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ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES Prof. Dr. O. Cahit ERALP.

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Presentation on theme: "ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES Prof. Dr. O. Cahit ERALP."— Presentation transcript:

1 ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES Prof. Dr. O. Cahit ERALP

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

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

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

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

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.

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 η c, R c vs is plotted.Axial compressor ¢  constant speed lines become vertical so η c, R c vs is plotted.

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.

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; ΔP 034 = P 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

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

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

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

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.

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.

15 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point And the NET POWER corresponding to selected OP is : m could be calculated knowing P 01, T 01 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). For this; variation of power with speed " P (N)" should be known. This will indicate whether the OP selected represents a valid solution (Equilibrium).

16 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 (T 03, N).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 (T 03, N). With a Propeller load - Power absorbed varies with as N 3 of propeller. Knowing ṁ and gear ratio, the load characteristics in terms of P out turbine vs N turbine can be plotted which corresponds to a single P output per constant speed curve i.e single point on a fixed C¢.With a Propeller load - Power absorbed varies with as N 3 of propeller. Knowing ṁ and gear ratio, the load characteristics in terms of P out turbine vs N turbine can be plotted which corresponds to a single P output per constant speed curve i.e single point on a fixed C¢. Only at this point the required output is given.Only at this point the required output is given.

17 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point FIG.3 Load Characteristics

18 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point Then the single point on each constant speed line of the C¢ has to be found.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.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.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.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.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.

19 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point Then the single point on each constant speed line of the C¢ has to be found.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.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.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.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.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.

20 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point FIG.4 Equiblirium Running Lines

21 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point The equilibrium running line for a generator set would correspond to a particular line of constantThe equilibrium running line for a generator set would correspond to a particular line of constant Each point on the line would represent a different value of T 03 and P out.Each point on the line would represent a different value of T 03 and P out. 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.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 η c.Looking at the C¢ and propeller equilibrium line, the operation is generally at a high η c.

22 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Procedure of Obtaining an Equilibrium Running Point Generator load results in a rapid drop in η c as the load is reduced.Generator load results in a rapid drop in η c 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.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).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 T 032 and hence from Combustion curves, f could be determined for an assumed  bWith the above findings T 032 and hence from Combustion curves, f could be determined for an assumed  b  then, sfc can be calculated.  then, sfc can be calculated.

23 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on single shaft gas turbine The following data refer to a SSGT operating at design speed:The following data refer to a SSGT operating at design speed: Ambient conditions:P a =1.013 bar, T a =288 K,  m =98%Ambient conditions:P a =1.013 bar, T a =288 K,  m =98% (Neglect all pressure losses!) (Neglect all pressure losses!) Calculate: T 03 for Power=3800 kW Calculate: T 03 for Power=3800 kW 1)Establish the T 03 for each point given on the CC 2)Establish (T 02 - T 01 ), (T 03 - T 04 ) and find P out 3)Plot T 03 vs P out to find the T 03 for P out =3800 kW

24 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on single shaft gas turbine 1)

25 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator The GG performs the same function for both the jet engine and free turbine engine.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.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.The compatibility of speed and flow are the same as the single shaft engine.Thus;

26 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator However, the pressure ratio of the turbine is not known.However, the pressure ratio of the turbine is not known. It must be determined by equating the turbine work to the compressor work.It must be determined by equating the turbine work to the compressor work. The work requirement;The work requirement; These equations are linked by (T 03 /T 01 ) and a trial-and- error procedure is necessary to determine T 03 for any arbitrary point on C¢These equations are linked by (T 03 /T 01 ) and a trial-and- error procedure is necessary to determine T 03 for any arbitrary point on C¢

27 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator a) Select a comp. OP b) Calculate c) Guess a value of P 03 /P 01 & calculate d) Find T 03 / T 01 from FLOW compatibility e) Using T 03 / T 01 calculate from SPEED COMPATIBILITY

28 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator f) With and P 03 / P 04 find c from T¢ g)Calculate h) Calculate (T 03 /T 01 ) using (  T 034 /T 03 ) and POWER COMPATIBILITY i) Check T 03 /T 01 with the "one" from flow compatibility (Step d) j) If different modify P 03 /P 04 and repeat the steps c to i until obtaining the correct T 03 /T 01

29 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator k) The agreement of T 03 /T 01 indicates that the turbine OP is compatible with the compressor OP for the temperature increase in CC satisfying T 03 /T 01. 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¢. 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 T 03 /T 01 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¢. This could be repeated for a series of points and points of constant T 03 /T 01 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¢.

