be obtained from C and T. Thus, Thus, knowing T 01, T 03 can be calculated. Slide 14 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point Having determined T 03, the SPEED COMPATIBILITY :Having determined T 03, the SPEED COMPATIBILITY : The compressor & turbine temperature changes can be determined.The compressor & turbine temperature changes can be determined. Slide 15P 04 /P c, the nozzle is"> Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Propelling Nozzle Characteristics for P 04 /P a > P 04 /P c, the nozzle is choked P 5 = P c > P a andfor P 04 /P a > P 04 /P c, the nozzle is choked P 5 = P c > P a and = const (not a function of P 04 /P a ). = const (not a function of P 04 /P a ). The similarity between this and the turbine is evident.The similarity between this and the turbine is evident. When the nozzle is chokedWhen the nozzle is choked GenerallyGenerally Slide 62 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 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 (V a ) on the equilibrium running line has to be considered.The equilibrium running line can be determined as for FT. Here the effect of forward speed (V a ) on the equilibrium running line has to be considered. FORWARD SPEED RAM PRESSURE RATIO = f(M a, i ) RAM PRESSURE RATIO = f(M a, i ) RAM P 02 increase P 04 increase P 04 /P 5 increase when choked maximum and independent of P 04 /P 45 thus V a. Slide 63 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Matching of GG with Nozzle Then the Turbine OP will be unchanged because of the compatibility of flow between turbine & 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.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.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.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 V a on ERL has to be considered.Since the running line is close to surge line at low,the effect of V a on ERL has to be considered. Slide 64 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Matching of GG with Nozzle Nozzle pressure ratio and Ram pressure ratio can be related as:Nozzle pressure ratio and Ram pressure ratio can be related as: The ram pressure ratio is:The ram pressure ratio is: Therefore, for a given intake efficiency i ;Therefore, for a given intake efficiency i ; P 04 /P a = f (GG parameters and flight Mach Number). P 04 /P a = f (GG parameters and flight Mach Number). *The same procedure as for the FPT can be followed to obtain the equilibrium running point. *The same procedure as for the FPT can be followed to obtain the equilibrium running point. Slide 65 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Matching of GG with Nozzle FIG. 12 Jet Engine Running Lines Slide 66 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Matching of GG with Nozzle For each compressor speed the calculation is repeated for several M a to cover the desired range of flight speed.For each compressor speed the calculation is repeated for several M a to cover the desired range of flight speed. The result A fan of Equilibrium RL of constant M a.The result A fan of Equilibrium RL of constant M a. These merge to a single RL at higher, where the nozzle is choked.These merge to a single RL at higher, where the nozzle is choked. Increasing M a pushes the equilibrium RL away from SL at low compressor speeds.Increasing M a pushes the equilibrium RL away from SL at low compressor speeds. Therefore, the Ram pressure rise allows the R c decrease for the required flow.Therefore, the Ram pressure rise allows the R c decrease for the required flow. Slide 67 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation of Thrust With Rotational-speed; Forward-speed; Altitude The Net Thrust of the jet is;The Net Thrust of the jet is; F = m (V 5 -V a ) + (P 5 -P a ) A 5 F net over the complete range of inlet conditionsF net over the complete range of inlet conditions (V a, ) is determined by ND quantities as: Since:Since: Slide 68 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation of Thrust With Rotational-speed; Forward-speed; Altitude When the Nozzle is UNCHOKED;When the Nozzle is UNCHOKED; with P 5 = P a and the pressure thrust is 0 since P 5 / P a = 1with P 5 = P a and the pressure thrust is 0 since P 5 / P a = 1 When the Nozzle is CHOKED;When the Nozzle is CHOKED;and where the critical pressureratio, P c / P 04 : Slide 69 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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) Slide 70 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation of Thrust With Rotational-speed; Forward-speed; Altitude There;There; The thrust for a given N/ T 01 = f (Ma) ;The thrust for a given N/ T 01 = f (Ma) ; although for choked flow there is a UNIQUE ERL. Increasing flight speed V a, m*V a = momentum drag increases P 02 increases (i.e RAM increases )Increasing flight speed V a, m*V a = momentum drag increases P 02 increases (i.e RAM increases ) At low N/ T 01, momentum drag increase predominates thus M a increases F n decreases.At low N/ T 01, momentum drag increase predominates thus M a increases F n decreases. At high N/ T 01, Ram pressure rise predominates Thus M a increases F n increasesAt high N/ T 01, Ram pressure rise predominates Thus M a increases F n increases Slide 71 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP ENGINE SPEED Although performance is expressed in terms of ND speed, N/ T 01, the actual mechanical speed N imposes a limit due to turbine stresses, and controlled.Although performance is expressed in terms of ND speed, N/ T 01, 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 the speed is kept well below this limit, the take-off thrust is substantially reduced. If N exceeds the correct limit:If N exceeds the correct limit: i) The centrifugal stresses increase with the square of speed N 2 ii) A rapid increase in Turbine Inlet Temperature T 03 (2% in N may cause 50 K in T 03 ) Slide 72 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP ENGINE SPEED Since the blade life is determined by CREEP, the time which the high speeds are permitted must be controlled.