Turbo Machinery Dynamics Part 2 pdf

increasing the bypass ratio from 0 to 5. Ideally the engine must have a fan pressure ratio of about 3, but this would call for two or more fan stages. In practice, only one fan stage is used to lower weight and fan noise, causing the core jet velocity to be much higher than the fan duct discharge velocity. Military engines such as TF-39 for C5A transport planes do not have such restrictions, have one-and-a-half fan stages, and hence a bypass ratio of 8 is used. Note that the best value for the bypass ratio of a given aircraft also depends on the engine and fuel weight, noise, and installation drag. Turbofan engines are ideal for subsonic applications. Supersonic conditions call for an afterburner, where the combustion of the mixed fan and gas generator exhausts occurs. The fan pressure ratio will then be subject to the conditions p t6 = p t3 , or p f = p c p t , and t f = t c t t . If aft combustion raises the mixed streams temperature to q a , the velocity at exhaust also is the same. Thrust expression then becomes (2.11) Equation (2.6) is modified for t f (2.12) Specific impulse takes the form (2.13) Engine performance for a =1 and p c of 24 at M 0 = 0 is shown in Fig. 2.5. For compari- son, the non-after-burning performance from Eqs. (2.7) and (2.8) is also shown. Note that p f varies with M 0 for the given matching items and a = 1, but in reality a also varies with M 0 . The thrust ratio of afterburning (or thrust-augmenting) to non-after-burning case is large, which has merit if the requirement is for a subsonic cruise followed by a supersonic burst in speed. Turboprop engines have similarities with the turbofan version, but have a considerably higher bypass ratio and consequent propulsive efficiency. A number of qualitative differ- ences exist between them. The propeller does not have a diffuser, so the tips are exposed to the airflow that combines the velocity of aircraft and the blade’s own peripheral tip speed. Hence, the propellers reach sonic speed at the tip even at medium flight speeds. Aircraft driven by turboprop engines are generally limited to Mach 0.6, primarily because the propellers tend to cause high noise levels and are inefficient during supersonic operation. Implementation of the propellers on the engine is through a gearbox. Thrust variation occurs with changes in altitude and speed in aircraft engines. The expression for thrust relies on total air mass flow through the engine, which changes with the flight Mach number, atmospheric density (hence altitude), and flow conditions within the engine. High-bypass engine thrust decreases with increases in the flight Mach number, as seen in Fig. 2.6, for different bypass ratios. Also, if takeoff requirements control the siz- ing of the engine, turbofan and turboprop engines will experience exponential decay in thrust with altitude. When a regenerative heat exchanger is added to a turboprop to withdraw heat from turbine exhaust and transfer it to the air entering the combustor, reduction in specific fuel I ah gc T M pa a f f = ( ) − − − − 0 0 2 1 10 0 0 0 θ θτ θτ γ θθ τ θθ ατ θτ αθ f tc tc = ++− + 0 0 1() / F dm dt a M af f (/)( ) () () 0 0 0 0 1 21 1+ = − − − α θθτ θτ γ AIRCRAFT POWER PLANT 23 24 APPLICATIONS FIGURE 2.5 Turbofan engine with afterburner—variation of thrust (upper), specific impulse (lower) with Mach number. FIGURE 2.6 Thrust variation with flight Mach number. consumption is obtained. But the high weight of the component rules out its usage where high compression capacity is required. In the preceding discussion the turbine inlet temperature q t was not changed in order to evaluate the impact of other cycle parameters. In Eq. (2.10) as q t increases, thermal efficiency, thrust, and specific impulse increase in turbofan engines, because jet velocity is reduced by increasing q t for a given bypass ratio. This can be observed by holding u e /u 0 constant as q t is