GasTurbine Engineering HandbookSecond Edition phần 5 potx

//INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 313 ± [275±318/44] 29.10.2001 4:00PM The losses as mentioned earlier can be further described: 1. Disc friction loss. This loss is from skin friction on the discs that house the blades of the compressors. This loss varies with different types of discs. 2. Incidence loss. This loss is caused by the angle of the air and the blade angle not being coincident. The loss is minimum to about an angle of Æ4  , after which the loss increases rapidly. 3. Blade loading and profile loss. This loss is due to the negative velocity gradients in the boundary layer, which gives rise to flow separation. 4. Skin friction loss. This loss is from skin friction on the blade surfaces and on the annular walls. 5. Clearance loss. This loss is due to the clearance between the blade tips and the casing. 6. Wake loss. This loss is from the wake produced at the exit of the rotary. 7. Stator profile and skin friction loss. This loss is from skin friction and the attack angle of the flow entering the stator. 8. Exit loss. This loss is due to the kinetic energy head leaving the stator. Figure 7-33 shows the various losses as a function of flow. Note that the compressor is more efficient as the flow nears surge conditions. Figure 7-34 also shows a typical axial-flow compressor map. Note the steepness of the constant speed lines as compared with a centrifugal compressor. The axial- flow compressor has a much smaller operating range than its counterpart in the centrifugal compressor. Stall Analysis of an Axial-Flow Compressor A typical vibration analyis identified a surge condition in the fifth stage of an axial compressor. A pressure transducer with a voltage output was used to obtain the frequency spectra. In the first four stages of the compressor, no outstanding vibration amplitudes were recorded. A signal was noted at 48N (N being the running speed), but the amplitude was not high, and it did not fluctuate. A measurement at the low-pressure bleed chamber taken from the fourth stage showed similar characteristics. The compressor high-pressure bleed chamber occurs after the eighth stage. A measurement at this chamber showed a high, fluctuating 48N signal. As there are 48 blades on the fifth- stage wheel, a problem in the fifth stage was suspected. However, above the fifth stage are blade rows of 86N (2  48N), so the analysis was not clearcut. It was found that the measurement at the high-pressure bleed chamber Axial-Flow Compressors 313 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 314 ± [275±318/44] 29.10.2001 4:00PM showed only a very small 86N amplitude compared to the high amplitude of the 48N frequency. Since blade rows of 86 blades were closer to the high- pressure bleed chamber, the expected high signal should have been 86N compared to 48N under normal operating conditions. This high amplitude Figure 7-33. Losses in an axial-flow compressor stage. Figure 7-34. Performance map of an axial-flow compressor. 314 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 315 ± [275±318/44] 29.10.2001 4:00PM of 48N indicated that it was the fifth stage that caused the high, fluctuating signal; thus, a stall condition in that section was probable. Figures 7-35, 7-36, 7-37, and 7-38 show the spectrum at speeds of 4100, 5400, 8000, and 9400 rpm. At 9400 rpm, the second and third harmonics of 48N were also very predominant. Next, the fifth-stage pressure was measured. Once again, a high amplitude at 48N was found. However, a predominant reading was also observed at 1200 Hz frequency. Figures 7-39 and 7-40 show the largest amplitudes at speeds of 5800 and 6800 rpm, respectively. At the compressor exit, predominate frequencies of 48N existed up to speeds of 6800 rpm. At 8400 rpm, the 48N and 86N frequencies were of about equal magnitudesÐthe only signal where the 48N and 86N frequen- cies were the same. The pressure was measured from a static port in the Figure 7-35. High-pressure bleed chamberÐ4100 rpm. Figure 7-36. High-pressure bleed chamberÐ5400 rpm. Axial-Flow Compressors 315 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 316 ± [275±318/44] 29.10.2001 4:00PM Figure 