PEMP RMD510. M.S.Ramaiah School of Advanced Studies, Bengaluru
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1 Turbine and Compressor Matching Session delivered by: Prof. Q. H. Nagpurwala 1
2 Session Objectives To discuss the operating characteristics of compressors and turbines To understand the basic conditions for compressor and turbine matching To discuss component matching in a single shaft gas turbine To discuss the matching of gas generator with free power turbine and nozzle 2
3 Introduction The main components of a gas turbine engine are: inlet diffuser, compressor, combustion chamber, turbine, and exhaust nozzle. The individual components are designed based on established procedures and their performances are obtained from actual tests. When these components are integrated t in an engine, the range of possible operating conditions is considerably reduced. The problem is to find corresponding operating points on the characteristics of each component when the engine is running at a steady speed or in equilibrium. The equilibrium running points for a series of speeds may be plotted to on the compressor characteristics and joined up to form an equilibrium running line or equilibrium running diagram. 3
4 Introduction The equilibrium running diagram also shows the proximity of the operating line to the compressor surge line. If it intersects the surge line, the gas turbine will not be capable of being brought up to full speed without some remedial action. It also shows whether the engine is operating in a region of adequate compressor efficiency. Ideally the operating line should lie near the locus of the points of maximum compressor efficiency. 4
5 Test Cases Three cases are discussed here: A single shaft gas turbine delivering shaft power A free turbine engine where the gas generator turbine drives the compressor and the power turbine drives the load A simple jet engine with a propelling nozzle The gas generator performs exactly the same function for both the free turbine engine and dthe jet engine. The flow characteristics of a free turbine and a nozzle are similar. Hence, the free turbine engine and the jet engine are thermodynamically similar and differ only in the manner in which the output is utilised. 5
6 Test Cases Brayton cycle for case (b) and (c) 6
7 Component Characteristics Compressor characteristics Turbine characteristics 7
8 Assumptions Turbine characteristic is represented by a single line, because it is found in practice that t turbines do not exhibit any significant variation in non-dimensional flow with nondimensional speed. Inlet and exhaust losses are considered negligible. Combustion chamber pressure loss is a fixed percentage of the compressor delivery pressure. 8
9 Single Shaft Gas Turbine Pressure ratio across the turbine is determined by the compressor pressure ratio and combustor pressure loss. Mass flow through turbine = Mass flow through compressor Bleed air + Fuel flow. Procedure for obtaining an equilibrium running gpoint is as follows: 9
10 Single Shaft Gas Turbine Compressor and turbine are directly coupled, hence Speed compatibility (1) Flow compatibility From combustor pressure loss: Assuming m 1 = m 3 = m (2) 10
11 Single Shaft Gas Turbine If T 01 is specified, then obtain T 03 from eqn (2) and from eqn (1). Obtain turbine efficiency from turbine characteristics using the known values of and p 03 /p 04. Turbine temperature drop (3) (4) (5) 11
12 Single Shaft Gas Turbine If the engine is coupled to a dynamometer on the test bed, then the load could be set independently of the speed and it would be possible to operate at any point on the compressor characteristic. If a propeller is the load, then Power N 3. The problem is to find the single point on each constant speed line of compressor characteristic which will give the required net power output at that speed. This can only be done by trial and error, taking several operating points on the in the figure in next slide. 12
13 Single Shaft Gas Turbine Generator runs at constant speed with load varied electrically. Each point on this line represents a different value of turbine inlet temperature and power output. Load characteristic ti Equilibrium i running lines of a propeller 13
14 Equilibrium Running of a Gas Generator A gas generator performs the same function for the free turbine engine and the jet engine. It generates high pressure, high temperature gas for expansion through the turbine or the nozzle. Eqns. 1 and 2 are applicable for speed and mass flow compatibility. The turbine pressure ratio is not known and can be determined by (6) Eqns. 1, 2 and 6 are all linked by the temperature ratio T 03 /T 01 and it is necessary to determine (by trial and error) the turbine inlet temperature required for operation at any arbitrary point on the compressor performance map. Assuming that the turbine non-dimensional lflow is independent d of the nondimensional speed, the procedure is as follows: 14