changed. Thrust per unit of airflow then becomes (2.14) and from Eq. (2.8), the specific impulse is (2.15) The effect of q t on specific impulse is displayed in Fig. 2.7. I increases continuously with q t , because cycle thermal efficiency also improves. The increased power produced by the gas generator portion is absorbed by the larger fan mass flow. Deviations from the ideal behavior discussed so far arise from factors such as imperfections in the diffusion of stream flow at the engine inlet, nonisentropic expansion and compression, incomplete combustion, under- and overexpansion in the exit nozzle, and bleeding of compressor air for turbine cooling. Specific heat c v in the compressor rises due to the increase in temperature, causing g = c p /c v to fall. Greater variations may be expected in the combustor because of the sharper rise in temperature and the formation of H 2 O and CO 2 . The application of tabulated values I ah gc T M u u p t t e =       −       −       +       0 00 0 2 1 1 1 1() / γ θ θ F dm dt a M u u e (/)( ) 0 0 0 1 1 + =−       α AIRCRAFT POWER PLANT 25 FIGURE 2.7 Turbine inlet temperature and specific impulse: turbofan engines. of thermodynamic properties of air and combustion gases in the cycle and performance calculations helps to alleviate the problem by including an accurate account of the effects. Free stream air reaches the inlet ahead of the aircraft. It may reduce in speed smoothly in subsonic inlet or may decelerate due to shock waves in supersonic conditions. Wall viscous shear in a subsonic flow causes the growth of the boundary layer, where the stagnation pressure of the fluid is low. Mixing this flow with the inviscid core flow drops the average stagnation pressure below p t0 of the free stream. In supersonic flight, compression through the series of shock waves causes further deterioration of the stagnation pressure. Losses vary markedly with M 0 , and for M 0 > 2 they are the prime source of diffuser pressure drop. Viscous shear on airfoils and end walls of flow passages is mostly responsible for losses in compressors and turbines and lower stagnation pressure occurring to a greater extent than in the inviscid flow in a diffuser. The reduced-level energy of this fluid then mixes with the base flow at the compressor and at the turbine exit. Shock losses in the fan and the first stage of the compressor are also prominent. The net result of these losses is to call for more energy input than for an ideal isentropic compressor. Compressor and turbine efficiencies h c and h t are displayed in Fig. 2.8 for a range of polytropic efficiency values typical of many turbofan engines. Losses in the compressor heat the air, requiring more energy to be put in, hence h c < h polytropic . On the other hand, turbine losses make energy available for subsequent expansion, and so h t > h polytropic . Burners are subject to losses arising from combustion and pressure drop. Incomplete combustion of a mixture of air and fuel results in the formation of CO and soot. Characterized by burner efficiency h b , it defines the change in enthalpy flux from the burner’s inlet to its exit and is divided by the energy content of the fuel flow. Heat value of the fuel, h, also plays a role, the lower value being more appropriate for gas turbines since water leaves the combustor in the form of vapor. Loss of stagnation pressure due to viscous effects, and to a limited extent by the addition of heat, will be represented in an expression for the burner stagnation pressure ratio p b . When expansion in the exhaust nozzle is correct, it causes the flow to expand isentrop- ically to ambient pressure within the nozzle. When the flow is not fully expanded, as may happen if the nozzle pressure ratio is large enough to cause the exit velocity to exceed Mach 1.0, further expansion occurs outside the nozzle without producing the corresponding thrust. The pressure ratio p e /p 0 is controlled by the geometry of the nozzle and by the ratio of stagnation and ambient pressures. 