Gas Turbine Engineering Handbook 2 Episode 7 docx

//INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 285 ± [275±318/44] 29.10.2001 4:00PM where:   medium density V  velocity D  impeller diameter   viscosity N  speed Using this assumption, one can apply this flow visualization method to any working medium. One designed apparatus consists of two large tanks on two different levels. The lower tank is constructed entirely out of plexiglass and receives a con- stant flow from the upper tank. The flow entering the lower tank comes through a large, rectangular opening, which houses a number of screens so that no turbulence is created by water entering the lower tank. The center of the lower tank can be fitted with various boxes for the various flow visual- ization problems to be studied. This modular design enables a rapid inter- changing of models and work on more than one concept at a time. To study the effect of laminar flow, the blades were slotted as shown in Figure 7-9. For the blade treatment cascade rig experiment, a plexiglass cascade was designed and built. Figure 7-10 shows the cascade. This cascade Figure 7-9. Perspective of compressor blade with treatment. Axial-Flow Compressors 285 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 286 ± [275±318/44] 29.10.2001 4:00PM was then placed in the bottom tank and maintained at a constant head. Figure 7-11 shows the entire setup, and Figure 7-12 shows the cascade flow. Note the large extent of the laminar-flow regions on the treated center blades as compared to the untreated blades. The same water tunnel was used for tests to study the effect of casing treat- ment in axial-flow compressors. In this study, the same Reynolds number and specific speeds were maintained as those experienced in an actual axial- flow compressor. In an actual compressor the blade and the passage are rotating with respect to the stationary shroud. It would be difficult for a stationary observer to obtain data on the rotating blade passage. However, if that observer were rotating with the blade passage, data would be easier to acquire. This was accomplished by holding the blade passage stationary with respect to the observer and rotating the shroud. Furthermore, since casing treatment affects the region around the blade tip, it was sufficient to study only the upper portion of the blade passage. These were the criteria in the design of the apparatus. The modeling of the blade passage required provisions for controlling the flow in and out of the passage. This control was accomplished by placing the blades, which partially form the blade passage, within a plexiglass tube. The tube had to be of sufficient diameter to accommodate the required flow through the passage without tube wall effect distorting the flow as it entered Figure 7-10. Cascade model in axial-flow test tank. FPO 286 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 287 ± [275±318/44] 29.10.2001 4:00PM or left the blade passage. This allowance was accomplished by using a tube three times the diameter of the blade pitch. The entrance to the blades was designed so that the flow entering the blades was a fully developed turbulent flow. The flow in the passage between the blade tip and the rotating shroud was laminar. This laminar flow was expected in the narrow passage. A number of blade shapes could have been chosen; therefore, it was necessary to pick one shape for this study which would be the most repre- sentative for casing treatment considerations. Since casing treatment is most effective from an acoustic standpoint in the initial stages of compression, the maximum point of camber was chosen toward the rear of the blade (Z  :6 chord). This type of blade profile is most commonly used for transonic flow and is usually in the initial stages of compression. The rotating shroud must be in close proximity to the blade tips within the tube. To get this proximity, a shaft-mounted plexiglass disc was suspended from above the blades. The plexiglass disc was machined as shown in Figure 7-13. The plexiglass tube was slotted so that the disc could be centered on the center line of the tube and its stepped section lowered through the two slots in the tube. Clearances between the slot edges and the disc were minimized. Figure 7-11. Apparatus for testing axial-flow cascade model. FPO Axial-Flow Compressors 287 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 288 ± [275±318/44] 29.10.2001 4:00PM One slot was cut directly above the blade passage emplacement. The other slot was sealed off to prevent leakage. As the disc was lowered into close proximity to the blade tips, the blade passage was completed. The clearance between disc and blade was kept at 0.035 of an inch. The disc, when spun from above, acted as the rotating shroud. There are only two basic casing treatment designs other than a blank designÐwhich corresponds to no casing treatment at all. The first type of casing treatment consists of radial grooves. A radial groove is a casing treatment design in which the groove is essentially parallel to the chordline of the blade. The second basic type is the circumferential groove. This type of casing treatment has its grooves perpendicular to the blade chordline. Figure 7-14 is a photograph of two discs showing the two types of casing Figure 7-12. Treatments on center cascade blade. FPO 288 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 289 ± [275±318/44] 29.10.2001 4:00PM treatment used. The third disc used is a