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ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES

ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES. Prof. Dr. O. Cahit ERALP. Prediction of Performance of Simple Gas Turbine. From cycle calculations it is possible to determine the PRESSURE RATIO ( R c ) w hich will give the best overall efficiency for a given T max .

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ME 423 Chapter 8 PREDICTION OF PERFORMANCE OF SIMPLE GAS TURBINES

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

  2. 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 RATEto 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 thedesign point. • That is running at the design speed N*, mass flow rate m* and pressure ratio R*. Prof. Dr. O. Cahit ERALP

  3. 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). Prof. Dr. O. Cahit ERALP

  4. 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. Prof. Dr. O. Cahit ERALP

  5. 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. Prof. Dr. O. Cahit ERALP

  6. 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. Prof. Dr. O. Cahit ERALP

  7. Component Characteristics¢ • Axial compressor ¢ constant speed lines become vertical so ηc , Rc vs is plotted. FIG.1 Compressor Characteristics Prof. Dr. O. Cahit ERALP

  8. 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 Prof. Dr. O. Cahit ERALP

  9. 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; Prof. Dr. O. Cahit ERALP

  10. Procedure of Obtaining an Equilibrium Running Point a) Select a constant speed line on the C¢ and choose an OP on this line thus N/ T01are selected. b) The corresponding point on the T¢ is obtained by the Compatibility of Speed and Flow. • COMPATIBILITY OF ROTATIONAL SPEED Prof. Dr. O. Cahit ERALP

  11. Procedure of Obtaining an Equilibrium Running Point • COMPATIBILITY OF FLOW • Here combustion chamber pressure loss P03/P02 = 1 - Pb/P02 • assume Prof. Dr. O. Cahit ERALP

  12. Procedure of Obtaining an Equilibrium Running Point and are fixed by the chosen OP on the is assumed to be constant. Neglecting inlet and exhaust pressure lossesPa = P01 = P04 is a function of Prof. Dr. O. Cahit ERALP

  13. 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 T01, T03 can be calculated. Prof. Dr. O. Cahit ERALP

  14. Procedure of Obtaining an Equilibrium Running Point • Having determined T03 , the SPEED COMPATIBILITY : • The compressor & turbine temperature changes can be determined. Prof. Dr. O. Cahit ERALP

  15. Procedure of Obtaining an Equilibrium Running Point • And the NET POWER corresponding to selected OP is : • 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).  Prof. Dr. O. Cahit ERALP

  16. 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 i.e single point on a fixedC¢. • Only at this point the required output is given. Prof. Dr. O. Cahit ERALP

  17. Procedure of Obtaining an Equilibrium Running Point • FIG.3 Load Characteristics Prof. Dr. O. Cahit ERALP

  18. 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 . Prof. Dr. O. Cahit ERALP

  19. 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 . Prof. Dr. O. Cahit ERALP

  20. Procedure of Obtaining an Equilibrium Running Point FIG.4 Equiblirium Running Lines Prof. Dr. O. Cahit ERALP

  21. Procedure of Obtaining an Equilibrium Running Point • The 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 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-LoadRunning Line for a Generator Set is obtained. • Looking at the C¢ and propeller equilibrium line, the operation is generally at a high ηc. Prof. Dr. O. Cahit ERALP

  22. 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. Prof. Dr. O. Cahit ERALP

  23. 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 • Establish the T03 for each point given on the CC • Establish (T02 - T01), (T03 - T04) and find Pout • Plot T03 vs Pout to find the T03 for Pout =3800 kW Prof. Dr. O. Cahit ERALP

  24. Example on single shaft gas turbine 1) Prof. Dr. O. Cahit ERALP

  25. 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; Prof. Dr. O. Cahit ERALP

  26. 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; • These equations are linked by (T03/T01) and a trial-and-error procedure is necessary to determine T03 for any arbitrary point on C¢ Prof. Dr. O. Cahit ERALP

  27. Equilibrium Running of a Gas Generator a) Select a comp. OP b) Calculate c) Guess a value of P03/P01 & calculate d) Find T03 / T01 from FLOW compatibility e) Using T03 / T01 calculate from SPEED COMPATIBILITY Prof. Dr. O. Cahit ERALP