26 APPLICATIONS FIGURE 2.8 Variation of compressor and turbine efficiencies with pressure ratio (Kerrebrock, 1992). Expressions for thrust and specific impulse observe modification when losses are included in the analysis. Using the station numbers in Fig. 2.1, the thrust from the fan flow becomes (2.16) The core engine flow takes the form (2.17) where (2.18) Total thrust per unit of airflow is (2.19) Specific impulse is (2.20) High-bypass turbofan engines with one fan have a limit of 1.6 for the fan pressure ratio. In Fig. 2.9, gains in thrust and specific impulse can be obtained by using a fan pressure ratio of 2.0 with a fan bypass ratio below 8, since the core jet velocity is larger than the fan jet velocity in the given range of bypass ratios. Effects of changes in the compressor pressure ratio, compressor and fan polytropic efficiency, and turbine efficiency can be observed from similar comparisons with the aid of graphs. 2.5 PERFORMANCE EVALUATION The performance of an engine system depends on the characteristics of the inlet, fan, compressor, combustor, turbine, and exhaust. Thermodynamic calculations given in the previous section do not relate to the shape, size, and form of the parts. The behavior of individual components, on the other hand, is determined by their mechanical characteristics and lim- iting factors. Interaction between the fluid and the surface it flows over, thermal effects, and struc- tural integrity define the limits of operation of a component, and hence of the engine system. Dynamic forces are created by the gas flowing through the designed shapes of passage walls, shock waves, and boundary layers. Gently varying cross sections in the channels control the flow velocity along the axis and, to a lesser extent, perpendicular to the axis. Shock waves introduce step changes in pressure, temperature, and velocity; a drop in the stagnation pressure of the bulk flow over solid surfaces thus exerts considerable changes in supersonic flows. In the proximity of end walls of passages between blades and nozzles, I F gdmdt aF dm dt ga f f == (/) (/) 0 0 F dm dt a MF dm dt u F dm dt u(/) (/) (/) 0 04 0 8 0 (1 ) 1+ = + +       αα f cT h f p b tc =+− 0 0 1 η θθτ [( ) ] F dm dt u f u u f uTR uT M R p p t cc 4 0 4 0 04 40 0 2 0 4 (1 ) 1 (1 ) 1 (/) =+ −++       −               γ F dm dt u u u uT uT M p p c 8 0 8 0 08 80 0 2 0 8 11 (/) =−+       −               α γ AIRCRAFT POWER PLANT 27 the vane velocity must change rapidly from the mainstream value to zero due to the no-slip condition. Fluid behavior in the region near the walls is controlled by pressure and viscous shear forces because the momentum is negligible. The boundary layer theory may be used to define a correction factor for the passage and to predict the time when flow separation occurs. When the flow separates from a wall, the diffusing effect of the downstream portion of the passage is lost, and the walls no longer control the flow. Exertion of fluid viscous shear stresses on passage walls also causes transfer of thermal energy between the fluid and the wall (Kerrebrock, 1992). An inlet (or diffuser) performs the task of bringing air from ambient to conditions demanded by the fan or the compressor while efficiently capturing the flow over a wide range of free-stream Mach numbers. Diffusers for a subsonic flight considerably differ from designs for a supersonic flight to decelerate the airflow to subsonic levels. Mach number M 2 at the fan is determined by the rotor speed and the air temperature, and is the largest at high altitude and full engine speed. Requirements are most significant when the aircraft takes off at full speed and high T 0 , but the variation in M 2 is not large from subsonic cruise when T 0 and rotor speed are low. A reduction of 20 percent from takeoff to high subsonic cruise may be generally