7-37. High-pressure bleed chamberÐ8000 rpm. Figure 7-38. High-pressure bleed chamberÐ9400 rpm. Figure 7-39. Fifth-stage bleed pressureÐ5800 rpm. 316 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 317 ± [275±318/44] 29.10.2001 4:00PM chamber. All other pressures were measured from the shroud, thus indicat- ing the phenomena occurred at the blade tip. Since the problem was isolated to the fifth stage, the conclusion was that the stall occurred at the fifth-stage rotor tip. A subsequent inspection confirmed the suspicion when cracks at the blade hubs were noticed. Bibliography Boyce, M.P., ``Transonic Axial-Flow Compressor,'' ASME Paper No. 67-GT-47. Boyce. M.P., ``Fluid Flow Phenomena in Dusty Air,'' (Thesis), University of Oklahoma Graduate College, 1969, p. 18. Boyce. M.P., Schiller, R.N., and Desai, A.R., ``Study of Casing Treatment Effects in Axial-flow Compressors,'' ASME Paper No. 74-GT-89. Boyce, M.P., ``Secondary Flows in Axial-flow Compressors with Treated Blades,'' AGARD-CCP-214 pp. 5-1 to 5-13, 1974. Carter, A.D.S., ``The Low-Speed Performance of Related Aerofoils in Cascade,'' Rep. R.55, British NGTE, September, 1949. Giamati, C.C., and Finger, H.B., ``Design Velocity Distribution in Meridional Plane,'' NASA SP 36, Chapter VIII (1965), p. 255. Graham, R.W. and Guentert, E.C., ``Compressor Stall and Blade Vibration,'' NASA SP 36, (1965) Chapter XI, p. 311. Hatch. J.E., Giamati, C.C., and Jackson, R.J., ``Application of Radial Equili- brium Condition to Axial-Flow Turbomachine Design Including Considera- tion of Change of Enthropy with Radius Downstream of Blade Row,'' NACA RM E54A20 (1954). Herrig, L.J., Emery, J.C., and Erwin, J.R., ``Systematic Two-Dimensional Cascade Tests of NACA 65 Series Compressor Blades at Low Speed,'' NACA R.M. E 55Hll (1955). Figure 7-40. Fifth-stage bleed pressureÐ6800 rpm. Axial-Flow Compressors 317 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 318 ± [275±318/44] 29.10.2001 4:00PM Holmquist, L.O., and Rannie, W.D., ``An Approximate Method of Calculating Three-Dimensional Flow in Axial Turbomachines'' (Paper) Meeting Inst. Aero. Sci., New York, January 24  ±28, 1955. Horlock, J.H., ``Axial Flow Compressors,'' Robert E. Krieger Publishing Company, 1973. Koller, U., Monig, R., Kosters, B., Schreiber, H-A, 1999, ``Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines. Part I: Design and Optimization,'' ASME 99-GT-95. Lieblein, S., Schwenk, F.C., and Broderick, R.L., ``Diffusion Factor for Estim- ating Losses and Limiting Blade Loading in Axial-Flow Compressor Blade Elements,'' NACA RM #53001 (1953). Mellor, G., ``The Aerodynamic Performance of Axial Compressor Cascades with Application to Machine Design,'' (Sc. D. Thesis), M.I.T. Gas Turbine Lab, M.I.T. Rep. No. 38 (1957). Stewart, W.L., ``Investigation of Compressible Flow Mixing Losses Obtained Downstream of a Blade Row,'' NACA RM E54120 (1954). 318 Gas Turbine Engineering Handbook //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 319 ± [319±336/18] 29.10.2001 4:01PM 8 Radial-Inflow Turbines The radial-inflow turbine has been in use for many years. It first appeared as a practical power-producing unit in the hydraulic turbine field. Basically a centrifugal compressor with reversed flow and opposite rotation, the radial- inflow turbine was the first used in jet engine flight in the late 1930s. It was considered the natural combination for a centrifugal compressor used in the same engine. Designers thought it easier to match the thrust from the two rotors and that the turbine would have a higher efficiency than the com- pressor for the same rotor because of the accelerating nature of the flow. The performance of the radial-inflow turbine is now being investigated with more interest by the transportation and chemical industries: in trans- portation, this turbine is used in turbochargers for both spark ignition and diesel engines; in aviation, the radial-inflow turbine is used as an expander in environmental control systems; and in the petrochemical industry, it is used in expander designs, gas liquefaction expanders, and other cryogenic sys- tems. Radial-inflow turbines are also used in various small gas turbines to power helicopters and as standby generating