  28. Equilibrium Running of a Gas Generator f) With and P03 / P04 find c from T¢ g)Calculate 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 Prof. Dr. O. Cahit ERALP

  29. Equilibrium Running of a Gas Generator k)The agreement of T03/T01 indicates that the turbine OP iscompatible 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¢.  Prof. Dr. O. Cahit ERALP

  30. Equilibrium Running of a Gas Generator • The 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. •  If not choked; before guessing P03 / P04 *Guess T03/T01 calculate N/T03 from speed compatibility   *calculate from flow compatibility *Then P03 / P04 and ηt can be obtained from T¢ *T034/T03canbe calculated and the GG work compatibility T03/T01 *Compare T03/T01 with the initial guess. Prof. Dr. O. Cahit ERALP

  31. Prof. Dr. O. Cahit ERALP

  32. 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 ii) The pressure ratio available is fixed by the compressor and GGT press ratios. Inlet and exit duct losses ignored. Prof. Dr. O. Cahit ERALP

  33. 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¢. iv) If from (i) and (iii) do not match; a new point on the constant speed C¢ has to be selected and thisprocedure hasto be repeated until the flowcompatibility 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. Prof. Dr. O. Cahit ERALP

  34. Off-design Operation of Free Turbine Engine • Equilibrium 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. • FT engine has quite a different load performance than the single shaft GT. Prof. Dr. O. Cahit ERALP

  35. Off-design Operation of Free Turbine Engine FIG.5 Equilirium Running Line for Free Turbine Prof. Dr. O. Cahit ERALP

  36. 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 so has a little effect on • Therefore, a mean value of ηt is taken at any given pressure ratio. Then, Now the GG turbine exit conditions can be mapped on the GGT¢. Prof. Dr. O. Cahit ERALP

  37. Off-design Operation of Free Turbine Engine FIG.6 Operation of Turbines in Series Prof. Dr. O. Cahit ERALP

  38. 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: Prof. Dr. O. Cahit ERALP

  39. Off-design Operation of Free Turbine Engine FIG. 7Compressor Pressure Ratio vs GGT Pressure Ratio • For any value of the compressor pressure ratio, GGT pressure ratio can be obtained. Thus 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. Prof. Dr. O. Cahit ERALP

  40. Variation of Power Output & Sfc with Output Speed of a Free Turbine Engine • Power output of a FT engine = ṁ Cpg T045 where FIG.8Variation of Power Output with Output Speed Prof. Dr. O. Cahit ERALP

  41. 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 • 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. Prof. Dr. O. Cahit ERALP

  42. Variation Of Power Output & sfc with Output Speed of a Free Turbine Engine • sfc increases as power is reduced, since as fuel flow decreases; Nc decreases, T03decreases; but as T03decreasescycledecreases. FIG.9Variation of sfc With Power Output Prof. Dr. O. Cahit ERALP

  43. 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 . sfc however, is a function of both Nc and Npt as Pout • 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. Prof. Dr. O. Cahit ERALP

  44. 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 decreaseunsuitable for traction (since m decrease out decrease) b) Normal curve of Internal Combustion Engineis 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. Prof. Dr. O. Cahit ERALP

  45. Torque Characteristics • Therefore, at constant Pout as Npt decrease tincrease. • The torque might stall at high t or very low Npt. With a reduction in Npt quite a large increase int 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) Prof. Dr. O. Cahit ERALP

  46. Torque Characteristics FIG.10 Torque Characteristics Prof. Dr. O. Cahit ERALP

  47. Example on gas turbinewith Free Power Turbine Given: • Calculate: • Power developed and the turbine ND flows • If the engine is running at same mechanical speed at ambient temp. of 268 K, calculate T03, P03/P04 and Poutassuming the following: • a)Combustion pressure loss remains constant. Prof. Dr. O. Cahit ERALP

  48. Example on Gas Turbinewith Free Power Turbine 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: Prof. Dr. O. Cahit ERALP

  49. Example on gas turbinewith Free Power Turbine • Solution: • Design Point Calculation: • OP on CC: Prof. Dr. O. Cahit ERALP

  50. Example on Gas Turbinewith Free Power Turbine GG Power Turbine: Prof. Dr. O. Cahit ERALP

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