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% N max Climb rating - reduction in fuel flow t < 30 min Climb rating - reduction in fuel flow t < 30 min at 98 % N max Cruise rating - further reduction in fuel and Cruise rating - further reduction in fuel and rotor speed at 95 % N max Slide 73 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Effect of Ambient Conditions on the take off rating T a :With Engine running at max speed, T a ,N/ T a hence N/ T 01 , hence N/ T 01 , along the equilibrium running line ; Therefore, T a Fn ( loss of thrust)Therefore, T a Fn ( loss of thrust) T 03 T 03 = ( T 03 / T 01 )*T 01 T 03 T 03 = ( T 03 / T 01 )*T 01 On a hot day T 03 > T 03max N is required, thus Fn On a hot day T 03 > T 03max N is required, thus Fn Slide 74 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Effect of Ambient Conditions on the take off rating P a :F n and P a in direct proportion (since (F / Pa)...) Altitude , P a and Ta ( up to 11000 m) since as P a F n but as T a F n Then F n but as T a F n Then F n Therefore ; thrust decreases with increase in altitude.Therefore ; thrust decreases with increase in altitude. Airports at high altitudes, especially around tropical zones are critical (Mexico-City, Nairobi ) suffer from this problem.Airports at high altitudes, especially around tropical zones are critical (Mexico-City, Nairobi ) suffer from this problem. Slide 75 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude Fuel consumption and fuel capacity of the aircraft determine the rangeFuel consumption and fuel capacity of the aircraft determine the range sfc (fuel flow /per unit thrust) indicates economysfc (fuel flow /per unit thrust) indicates economy Both are functions of N/ T 01 and M a. With combustion efficiency b assumed,With combustion efficiency b assumed, fuel consumption can be determined from : m,f/a curves, with T 032. Slide 76 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude Dependence of fuel flow on Ambient conditions can be eliminated by ND fuel flowDependence of fuel flow on Ambient conditions can be eliminated by ND fuel flow The fuel parameter slightly depends on M a when based on T 01 and P 01. They merge to a single line, for the choked nozzle conditions.The fuel parameter slightly depends on M a when based on T 01 and P 01. They merge to a single line, for the choked nozzle conditions. Slide 77 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation in fuel consumption & sfc with rotational Speed, forward speed & altitude FIG. 14 S.f.c. Curves Slide 78 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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.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.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.Many high performance compressors have a kink in the SL. A running line intersecting SL at low N/ T 01 and at the kink is shown in Figure 15.A running line intersecting SL at low N/ T 01 and at the kink is shown in Figure 15. To overcome ERL is lowered down in dangerous regions. Slide 79 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Methods of Displacing the equilibrium running line BLOW-OFF is a method to achieve this.BLOW-OFF is a method to achieve this. Air is bled from some intermediate compressor stage.Air is bled from some intermediate compressor stage. Some turbine work is wasted. blow-off valve only operates when it is essential. blow-off valve only operates when it is essential. Variable Area Propelling Nozzle; an alternative method to blow-off.Variable Area Propelling Nozzle; an alternative method to blow-off. Either method will produce a reduction in P 02 /P 01 at a given N/ T 01, hence lower the ERL.Either method will produce a reduction in P 02 /P 01 at a given N/ T 01, hence lower the ERL. Slide 80 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Methods of Displacing the equilibrium running line FIG. 15 Effect of Blow-off and Increased Nozzle Area Slide 81 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Methods of Displacing the equilibrium running line FIG. 16 Effect of Variable Area Propelling Nozzle Slide 82 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Methods of Displacing the equilibrium running line In a variable area nozzle as nozzle area increases, A 5 increases (P 03 /P 04 ,so P 034 /T 03 ).In a variable area nozzle as nozzle area increases, A 5 increases (P 03 /P 04 ,so P 034 /T 03 ). If N/ T 01 is held constant P 02 /P 01 . If N/ T 01 is held constant P 02 /P 01 . Therefore, RL will be moved away from SL. To keep N/ T 01 constant fuel flow to be reduced. Therefore, RL will be moved away from SL. To keep N/ T 01 constant fuel flow to be reduced. for N/ T 01 held constant and A 5 ;for N/ T 01 held constant and A 5 ; ERL will be removed away from SL.