30 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Equilibrium Running of a Gas Generator The matching procedure outlined here has been developed on the assumption that turbine ¢ do not exhibit a variation ofwithThe matching procedure outlined here has been developed on the assumption that turbine ¢ do not exhibit a variation ofwith This is true if the flow correspond to choked mass flows. This is true if the flow correspond to choked mass flows. If not choked; before guessing P 03 / P 04 If not choked; before guessing P 03 / P 04 *Guess T 03 /T 01 calculate N / T 03 from speed compatibility *calculate from flow compatibility *calculate from flow compatibility *Then P 03 / P 04 and η t can be obtained from T¢ *  T 034 /T 03 can be calculated and the GG work compatibility  T 03 /T 01 *Compare T 03 /T 01 with the initial guess. *Compare T 03 /T 01 with the initial guess.

31 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP

32 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 where where ii) The pressure ratio available is fixed by the compressor and GGT press ratios. ii) The pressure ratio available is fixed by the compressor and GGT press ratios. Inlet and exit duct losses ignored. Inlet and exit duct losses ignored.

33 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off-design Operation of Free Turbine Engine iii) Having found the pressure ratio across the power Turbine, the value of can be found from the FT¢. iii) Having found the pressure ratio across the power Turbine, the value of can be found from the FT¢. iv) If 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 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.For each 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.

34 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off-design Operation of Free Turbine Engine Equilibrium running line can be produced for differentEquilibrium running line can be produced for different on C¢. The running line for the FT engine is independent of the load and determined by the swallowing capacity ( ṁ ) of the PT. 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.FT engine has quite a different load performance than the single shaft GT.

35 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off-design Operation of Free Turbine Engine FIG.5 Equilirium Running Line for Free Turbine

36 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 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 so has a little effect onThe 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 so has a little effect on Therefore, a mean value of η t is taken at any given pressure ratio. Then,Therefore, a mean value of η t is taken at any given pressure ratio. Then, Now the GG turbine exit conditions can be mapped on the GGT¢. Now the GG turbine exit conditions can be mapped on the GGT¢.

37 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off-design Operation of Free Turbine Engine FIG.6 Operation of Turbines in Series

38 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off-design Operation of Free Turbine Engine The flow compatibility between the 2 turbines places a major restriction on the OP of GGT.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.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)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).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 R c as:The turbine pressure ratios can be expressed in terms of the R c as:

39 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 and  T 034 /T 03 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.For any value of the compressor pressure ratio, GGT pressure ratio can be obtained. Thus and  T 034 /T 03 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.

40 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation of Power Output & Sfc with Output Speed of a Free Turbine Engine Power output of a FT engine = ṁ C pg  T 045Power output of a FT engine = ṁ C pg  T 045 where where FIG.8 Variation of Power Output with Output Speed

41 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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);power output for each equilibrium running point (one for each compressor speed); i) P 04 /P a will be known ii) T 04 can be calculated from T 04 = T 03 -  T 034 knowing P a, T a ; m can be found from Free turbines are used to drive a variety of loads each of which are different (pump, propeller, electric generator), each with different vs N pt ¢.These curves are quite flat in the higher N pt region where  pt is fairly constant.Free turbines are used to drive a variety of loads each of which are different (pump, propeller, electric generator), each with different vs N pt ¢.These curves are quite flat in the higher N pt region where  pt is fairly constant.

42 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Variation Of Power Output & sfc with Output Speed of a Free Turbine Engine sfc increases as power is reduced, since as fuel flow decreases; N c decreases, T 03 decreases; but as T 03 decreases  cycle decreases.sfc increases as power is reduced, since as fuel flow decreases; N c decreases, T 03 decreases; but as T 03 decreases  cycle decreases. FIG.9 Variation of sfc With Power Output

43 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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 eachFuel 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. sfc however, is a function of both N c and N pt as P out. sfc however, is a function of both N c and N pt as P out The off-design performance can be expressed by plotting sfc vs P out for different N pt. This shows the performance of the unit when coupled to different types of loads.The off-design performance can be expressed by plotting sfc vs P out for different N pt. This shows the performance of the unit when coupled to different types of loads. Although for convenience N comp is chosen as the independent variable; in practice the fuel flow is the independent variable. A chosen value of fuel flow and (T 03 ) determines N comp and therefore P out. Although for convenience N comp is chosen as the independent variable; in practice the fuel flow is the independent variable. A chosen value of fuel flow and (T 03 ) determines N comp and therefore P out.