expected. An internal compression diffuser takes the form of a convergent-divergent channel where supersonic flow is reduced in speed, by a series of weak compression waves, to sonic velocity, then down to subsonic condition. Pressure recovery is enhanced at high M 0 by taking advantage of the fact that a series of weak shocks produce much less loss of the stagnation pressure than one strong shock, and may be used to advantage in the external compression inlets to form an oblique shock. A combination of internal and external compression through an 28 APPLICATIONS FIGURE 2.9 Thrust and specific impulse in turbofan engines with losses. oblique shock with internal compression inside the lip provides an added benefit of reduced drag from the cowling. Axisymmetric diffuser designs are popular for pod-mounted engine installations. Figure 2.10 conceptually illustrates a typical arrangement, where the conditions correspond to (a) ideal shock-free operation, (b) supersonic flow up to inlet lip followed by subsonic flow behind it, (c) flight Mach number increased to critical so that a normal shock stands just at the lip, and (d) back pressure adjusted so that the shock stands at the throat are shown in the diagram. Flow areas are denoted by A with appropriate sub- scripts. Figure 2.11 provides off-design performance characteristics of the simple internal compression inlet described in Fig. 2.10 due to varying airflow mass. When flow is supersonic up to the throat, the shock moves downstream into the divergent portion of the throat. This mode of operation is shown for M 0 = 3. For lower flow Mach numbers, the bow shock remains in front of the inlet. The most advantageous operating point is just above critical as marked by the circles in Fig. 2.11. External compression inlets do not face complications from starting and stopping, and hence their behavior is simpler. Characteristics for an external compression inlet are shown in Fig. 2.12. The temperature ratio across a fan or compressor stage depends on the tangential Mach number of the rotor, M T , axial flow Mach number, M b or M a , and flow geometry as dictated by the blade configuration. Hence, parameters such as t s for the stage can be correlated as a function of M T and M a . This also implies that the stage efficiency h s is a function only of M T , M a and flow geometry, and the stage pressure ratio p s = p s (M a , M T ) if the Reynolds number is large enough, in the range of 3 × 10 5 , based on blade chord. Figure 2.13 illustrates the performance characteristics of a fan stage without inlet guide vanes for high axial Mach AIRCRAFT POWER PLANT 29 FIGURE 2.10 Inlet arrangement (a) isentropic diffusion for M < 1, (b) operation with shock ahead of lip, (c) flight Mach increased to critical, (d) shock at throat (Kerrebrock, 1992). A 0 A c A t A 0 c A A t M 0 M 0 1 1 ( a ) ( b ) A 0 A c A t A 0 A c A t A n Variable nozzle M 0 M 0 1 1 ( c ) ( d ) numbers. A low tangential Mach number helps minimize noise; supersonic tip speed yields a higher pressure ratio. Interesting items may be observed in the maps. At a given speed, as the mass flow reduces, pressure ratio rises until it reaches a bound where the flow becomes unsteady, as indicated by the stall line. Pressure ratio is virtually unchanged by the mass flow at low corrected speeds due to the absence of inlet guide vanes. As N√q increases, the constant speed characteristics become steeper. Multistage compressors consist of a number of stator and rotor stages placed in series on a single shaft. Hence they operate at the same mass flow and speed. Flow area reduces pro- gressively in the stages in order to maintain axial flow velocity, and may be accomplished by reducing the tip radius, increasing the root radius, or both simultaneously. The reduced tip radius decreases the tangential Mach number, reduces air temperature rise, and lowers the pressure ratio of downstream stages. The blade