Gas Turbine Engineering Handbook 2 Episode 8 potx

//SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 335 ± [319±336/18] 29.10.2001 4:01PM be an inertia type to remove most of the larger particles. The exducer fatigue problem is serious in a radial turbine, although it varies with blade loading. The exducer should be designed so that it has a natural frequency four times above the blade passing frequency. Noise problems in a radial-inflow turbine come from four sources: 1. Pressure fluctuations 2. Turbulence in boundary layers 3. Rotor wakes 4. External noise Severe noise can be generated by pressure fluctuations. This noise is created by the passage of the rotor blades through the varying velocity fields produced by the nozzles. The noise generated by turbulent flow in boundary layers occurs on most internal surfaces. However, this noise source is negligible. Noise generated from rotor flow is due to the wakes generated downstream in the diffuser. The noise generated by the rotor exducer is considerable. The noise consists of high-frequency components and is proportional to the eighth power of the relative velocity between the wake and the free stream. Outside noise sources are many, but the gear box is the primary source. Intense noise is generated by pressure fluctuations that result from tooth interactions in gearboxes. Other noises may result from out-of-balance conditions and vibra- tory effects on mechanical components and casings. Figure 8-16. Boundary-layer formation in a radial-flow impeller. Radial-Inflow Turbines 335 //SYS21///INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 8.3D ± 336 ± [319±336/18] 29.10.2001 4:01PM 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. ``Per- formance and Exit Flow Characteristics of Mixed Flow Turbines,'' Interna- tional Journal of Rotating Machinery, 3(4): 277  ±293. Baines, N.A., Hajilouy-Benisi, A., and Yeo, J.H., 1994. ``The Pulse Flow Perform- ance and Modeling of Radial Inflow Turbines,'' IMechE, Paper No. a405/017. Balje, O.E., ``A Contribution to the Problem of Designing Radial Turbo- machines,'' Trans. ASME, Vol. 74, p. 451 (1952). Benisek, E., 1998. ``Experimental and Analytical Investigation for the Flow Field of a Turbocharger Turbine,'' IMechE, Paper No. 0554/027/98. Benson, R.S., ``A Review of Methods for Assessing Loss Coefficients in Radial Gas Turbines,'' International Journal of Mechanical Sciences, 12 (1970), pp. 905  ±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, C., ``Efficiency and Performance Characteristics of Radial Turbines,'' SAE Paper 660754, October, 1966. Shepherd, D.G., Principles of Turbomachinery, New York, The Macmillan Company, 1956. 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, 1950. Wallace, F.J., and Pasha, S.G.A., 1972, Design, Construction and Testing of a Mixed-Flow Turbine. Winterbone, D.E., Nikpour, B., and Alexander, G.L., 1990, ``Measurement of the Performance of a Radial Inflow Turbine in Conditional Steady and Unsteady Flow,'' IMechE, Paper No. 0405/015. 336 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 337 ± [337±369/33] 29.10.2001 4:02PM 9 Axial-Flow Turbines Axial-flow turbines are the most widely employed turbines using a compres- sible fluid. Axial-flow turbines power most gas turbine unitsÐexcept the smaller horsepower turbinesÐand they are more efficient than radial-inflow turbines in most operational ranges. The axial-flow turbine is also used in steam turbine design; however, there are some significant differences between the axial-flow turbine design for a gas turbine and the design for a steam turbine. Steam turbine development preceded the gas turbine by many years. Thus, the axial-flow turbine used in gas turbines is an outgrowth of steam turbine technology. In recent years the trend in high turbine inlet temperatures in gas turbines has required various cooling schemes. These schemes are described in detail in this chapter with attention to both cooling effectiveness and aerodynamic effects. Steam turbine development has resulted in the design of two turbine types: the impulse turbine and the reaction turbine. The reaction turbine in most steam turbine designs has a 50% reaction level that has been found to be very efficient. This reaction level varies considerably in gas turbines and from hub to tip in a single-blade design. Axial-flow turbines are now designed with a high work factor (ratio of stage work to square of blade speed) to obtain lower fuel consumption and reduce the noise from the turbine. Lower fuel consumption and lower noise requires the design of higher by-pass ratio engines. A high by-pass ratio engine requires many turbine stages to drive the high-flow, low-speed fan. Work is being conducted to develop high-work, low-speed turbine stages that have high efficiencies. Turbine Geometry The axial-flow turbine, like its counterpart the axial-flow compressor, has flow, which enters and leaves in the axial direction. There are two types of axial 337 