44 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP 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).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. 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 N c. This is because the compressor can supply an essentially constant flow at a given compressor speed irrespective of the FT speed.

45 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Torque Characteristics Therefore,Therefore, at constant P out as N pt decrease   increase. The torque might stall at high  or very low N pt.The torque might stall at high  or very low N pt. With a reduction in N pt quite a large increase in   can be obtained efficiently. 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)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)

46 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Torque Characteristics FIG.10 Torque Characteristics

47 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Given: Example on gas turbine with Free Power Turbine Calculate: Power developed and the turbine ND flowsPower developed and the turbine ND flows If the engine is running at same mechanical speed at ambient temp. of 268 K, calculate T 03, P 03 / P 04 and P out assuming the following:If the engine is running at same mechanical speed at ambient temp. of 268 K, calculate T 03, P 03 / P 04 and P out assuming the following: a)Combustion pressure loss remains constant.

48 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on Gas Turbine with Free Power Turbine b)Both turbines are choking with values of and as calculated above. No change in b)Both turbines are choking with values of and as calculated above. No change in c)At 268 K and the same N, the 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 is: P02 / P01P02 / P01P02 / P01P02 / P

49 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine Solution: Solution: Design Point Calculation:Design Point Calculation: OP on CC:

50 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on Gas Turbine with Free Power Turbine GG Power Turbine:

51 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on Gas Turbine with Free Power Turbine

52 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine OFF DESIGN OFF DESIGN At T a = T 01 =268K At T a = T 01 =268K If the PT remains choked, the GGT will be constrained to operate at a fixed ND point and thus the value ofIf the PT remains choked, the GGT will be constrained to operate at a fixed ND point and thus the value of as for the design condition as for the design condition The Work Compatibility:

53 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine hence Flow Compatibility Now the problem is to find the OP that satisfies A and B simultaneously for With the variation in efficiency;

54 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine With the constant value of CC loss Iterations Tabulated :

55 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine With the constant value of CC loss Iterations Tabulated:

56 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine Solving Graphically the required pressure ratio : Solving Graphically the required pressure ratio : P 02 / P 01 = 6.41 with T 03 / T 01 = 4.34 Therefore; T o3 = 4.34*268=1163K Therefore; T o3 = 4.34*268=1163K P developed can be calculated; P developed can be calculated; since the GGT still operates at the same ND point since the GGT still operates at the same ND point

57 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Example on gas turbine with Free Power Turbine Power outputPower output P = 32.7kg/s* 1.147J/kg.K*179,6K*0,99= 6680kW Thus on a cold day a decrease of T amb to T o1 =268K results in a decrease of max. cycle temperature from 1200K to 1163K.Thus on a cold day a decrease of T amb to T o1 =268K results in a decrease of max. cycle temperature from 1200K to 1163K. T 03 /T 01 increases from 4.17 to 4.34 due to the increasedT 03 /T 01 increases from 4.17 to 4.34 due to the increased Power increases from 5910 to 6680 kW. This is due to increase of mass flow rate and compressor pressure ratio.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 T a on GT is evident also the adverse effect of increase of T a.The beneficial effect of low T a on GT is evident also the adverse effect of increase of T a.

58 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Off Design Operation Of The Jet Engine Propelling Nozzle Characteristics The propelling nozzle area is determined from the design point calculations.The propelling nozzle area is determined from the design point calculations. A fixed nozzle area has a major influence on theA fixed nozzle area has a major influence on the off-design operation. off-design operation. The nozzle ¢ in terms of ND variables is given in terms of and P 04 /P aThe nozzle ¢ in terms of ND variables is given in terms of and P 04 /P a

59 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Propelling Nozzle Characteristics For a nozzle of given area and  jFor a nozzle of given area and  j These are valid up to the critical point.These are valid up to the critical point. The CRITICAL point of the nozzle is when The CRITICAL point of the nozzle is when

60 Prediction of Performance for GT Me 423 Spring 2006Prof. Dr. O. Cahit ERALP Propelling Nozzle Characteristics FIG.11 Propelling Nozzle Characteristics

61 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

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, η i ) RAM PRESSURE RATIO = f(M a, η 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.

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.

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.

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

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.

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:

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 :

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)

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

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 )

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

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 

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 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.

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 Δ T 032.

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.

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

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.

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.

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

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

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 ΔP 034 /T 03 ↑).In a variable area nozzle as nozzle area increases, A 5 increases (P 03 /P 04 ↑,so ΔP 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.


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