height is shorter when the root radius is increased, so tip clearances are more difficult to control. Stress in supporting disks below the blades also rises. Performance map of an HP ratio compressor is shown in Fig. 2.14. The discussion on compressors relates to turbines in several ways, except for two spe- cial items: (a) increased gas temperature at turbine inlet and (b) falling pressures as flow progresses through a turbine, as opposed to rising pressures in a compressor. High gas temperature leads to lower tangential Mach numbers for turbine blades than for compressor 30 APPLICATIONS FIGURE 2.11 Off-design performance of internal compression inlet (Kerrebrock, 1992). FIGURE 2.12 Off-design performance of external compression inlet (Kerrebrock, 1992). blades, relatively easing the aerodynamic problems. Also, the falling pressure in turbines thins the boundary layers to reduce separation concerns. Compressor efficiency has a stronger impact on the overall engine system than turbine efficiency. Still, high-bypass turbofan engines rely heavily on turbine efficiency. As noted before, an increased turbine inlet temperature improves thermal efficiency, but generous provisions for cooling must be made. As a consequence, the previous definition of efficiency needs modification. The ratio of actual turbine work to the total airflow, including cooling and ideal work that would be attained in expanding that flow through the defined pressure range, defines the turbine efficiency. Cooling flow may also be assumed to expand through the same pressure differential as the primary flow. Cooling flow impacts the turbine efficiency in multiple ways. Cooling air exiting from the blades causes a higher AIRCRAFT POWER PLANT 31 FIGURE 2.13 Highly loaded fan stage performance map—tangential Mach 0.96 (upper); tangential Mach 1.5 (lower). level of drag. It also suffers a pressure loss while traversing the cooling passage, so it has a lower stagnation pressure when mixed with the main downstream flow for a given t t . Note that the entropy of the total flow increases due to the heat transfer from the hot primary flow to the cooling flow. Empirical representation of turbine efficiency in terms of corrected parameters follows on similar lines as that for a compressor. The corrected speed N/√q indicates the tangential Mach number, where q is the inlet stagnation temperature divided by the standard reference temperature and N is the physical rotor speed. Corrected weight flow Wd/√q represents the axial Mach number. Figure 2.15 provides details of the performance characteristics for a typical, single-stage 50 percent midradius reaction turbine. Because gas mass flow is mostly independent of speed for p t > 2.5, parameter (Wd/√q)/(N/√q) is used for the abscissa. All speed characteristics then compress into a single curve, so the turbine mass 32 APPLICATIONS FIGURE 2.14 Compressor performance map. FIGURE 2.15 Turbine performance map. [...]... provided in Fig 2. 1, matching of the compressor, combustor, and turbine modules implies satisfaction of the following relationships (Kerrebrock, 19 92) Nt = Nc, or Nc N = t θ1 2 Tt 2 Tt1 (2. 21) W2 = (1 + f )W1 or W θ p W2 θ = (1 + f ) 1 1 t1 δ 2 A2 2 δ1 A1 pt 2 Tt 2 A1 Tt1 A2 (2. 22) W1cpc(Tt7 − Tt1) = W2cpt(Tt2 − Tt3) or 1− c pc Tt 3 Tt1  Tt 7  = −1 Tt 2 (1 + f )c pt Tt 2  Tt1    (2. 23) f, Tt2, and Tt7... T T hf = t2 − t7 c pTt1 Tt1 Tt1 (2. 24) Turbine nozzles are usually choked at full power Then (W2 /A2d2)√d2 has a unique value as determined by the turbine nozzle geometry Equation (2. 22) may then be expressed in terms of pt7 /pt1 as a function of (W1/A1d1)√d1 and Tt2 /Tt1 pt 7  (1 + f )( A1/ A2 )  W1 θ1 =  pt1  π (W θ / A δ  A1δ1  b 2 2 2 2 Tt 2 Tt1 (2. 25) 34 APPLICATIONS FIGURE 2. 16 Gas generator... W2.5 θ = (1 + f ) 0.5 1 t1 δ 2. 5 A2.5 2. 5 δ1 A0.5 pt 2. 5 (2. 27) Tt 2. 5 A0.5 Tt1 A2.5 (2. 