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 338 ± [337±369/33] 29.10.2001 4:02PM turbines: (1) impulse type, and (2) reaction type. The impulse turbine has its entire enthalpy drop in the nozzle; therefore it has a very high velocity entering the rotor. The reaction turbine divides the enthalpy drop in the nozzle and the rotor. Figure 9-1 is a schematic of an axial-flow turbine, also depicting the distribution of the pressure, temperature, and the absolute velocity. Most axial flow 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 compar- able 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 of the blades in the turbines. Devel- opment of directionally solidified blades as well as the new single crystal blades, with the new coatings, and the new cooling schemes, are responsible for the increase in firing temperatures. The high-pressure ratio in the com- pressor also causes the cooling air used in the first stages of the turbine to be very hot. The temperatures leaving the gas turbine compressor can reach as high as 1200  F (649  C). Thus the present cooling schemes need revisiting, Combustor Nozzle Blades NB B BB BNN N HPT o, o, o V abs PT s, s Figure 9-1. Schematic of an axial flow turbine flow characteristics. 338 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 339 ± [337±369/33] 29.10.2001 4:02PM and the cooling passages are in many cases also coated. The cooling schemes are limited in the amount of air they can use, before there is a negating an effort in overall thermal efficiency due to an increase in the amount of air used in cooling. The rule of thumb in this area is that if you need more than 8% of the air for cooling you are loosing the advantage from the increase in the firing temperature. The new gas turbines being designed, for the new millennium, are inves- tigating the use of steam as a cooling agent for the first and second stages of the turbines. Steam cooling is possible in the new combined cycle power plants, which is the base of most of the new high performance gas turbines. Steam, as part of the cooling as well as part of the cycle power, will be used in the new gas turbines in the combined cycle mode. The extra power obtained by the use of steam is the cheapest MW/$ available. The injection of about 5% of steam by weight of air amounts to about 12% more power. The pressure of the injected steam must be at least 40 Bar above the compressor discharge. The way steam is injected must be done very carefully so as to avoid compressor surge. These are not new concepts and have been used and demonstrated in the past. Steam cooling for example was the basis of the cooling schemes proposed by the team of United Technology and Stal-Laval in their conceptual study for the U.S. department study on the High Turbine Temperature Technology Program, which was investigating Firing Temperatures of 3000  F (1649  C), in the early 1980s. There are three state points within a turbine that are important when analyzing the flow. They are located at the nozzle entrance, the rotor entrance, and at the rotor exit. Fluid velocity is an important variable governing the flow and energy transfer within a turbine. The absolute velocity (V ) is the fluid velocity relative to some stationary point. Absolute velocity is important when analyzing the flow across a stationary blade such as a nozzle. When consider- ing the flow across a rotating element or rotor blade, the relative velocity W is important. Vectorially, the relative velocity is defined W *  V * À U * 9-1 where U is the tangential velocity of the blade. This relationship is shown in Figure 9-2. The subscript z used in Figure 9-2 denotes the axial velocity, while  denotes the tangential component. Two angles are defined in Figure 9-2. The first angle is the air angle , which is defined with respect to the tangential direction. The air angle  represents the direction of the flow leaving the nozzle. In the rotor, the air angle  represents the angle of the absolute velocity leaving the rotor. The blade angle  is the angle the relative velocity makes with the tangential Axial-Flow Turbines 339 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 340 ± [337±369/33] 29.10.2001 4:02PM direction. It is the angle of the rotor blade under ideal conditions (no incidence angle). Degree of Reaction The degree of reaction in an axial-flow turbine is the ratio of change in the static enthalpy to the change in total enthalpy R  h 1 À h 4 h 01 À h 04 9-2 A rotor with a constant radius and an axial velocity constant throughout can be written R  W 4 2 À W 3 2  V 3 2 À V 4 2 W 4 2 À W 3 2  9-3 Figure 9-2. Stage nomenclature and velocity triangles. FPO 340 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 341 ± [337±369/33] 29.10.2001 4:02PM From the previous relationship, it is obvious that for a zero-reaction turbine (impulse turbine) the relative exit velocity is equal to the relative inlet velocity. Most turbines have a degree of reaction between 0 and 