blank, representing the present type of casing. The results indicate that the radial casing treatment is most effective in reducing leakage and also in increasing the surge-to-stall margin. Figure 7-15 shows the leakage at the tips for the various casing treatments. Figure 7-16 shows the velocity patterns observed by the use of various casing treatments. Note that for the treatment along the chord (radial), the flow is maximum at the tip. This flow maximum at the tip indicates that the chance of rotor tip stall is greatly reduced. Energy Increases In an axial flow compressor air passes from one stage to the next with each stage raising the pressure and temperature slightly. By producing low- pressure increases on the order of 1.1:1  ±1.4:1, very high efficiencies can be obtained. The use of multiple stages permits overall pressure increases up to Figure 7-13. Details of the various casing treatments. Each treatment was on a separate disc. Axial-Flow Compressors 289 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 290 ± [275±318/44] 29.10.2001 4:00PM Figure 7-14. Two discs with casing treatment. Figure 7-15. Mass flow leakage at tips for various casing treatments. FPO 290 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 291 ± [275±318/44] 29.10.2001 4:00PM 40:1. Figure 7-3 shows the pressure, velocity, and total enthalpy variation for flow through several stages of an axial flow compressor. It is important to note here that the changes in the total conditions for pressure, temperature, and enthalpy occur only in the rotating component where energy is inputted into the system. As seen also in Figure 7-3, the length of the blades, and the annulus area, which is the area between the shaft and shroud, decreases through the length of the compressor. This reduction in flow area compen- sates for the increase in fluid density as it is compressed, permitting a constant axial velocity. In most preliminary calculations used in the design of a compressor, the average blade height is used as the blade height for the stage. The rule of thumb for a multiple stage gas turbine compressor would be that the energy rise per stage would be constant, rather than the commonly Figure 7-16. Velocity patterns observed in the side view of the blade passage for various casing treatments. Axial-Flow Compressors 291 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 292 ± [275±318/44] 29.10.2001 4:00PM held perception that the pressure rise per stage is constant. The energy rise per stage can be written as: ÁH  H 2 À H 1  N S 7-6 where: H 1 , H 2  Inlet and Exit Enthalpy Btu=lb m (kJ=kg) N s  number of stages Assuming that the gas is thermally and calorically perfect (c p , and  are constant) equation 7-1 can be rewritten as: ÁT stage  T in P 2 P 1 hi À1  À1 45 N s 7-7 where: T in  Inlet Temperature (  F,  C) P 1 , P 2  Inlet and Exit Pressure (psia; bar) Velocity Triangles As stated earlier, an axial-flow compressor operates on the principle of putting work into the incoming air by acceleration and diffusion. Air enters the rotor as shown in Figure 7-17 with an absolute velocity (V ) and an angle  1 , which combines vectorially with the tangential velocity of the blade (U ) to produce the resultant relative velocity W 1 at an angle  2 . Air flowing through the passages formed by the rotor blades is given a relative velocity W 2 at an angle  4 , which is less than  2 because of the camber of the blades. Note that W 2 is less than W 1 , resulting from an increase in the passage width as the blades become thinner toward the trailing edges. Therefore, some diffusion will take place in the rotor section of the stage. The combination of the relative exit velocity and blade velocity produce an absolute velocity V 2 at the exit of the rotor. The air then passes through the stator, where it is turned through an angle so that the air is directed into the rotor of the next stage with a minimum incidence angle. The air entering the rotor has an axial component at an absolute velocity V z1 and a tangential component V 1 . 292 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 293 ± [275±318/44] 29.10.2001 4:00PM Applying the Euler turbine equation H  1 g c U 1 V 1 À U 2 V 2 7-8 and assuming that the blade speeds at the inlet and exit of the compressor are the same and noting the relationships, V 1  V z1 tan  1 7-9 V 2  V z2 tan  3 7-10 Equation (7-1) can be written H  U 1 g c V z1 tan  2 À V z2 tan  3 7-11 Figure 7-17. Typical velocity triangles for an axial-flow compressor. Axial-Flow Compressors 293 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 7.3D ± 294 ± [275±318/44] 29.10.2001 4:00PM Assuming that the axial component (V z ) remains unchanged, H  UV z g c tan  1 À tan  3 7-12 The previous relationship is in terms of the absolute inlet and outlet vel- ocities. By rewriting the previous equation in terms of the blade angles or the relative air angles, the following relationship is obtained: U 1 U 2  V z1 tan  1  V z1 tan  2  V z2 tan  3  V z2 tan  4 Therefore, H  UV z g c tan  2 À tan  4 7-13 The previous relationship can be written to calculate the pressure rise in the stage c p T in P 2 P 1  À1  À1 45  UV 2 g c tan  2 À tan  4 7-14 which can be rewritten P 2 P 1  UV z g c c p T in tan  2 À tan  4 1 &'  1 7-15 The velocity triangles can be joined together in several different ways to help visualize the changes in velocity. One of the methods is to simply join these triangles into a connected series. The two triangles can also be joined and superimposed using the sides formed by either the axial velocity, which is assumed to remain constant as shown in Figure 7-18a, or the blade speed as a common side, assuming that the inlet and exit blade speed are the same as shown in Figure 7-18b. Degree of Reaction The degree of reaction in an axial-flow compressor is defined as the ratio of the change of static head in the rotor to the head generated in the stage 294 Gas Turbine Engineering Handbook [...]