28) AIRCRAFT POWER PLANT 35 Because of the bypass, W1/W0.5 = 1 + α Either the fan nozzle area or the pressure ratio of the LP compressor and the nozzle area of the LP turbine must be known The power expression then takes the form 1− (1 + α )c pc Tt1  Tt 0.5  Tt 3 = − 1 Tt 2. 5 (1 + f )c pt Tt 2. 5  Tt1   (2. 29)... (2. 21) to (2. 25), except for the substitution of a gas generator in place of the combustor To illustrate, consider a turbofan engine with separate fan and core nozzles Station number 2. 5 is added in Fig 2. 1 between the high- and low-pressure turbines and number 0.5 just aft of the fan in the core stream Corresponding to Eqs (2. 21) and (2. 22) the expressions are N1t = N1c or N1c N = 1t θ1 θ 2. 5 Tt 2. 5... are FIGURE 2. 29 LARZAC turbofan engine (Leinhos, Schmid, and Fottner, 20 00) 47 AIRCRAFT POWER PLANT Sensor 3 φ = 116° Sensor 2 φ = 044° Vcross,rel = 1.0 Sensor 3 φ = 116° V = 1.0 Sensor 2 cross,rel φ = 044° φ, nLPC φ, nLPC Pt,loc Pt,mom Sensor 4 φ = 188° Sensor 1 φ = 3 32 Sensor 5 φ = 26 0° Pt,loc Pt,mom 1.03 Sensor 4 1. 02 φ = 188° 1.00 0.99 0.97 0.96 0.94 0.93 Sensor 1 φ = 3 32 1.03 1. 02 1.00 0.99... the midspeed range, but they do not grow into a rotating stall 48 APPLICATIONS 95 2. 2 2. 1 89 Pressure ratio 2 CO COUNTER 1.9 84 80 1.8 76 1.7 95 72 89 1.6 nLPC 84 1.5 1.4 72 300 76 79.5 Tt2 rel 81.5 350 400 450 Corrected mass flow, kg K/s.bar FIGURE 2. 31 Low-pressure compressor map (Leinhos, Schmid, and Fottner, 20 00) 2. 11 ATTACHMENT WITH AIRCRAFT Installation under the wings is perhaps the most popular... can adversely affect high-bypass turbofan engines And the increased possibility of foreign object ingestion from the ground must PSD × 10−8 3 2 0 20 LPC revs −40 1 0 −1 −0.8 −0.6 −0.4 −0 .2 0 0 .2 0.4 f/frotation 0.6 0.8 1 FIGURE 2. 32 Power spectral density, 2nd harmonic spatial Fourier transformation (Leinhos, Schmid, and Fottner, 20 00) 49 AIRCRAFT POWER PLANT FIGURE 2. 33 European airbus A340 (Courtesy:... Power 4(3) :23 6 24 4, 1988 Filipenko, V G., “Experimental investigation of flow distortion effects on the performance of radial discrete-passage diffusers,” Ph.D Thesis, MIT Press, Cambridge, Mass., 1991 Federal Register 38, no 136, pp 19088–19103, 1973 Federal Register 41, no 159, pp 34 722 –34 725 , 1976 Federal Register 47, no 25 1, pp 584 62 58474, 19 82 Federal Register 55, no 155, pp 328 56– 328 66, 1990... Turbines, 2d ed., MIT Press, Cambridge, Mass., 19 92 Leinhos, D C., Schmid, N R., and Fottner, L., “Influence of transient inlet distortions on the instability inception of a low-pressure compressor in a turbofan engine,” ASME Paper # 20 00-GT-505, New York, 20 00 McDougall, N M., Cumpsty, N A., and Hynes, T P., “Stall inception in axial compressors,” ASME Journal of Turbo- Machinery 1 12: 116– 125 ,1990 National... technologies for future turbofans,” ASME Paper # 95-GT-4 02, New York, 1995 Tryfonidis, M., Etchevers, O., Paduano, J D., Epstein, A H., and Hendricks, G J., “Prestall behavior of several high speed compressors,” ASME Journal of Turbo- Machinery 117(1): 62 80, 1995 Wadia, A R and James, F D., “F110-GE-1 32: Enhanced power through low-risk derivative technology,” ASME Paper # 20 00-GT-578, New York, 20 00 BIBLIOGRAPHY . relationships (Kerrebrock, 19 92) N t = N c , or (2. 21) W 2 = (1 + f )W 1 or (2. 22) W 1 c pc (T t7 − T t1 ) = W 2 c pt (T t2 − T t3 ) or (2. 23) f, T t2 , and T t7 are related by (2. 24) Turbine nozzles. (W 1 /A 1 d 1 )√d 1 and T t2 /T t1 . (2. 25) p p fAA WA W A T T t t b t t 7 1 12 222 2 11 11 2 1 (1 )( ) ( = +         / / πθδ θ δ hf cT T T T T pt t t t t1 2 1 7 1 =− 1 (1 ) 1 3 2 1 2 7 1 −= + −       T T c fc T T T T t t pc pt t t t t W A f Wp Ap T T A A t t t t 2 22 2 111 11. ) 1 3 2 1 2 7 1 −= + −       T T c fc T T T T t t pc pt t t t t W A f Wp Ap T T A A t t t t 2 22 2 111 11 2 2 1 1 2 (1 ) δ θ θ δ =+ N NT T c tt t θθ 12 2 1 = AIRCRAFT POWER PLANT 33 Assuming a value of T t2 /T t1 = 6.0, 90 percent turbine efficiency,

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