1; negative reaction turbines have much lower efficiencies and are not usually used. Utilization Factor In a turbine, not all energy supplied can be converted into useful workÐ even with an ideal fluid. There must be some kinetic energy at the exit that is discharged due to the exit velocity. Thus, the utilization factor is defined as the ratio of ideal work to the energy supplied E  H id H id  V 4 2 2g 9-4 and it can be written in terms of the velocity for a single rotor with constant radius E  V 3 2 À V 4 2 W 4 2 À W 3 2  V 3 2 W 4 2 À W 3 2  9-5 Work Factor In addition to the degree of reaction and the utilization factor, another parameter used to determine the blade loading is the work factor À  Áh  U 2 9-6 and it can be written for a constant radius turbine À  V 3 À V 4 U 9-7 The previous equation can be further modified for the maximum utiliza- tion factor where the absolute exit velocity is axial and no exit swirl exists À  V 3 U 9-8 Axial-Flow Turbines 341 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 342 ± [337±369/33] 29.10.2001 4:02PM The value of the work factor for an impulse turbine (zero reaction) with a maximum utilization factor is two. In a 50% reaction turbine with a max- imum utilization factor the work factor is one. In recent years the trend has been toward high work factor turbines. The high work factor indicates that the blade loading in the turbine is high. The trend in many fan engines is toward a high by-pass ratio for lower fuel consumption and lower noise levels. As the by-pass ratio increases, the relative diameter of the direct-drive fan turbine decreases, resulting in lower blade tip speeds. Lower blade tip speeds mean that with conventional work factors, the number of turbine stages increases. Considerable research is being conducted to develop turbines with high work factors, high blade loadings, and high efficiencies. Figure 9-3 shows the effect of turbine stage work and efficiency. This diagram indicates that efficiency drops consider- ably as the work factor increases. There is little information on turbines with work factors over two. Velocity Diagrams An examination of various velocity diagrams for different degrees of reaction is shown in Figure 9-4. These types of blade arrangements with varying degrees of reaction are all possible; however, they are not all prac- tical. Figure 9-3. Effect of stage work on efficiency. 342 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 343 ± [337±369/33] 29.10.2001 4:02PM Examining the utilization factor, the discharge velocity (V 4 2 =2), represents the kinetic energy loss or the unused energy part. For maximum utilization, the exit velocity should be at a minimum and, by examining the velocity diagrams, this minimum is achieved when the exit velocity is axial. This type of a velocity diagram is considered to have zero exit swirl. Figure 9-5 shows the various velocity diagrams as a function of the work factor and the turbine type. This diagram shows that zero exit swirl can exist for any type of turbine. Zero exit swirl diagram. In many cases the tangential angle of the exit velocity (V 4 ) represents a loss in efficiency. A blade designed for zero exit swirl (V 4  0) minimizes the exit loss. If the work parameter is less than two, this type of diagram produces the highest static efficiency. Also, the total effici- ency is approximately the same as the other types of diagrams. If À is greater than 2.0, stage reaction is usually negative, a condition best avoided. Impulse diagram. For the impulse rotor, the reaction is zero, so the relative velocity of the gas is constant, or W 3  W 4 . If the work factor is less than 2.0, the exit swirl is positive, which reduces the stage work. For this reason, an impulse diagram should be used only if the work factor is 2.0 or Figure 9-4. Turbine velocity triangles showing the effect of various degrees of reaction. Axial-Flow Turbines 343 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 9.3D ± 344 ± [337±369/33] 29.10.2001 4:02PM greater. This type of diagram is a good choice for the last stage because for À greater than 2.0, an impulse rotor has the highest static efficiency. Symmetrical diagram. The symmetrical-type diagram is constructed so that the entrance and exit diagrams have the same shape: V 3  W 4 and V 4  W 3 . This equality means that the reaction is R  0:5 9-9 If the work factor À equals 1.0, then the exit swirl is zero. As the work factor increases, the exit swirl increases. Since the reaction of 0.5 leads to a high total efficiency, this design is useful if the exit swirl is not counted as a loss as in the initial and intermediate stages. Impulse Turbine The impulse turbine is the simplest type of turbine. It consists of a group of nozzles followed by a row of blades. The gas is expanded in the nozzle, converting the high thermal energy into kinetic energy. This conversion can be represented by the following relationship: V 3   2Áh 0 p 9-10 The high-velocity gas impinges on the blade where a large portion of the kinetic energy of the moving gas stream is converted into turbine shaft work. Figure 9-5. Effect of diagram type and stage work factor on velocity diagram shape. 