units. The radial-inflow turbine's greatest advantage is that the work produced by a single stage is equivalent to that of two or more stages in an axial turbine. This phenomenon occurs because a radial-inflow turbine usually has a higher tip speed than an axial turbine. Since the power output is a function of the square of the tip speed (PU 2 ) for a given flow rate, the work is greater than in a single-stage axial-flow turbine. The radial-inflow turbine has another advantage: its cost is much lower than that of a single or multistage axial-flow turbine. The radial-inflow turbine has a lower turbine efficiency than the axial-flow turbine; how- ever, lower initial costs may be an incentive to choosing a radial-inflow turbine. 319 //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 320 ± [319±336/18] 29.10.2001 4:01PM The radial-inflow turbine is especially attractive when the Reynolds num- ber R e  UD=becomes low enough (R e  10 5 À10 6 ) that the efficiency of the axial-flow turbine is below that of a radial-inflow turbine, as shown in Figure 8-1. The effect of specific speed N s  N  Q p =H 3=4 ÀÁ and specific diameter D s  DH 1=4 =  Q p ÀÁ on the efficiency of a turbine is shown in Figure 8-2. Radial-inflow turbines are more efficient at a Reynolds number between 10 5 and 10 6 and specific speeds below N s  10. Description The radial-inflow turbine has many components similar to those of a centrifugal compressor. However, the names and functions differ. There are two types of radial-inflow turbines: the cantilever radial-inflow turbine and the mixed-flow radial-inflow turbine. Cantilever blades are often two- dimensional and use nonradial inlet angles. There is no acceleration of the Figure 8-1. Influence of Reynolds number on turbine stage efficiency. 320 Gas Turbine Engineering Handbook //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 321 ± [319±336/18] 29.10.2001 4:01PM flow through the rotor, which is equivalent to an impulse or low-reaction turbine. The cantilever-type radial-inflow turbine is infrequently used because of low efficiency and production difficulties. This type of turbine also has rotor blade flutter problems. The radial-inflow turbine can be the cantilever type as shown in Figure 8-3, or the mixed-flow type as shown in Figure 8-4. The mixed-flow radial-inflow turbine is a widely used design. Figure 8-5 shows the components. The scroll or collector receives the flow from a single duct. The scroll usually has a decreasing cross-sectional area around the circumference. In some designs the scrolls are used as vaneless nozzles. The nozzle vanes are omitted for economy to avoid erosion in turbines where fluid or solid particles are trapped in the air flow. Frictional flow losses in vaneless designs are greater than in vaned nozzle designs because of the nonuniformity of the flow and the greater distance the accelerating air flow must travel. Vaneless nozzle configurations are used extensively in turbochargers where efficiency is not important, since in most engines the amount of energy in the exhaust gases far exceeds the energy needs of the turbocharger. Figure 8-2. N s D s diagram for a turbine stage. Efficiency is on a total-to-total basis; that is, it is related to inlet and exit stagnation conditions. Diagram values are suitable for machine Reynolds number R e ! 10 6 . (Balje, O.E., ``A Study of Reynolds Number Effects in Turbomachinery,'' Journal of Engineering for Power, ASME Trans., Vol. 86, Series A, p. 227.) Radial-Inflow Turbines 321 //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 322 ± [319±336/18] 29.10.2001 4:01PM Figure 8-3. Cantilever-type radial-inflow turbine. Figure 8-4. Mixed-flow-type radial-inflow turbine. 322 Gas Turbine Engineering Handbook [...]