15 Equilibrium Running of a Gas Generator (4) (2) (1) (3) (6) (2)
16 Equilibrium Running of a Gas Generator (2) (6) Calculations can be carried out for a large number of points and the results can be presented on the compressor characteristics by the locus of constant T 03 /T 01 (see figure in slide 18). However, the flow compatibility with the component downstream (power turbine or nozzle) will restrict t the operating zone on the compressor characteristic. 16
17 Equilibrium Running of a Gas Generator Note: (1) (2) (3) (6) 17
18 Equilibrium Running of a Gas Generator 18
19 Matching of Gas Generator with Free Turbine The mass flow leaving the gas generator is equal to that entering the power turbine. Pressure ratio across the power turbine is fixed by the pressure ratios across the compressor and gas generator turbine. The characteristic of the power turbine will have the same form as of the gas generator turbine, but it is represented by the parameters The mass flow parameter of the power turbine (7) where (8) 19
20 Matching of Gas Generator with Free Turbine The corresponding pressure ratio across the power turbine can be given as For stationary gas turbines (ignoring the inlet and exit duct losses), p o1 = p a and the power turbine outlet pressure is also p a. (7) in slide
21 Matching of Gas Generator with Free Turbine (a) Iteration for gas generator (b) Overall iteration procedure for free power turbine 21
22 Matching of Gas Generator with Free Turbine in Slide 18. in Slide
23 Matching of Gas Generator with Nozzle Propelling Nozzle Characteristics The propelling nozzle area for a jet engine is fixed from design point calculations. Once the nozzle size is fixed, it has major influence on off-design operation. The mass flow parameter is given by (12) A5 is the effective nozzle area (13) (14) 23
24 Matching of Gas Generator with Nozzle Propelling Nozzle Characteristics (14) () (13) () in Slide 25 (14) (16) 24
25 Matching of Gas Generator with Nozzle Propelling Nozzle Characteristics Likewise, with the nozzle unchoked, is given by eqn.13; whereas when it is choked, C 5 is the sonic velocity and M 5 is unity. Recalling that we have the general relation (17) and when the nozzle is choked, we have (18) 25
26 Matching of Gas Generator with Nozzle The flow characteristics of nozzle and free turbine are similar. For operation of a jet engine under static conditions, the behaviour of nozzle is same as that of a free turbine. Hence, the equilibrium running line can be determined according to the flow chart of slide 21, with the nozzle characteristic replacing the power turbine characteristic. In flight conditions, the effect of forward speed needs to be considered. Forward speed produces a ram pressure ratio, which is a function of both flight Mach number and intake efficiency. The compressor delivery pressure and nozzle inlet pressure increase, leading to increase in nozzle pressure ratio. If the nozzle chokes, then the mass flow rate becomes maximum and is independent of nozzle pressure ratio and dforward speed. Hence, the turbine operating point will also remain unchanged. Therefore, under choked nozzle condition, the equilibrium running line will be uniquely determined by the fixed turbine operating point and will be independent of the flight speed. 26
27 Matching of Gas Generator with Nozzle Usually the nozzle is choked during take-off, climb and cruise, and may remain unchoked while preparing to land or taxiing, when the thrust is significantly reduced. Hence, the running line is affected at low forward speeds when the engine rotational speed is also low and the running line is close to the surge line. The nozzle pressure ratio p 04 /p a is linked to the ram pressure ratio The ram pressure ratio is given by (19) (20) Now the procedure of flow chart (slide 21) can be followed with eqn. 19 substituted for eqn. 8, but for each compressor speed line the calculation is repeated for several values of M a covering the desired range of flight speed. 27
28 Matching of Gas Generator with Nozzle The result is a fan of equilibrium running lines of constant M a, merging into a single running line at higher compressor speeds when the nozzle is choked. Increasing the Mach number pushes the equilibrium running line away from the surge line at low compressor speeds, because the ram pressure rise allows the compressor to utilise a lower pressure ratio for pushing the required flow through the nozzle. Jet engine running lines 28
29 Session Summary Gas turbine component characteristics have been explained. The procedure for matching of turbine and compressor in a simple single shaft gas turbine is discussed. Equilibrium running of a basic gas generator is discussed. The procedures of matching the gas generator to a power turbine and a propelling nozzle are explained. 29
30 Thank you 30
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