344 Gas Turbine Engineering Handbook [...]... (4 72 C), approximately 20  F (10 C) per year The (15 38 C) 28 00 26 00 Firing Temperature °F (°C) (1316°C) 24 00 Steam Cooling ( 120 4°C) 22 00 20 00 Advanced Air Cooling (9 82 C) 180 0 Convential Air Cooling 1600 Firing Temperature (760°C) 1400 RENE 77 GTD111 IN 733 GTD 111 DS U 500 Blade Metal Temperature GTD 111 SC GTD 111 SC 120 0 (5 38 C) 1000 1950 1960 1970 1 980 1990 20 00 YEAR Figure 9- 12 Firing temperature... ± 366 ± [337±369/33] 29 .10 .20 01 4:02PM 366 Gas Turbine Engineering Handbook The change in enthalpy is given by h2a ˆ h2s ‡ !V3 2 =2 …9 -20 † This loss is now to be recomputed for the rotor The off-design characteristics of a turbine are as important to define as the design-point characteristics Figure 9 -29 shows the effect of the speed-to- Figure 9 -27 Blade geometry loss Figure 9 - 28 Incidence angle loss... //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 3 62 ± [337±369/33] 29 .10 .20 01 4:02PM 3 62 Gas Turbine Engineering Handbook Table 9-1 Summary of Creep Life Experiments Time to 1% Creep Strain (hrs) Blade Cooling Design Strut design Film convection Transpiration Multiple small-hole Water cooled Steam cooled Based on Initial Conditions Based on Average Conditions 24 30 186 25 30 480 0 150 150 47,900 46,700... temperature increase with blade material improvement 20 10 //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 3 52 ± [337±369/33] 29 .10 .20 01 4:02PM 3 52 Gas Turbine Engineering Handbook importance of this increase can be appreciated by noting that an increase of 100 F (56 C) in turbine firing temperature can provide a corresponding   increase of 8 13% in output and 2 4% improvement in simple-cycle efficiency... NASA, TM X -21 76, 1971 //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 3 68 ± [337±369/33] 29 .10 .20 01 4:02PM 3 68 Gas Turbine Engineering Handbook Benign, F., Rust, H Jr., and Moffitt, T.P., ``Cold-Air Investigation of a Turbine with Transpiration-Cooled Stator Blades, IIIÐPerformance of Stator with Wire-Mesh Shell Blading,'' NASA, TM X -21 66, 1971 Brown, L.E., ``Axial Flow Compressor and Turbine Loss... base into two central //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 355 ± [337±369/33] 29 .10 .20 01 4:02PM Axial-Flow Turbines Figure 9-14 Strut insert blade Figure 9-15 Temperature distribution for strut insert design, °F (cooled) 355 //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 356 ± [337±369/33] 29 .10 .20 01 4:02PM 356 Gas Turbine Engineering Handbook Figure 9-16 Film and convection-cooled... exit flow Figure 9 -26 Growth of displacement and momentum thickness on an airfoil //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 365 ± [337±369/33] 29 .10 .20 01 4:02PM Axial-Flow Turbines 365 Table 9 -2 Turbine Loss Values in the Overall Stage Loss Mechanics Profile Endwall Secondary flow Rotor incidence Tip clearance Wheel disc Loss (%)  2 4  1 1 /2 4  1 2  1±3  1 1 /2 3  1 2 Tip clearance loss... from  ˆ 2: 5 …cot 2 ‡ cot 1 † sin2 2 …9- 18 The loss coefficient can now be computed  5 1=4 10 ‰…1 ‡ ! †…0:975 ‡ 0:075=AR† À 1Š!i !ˆ Re …9-19† where AR is the aspect ratio (h=c), ! is the loss from blade geometry seen in Figure 9 -27 , !i is the loss due to the incidence angle seen in Figure 9 - 28 , and Re ˆ V3 Dn =v3 where Dn ˆ (2AR s sin 2 )=( sin 2 ‡ AR) //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER... impulse turbine, except for frictional and turbulence effect This loss varies from about 20 % for very high-velocity turbines (3000 ft/sec) to about 8% for low-velocity turbines (500 ft/sec) Since the blade speed ratio is equal to ( cos ) =2 for maximum utilization, the energy transferred in an impulse turbine can be written • • P ˆ mU…2U† ˆ 2mU 2 …9-14† The Reaction Turbine The axial-flow reaction turbine. .. Nozzle Ps Total Pressure Vo Absolute Velocity Ps Static Pressure Figure 9 -8 Pressure and velocity distributions in a Ratteau-type impulse turbine Figure 9-9 Effect of velocity and air angle on utilization factor //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 3 48 ± [337±369/33] 29 .10 .20 01 4:02PM 3 48 Gas Turbine Engineering Handbook of the blade speed to the inlet velocity, is a useful parameter to .  W 4 2 À W 3 2  V 3 2 À V 4 2 W 4 2 À W 3 2  9-3 Figure 9 -2. Stage nomenclature and velocity triangles. FPO 340 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER. (4 72  C), approximately 20  F (10  C) per year. The 1000 120 0 1400 1600 180 0 20 00 22 00 24 00 26 00 28 00 1950 1960 1970 1 980 1990 20 00 20 10 YEAR Firing Temperature F (°C)° U 500 RENE 77 IN 733 GTD111 GTD. No. 0405/015. 336 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 9.3D ± 337 ± [337±369/33] 29 .10 .20 01 4:02PM 9 Axial-Flow Turbines Axial-flow turbines are the