... W2 and V2 ˆ W1 as seen in Figure 7- 19, the Figure 7- 19 Symmetrical velocity triangle for 50% reaction stage //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 29 7 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Axial-Flow Compressors 29 7 head delivered in velocity as given by the Euler turbine equation can be expressed 1 2 2 2 2 2 2 ‰…U1 À U2 † ‡ …V1 À V2 † ‡ …W2 À W1 †Š 2gc 1 2 2 Hˆ …W2 À W1 † 2gc Hˆ 7 -22 † 7 -23 †... (26 -10-01)/CHAPTER 7. 3D ± 29 5 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Axial-Flow Compressors 29 5 Figure 7- 18 Velocity triangles Rˆ Hrotor Hstage 7- 16† The change in static head in the rotor is equal to the change in relative kinetic energy: Hr ˆ 1 …W1 2 À W1 2 † 2gc 7- 17 //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 29 6 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM 29 6 Gas Turbine Engineering Handbook and W1 2. .. 29 .10 .20 01 4:00PM 29 6 Gas Turbine Engineering Handbook and W1 2 ˆ Vz1 2 ‡ …Vz1 tan 2 2 7- 18† 2 7- 19† W2 2 ˆ Vz2 2 ‡ …Vz2 tan 4 † Therefore, Hr ˆ Vz 2 …tan2 2 À tan2 4 † 2gc Thus, the reaction of the stage can be written Rˆ Vz tan2 2 À tan2 4 2U tan 2 À tan 4 7 -20 † Simplifying the previous equation, Rˆ Vz …tan 2 ‡ tan 4 † 2U 7 -21 † In the symmetrical axial-flow stage, the blades and their orientation... Type of Stall Progressive 1.39 2. 14 1.66 1 .2 0 .76 1.30 2. 14 1.10 1.10 2. 02 1. 47 2. 02 1 .71 0 .24 5 0.48 0.36 0.10 0.45 0. 12 0.816 0.634 0.565 Ð Radial Extent of Stall Zone Partial 0. 420 0. 475 0. 523 0.305 0. 87 0.36 0 .25 0 .25 0 .25 0 .23 0.48 0.48 0.49 6, 8 1 2 1 1 1 3 2 1 2 0 .76 Solid body Vortex transonic Weight-flow Fluctuation during stall, DpV/p V 3 4 5 1 8 1 7 8 5 3 4 3 2 0.90 0.80 Free vortex Propagation... a function of incidence angle //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 3 02 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM 3 02 Gas Turbine Engineering Handbook Figure 7 -23 Incidence angle for zero-camber airfoil Figure 7 -24 Slope of incidence angle variation with air angle //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 303 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Axial-Flow Compressors 303 The incidence angle... Progressive 2 À Partial 2 À 0. 57 2 À Type of Stall 2 À Periodicity 2 À Radial Extent of Stall Zone 2 À 3 4 5 6 7 4 5 6 Propagation Rate, Stall Speed, abs/ Rotor Speed 2 À Number of Stall Zones //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 311 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Axial-Flow Compressors 2 À 2 À 0. 57 Partial Intermittent Progressive 2 À 2 À Progressive Progressive 2 À Steady Steady 2 À Partial... Figure 7- 36 High-pressure bleed chamberÐ5400 rpm //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 316 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM 316 Gas Turbine Engineering Handbook Figure 7- 37 High-pressure bleed chamberÐ8000 rpm Figure 7- 38 High-pressure bleed chamberÐ9400 rpm Figure 7- 39 Fifth-stage bleed pressureÐ5800 rpm //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 3 17 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM... 4:00PM 306 Gas Turbine Engineering Handbook Figure 7 -28 The NACA 65 series of cascade airfoils Figure 7 -29 Approximate relation between camber () and CLO of NACA 65 series //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 3 07 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Axial-Flow Compressors 3 07 Figure 7- 30 The NACA 65 series cascade data (Courtesy of G Mellor, Massachusetts Institute of Technology, Gas Turbine. .. shape as shown in the following relationship: p f ˆ mf  1= ‡ 12: 15 t=c…1 À =8:0† ‡ 3:33…M1 À 0 :75 † 7 -28 † Figure 7 -25 Correction factor for blade thickness and incidence angle calculation //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 304 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM 304 Gas Turbine Engineering Handbook Figure 7 -26 Mach-number correction for incidence angle where mf is a function of... whole blade length Table 7- 1 shows the characteristics of rotating stall for single and multistage axial-flow compressors Figure 7- 32 Propagating stall in a cascade //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 310 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM 310 Gas Turbine Engineering Handbook Table 7- 1 Summary of Rotating Stall Data Single-Stage Compressors Number Of Stall Zones 0.50 0. 72 0.60 0.60 0.50 0.50 . V z1 2 V z1 tan  2  2 7- 18 W 2 2  V z2 2 V z2 tan  4  2 7- 19 Therefore, H r  V z 2 2g c tan 2  2 À tan 2  4  Thus, the reaction of the stage can be written R  V z 2U tan 2  2 À. (26 -10-01)/CHAPTER 7. 3D ± 29 7 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM head delivered in velocity as given by the Euler turbine equation can be expressed H  1 2g c U 2 1 À U 2 2 V 2 1 À V 2 2 W 2 2 À W 2 1 . V 1 . 29 2 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26 -10-01)/CHAPTER 7. 3D ± 29 3 ± [ 27 5±318/44] 29 .10 .20 01 4:00PM Applying the Euler turbine equation H  1 g c U 1 V 1 À U 2 V 2  7- 8 and