... isentropic efficiency and obtained by combining the previous two equations  1À is ˆ or P 05 Poi poly À1 P 05 1À Poi À1 4 poly   À1 5 P 05 1n 1 À is ‡ is Poi     ˆ À1 P 05 1n Poi …8-10† …8-11† //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 328 ± [319±336/18] 29.10.2001 4:01PM 328 Gas Turbine Engineering Handbook Figure 8-9 Enthalpy-entropy diagram for a multistage turbine The relationship... Flow Performance and Modeling of Radial Inflow Turbines,'' IMechE, Paper No a4 05/ 017 Balje, O.E., ``A Contribution to the Problem of Designing Radial Turbomachines,'' Trans ASME, Vol 74, p 451 (1 952 ) Benisek, E., 1998 ``Experimental and Analytical Investigation for the Flow Field of a Turbocharger Turbine,'' IMechE, Paper No 055 4/027/98 Benson, R.S., ``A Review of Methods for Assessing Loss Coefficients... [319±336/18] 29.10.2001 4:01PM 334 Gas Turbine Engineering Handbook Figure 8-14 Meridional velocity distribution from hub to shroud along the blade length Figure 8- 15 Relative velocity distribution of suction and pressure side along the blade length //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 3 35 ± [319±336/18] 29.10.2001 4:01PM Radial-Inflow Turbines 3 35 Figure 8-16 Boundary-layer formation... Turbine Engineering Handbook Total pressure decrease in the nozzle and outlet diffuser are only from frictional losses In an ideal nozzle or diffuser the total pressure drop is zero Isentropic efficiency is defined as the ratio of the actual work to the isentropic enthalpy decrease, which is the expansion from the inlet total pressure to the outlet total pressure is ˆ h0i À h 05 h0i À h05is …8 -5 The... Characteristics of Radial Turbines,'' SAE Paper 660 754 , October, 1966 Shepherd, D.G., Principles of Turbomachinery, New York, The Macmillan Company, 1 956 Vavra, M.H., ``Radial Turbines,'' Pt 4., AGARD-VKI Lecture Series on Flow in Turbines (Series No 6), March, 1968 Vincent, E.T., ``Theory and Design of Gas Turbines and Jet Engines,'' New York, McGraw-Hill, 1 950 Wallace, F.J., and Pasha, S.G.A., 1972, Design,... turbines consist of more than one stage, the front stages are usually impulse (zero reaction) and the later stages have about 50 % reaction The impulse stages produce about twice the output of a comparable 50 % reaction stage, while the efficiency of an impulse stage is less than that of a 50 % reaction stage The high temperatures that are now available in the turbine section are due to improvements of the metallurgy... //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 336 ± [319±336/18] 29.10.2001 4:01PM 336 Gas Turbine Engineering Handbook Bibliography Abidat, M.I., Chen, H., Baines, N.C., and Firth, M.R., 1992 ``Design of a Highly Loaded Mixed Flow Turbine,'' Proc Inst Mechanical Engineers,  Journal Power 8 Energy, 206: 95 107 Arcoumanis, C., Martinez-Botas, R.F., Nouri, J.M., and Su, C.C., 1997 ``Performance and Exit... defined as the ratio of the total head to the total head plus the absolute exit velocity ˆ H‡ H À1 2 2 V4 Á …8-3† //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 3 25 ± [319±336/18] 29.10.2001 4:01PM Radial-Inflow Turbines 3 25 The relative proportions of energy transfers obtained by a change of static and dynamic pressure are used to classify turbomachinery The parameter used to describe this... Turbines,'' International Journal of Mechanical Sciences, 12 (1970),  pp 9 05 932 Karamanis, N Martinez-Botas, R.F., Su, C.C., ``Mixed Flow Turbines: Inlet and Exit flow under steady and pulsating conditions,'' ASME 2000-GT-470 Knoernschild, E.M., ``The Radial Turbine for Low Specific Speeds and Low Velocity Factors,'' Journal of Engineering for Power, Trans ASME, Serial A,  Vol 83, pp 1±8 (1961) Rodgers,... Gas Turbine Engineering Handbook Figure 8-12 Exit velocity diagrams for a radial-inflow turbine 6 7 Incidence loss This loss is minimal at design conditions but will increase with off-design operation These losses vary from about 1 ¤2±11¤2% Exit loss The fluid leaving a radial-inflow turbine constitutes a loss of about one-quarter of the total exit head This loss varies from about  2 5% The external . NACA RM E54A20 (1 954 ). Herrig, L.J., Emery, J.C., and Erwin, J.R., ``Systematic Two-Dimensional Cascade Tests of NACA 65 Series Compressor Blades at Low Speed,'' NACA R.M. E 55 Hll (1 955 ). Figure. previous two equations  is  1 À P 05 P oi   poly À1  1 À P 05 P oi À1  8-10 or  poly  1n 1 À is   is P 05 P oi  À1  45  À 1   1n P 05 P oi  8-11 Figure 8-8. Relationship. Meridional Plane,'' NASA SP 36, Chapter VIII (19 65) , p. 255 . Graham, R.W. and Guentert, E.C., ``Compressor Stall and Blade Vibration,'' NASA SP 36, (19 65) Chapter XI, p. 311. Hatch. J.E., Giamati,