GasTurbine Engineering HandbookSecond Edition phần 4 doc

//INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 231 ± [219±274/56] 29.10.2001 3:59PM close to the sonic velocity or greater than it, a shock wave takes place in the inducer section. A shock wave produces shock loss and chokes the inducer. Figure 6-12 shows the effect of inlet prewhirl on compressor efficiency. There are three kinds of prewhirl: 1. Free-vortex prewhirl. This type is represented by r 1 V 1  constant with respect to the inducer inlet radius. This prewhirl distribution is shown in Figure 6-13. V 1 is at a minimum at the inducer inlet shroud radius. Therefore, it is not effective in decreasing the relative Mach number in this manner. 2. Forced-vortex prewhirl. This type is shown as V 1 =r 1  constant. This prewhirl distribution is also shown in Figure 6-14. V 1 is at a maximum at the inducer inlet shroud radius, contributing to a decrease in the inlet relative Mach number. Figure 6-13. Prewhirl distribution patterns. Figure 6-14. Euler work distribution at an impeller exit. Centrifugal Compressors 231 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 232 ± [219±274/56] 29.10.2001 3:59PM 3. Control-vortex prewhirl. This type is represented by V 1  AR 1  B=r 1 , where A and B are constants. This equation shows the first type with A  0, B T 0, and the second type with B  0, A T 0. Euler work distributions at an impeller exit, with respect to the impeller width, are shown in Figure 6-14. From Figure 6-14, the prewhirl distribution should be made not only from the relative Mach number at the inducer inlet shroud radius, but also from Euler work distribution at the impeller exit. Uniform impeller exit flow conditions, considering the impeller losses, are important factors in obtaining good compressor performance. Impeller An impeller in a centrifugal compressor imparts energy to a fluid. The impeller consists of two basic components: (1) an inducer like an axial-flow rotor, and (2) the radial blades where energy is imparted by centrifugal force. Flow enters the impeller in the axial direction and leaves in the radial direc- tion. The velocity variations from hub to shroud resulting from these changes in flow directions complicate the design procedure for centrifugal compres- sors. C.H. Wu has presented the three-dimensional theory in an impeller, but it is difficult to solve for the flow in an impeller using the previous theory without certain simplified conditions. Others have dealt with it as a quasi- three-dimensional solution. It is composed of two solutions, one in the meridional surface (hub-to-shroud), and the other in the stream surface of revolution (blade-to-blade). These surfaces are illustrated in Figure 6-15. By the application of the previous method using a numerical solution to the complex flow equations, it is possible to achieve impeller efficiencies of more than 90%. The actual flow phenomenon in an impeller is more com- plicated than the one calculated. One example of this complicated flow is shown in Figure 6-16. The stream lines observed in Figure 6-16 do not cross, but are actually in different planes observed near the shroud. Figure 6-17 shows the flow in the meridional plane with separation regions at the inducer section and at the exit. Experimental studies of the flow within impeller passages have shown that the distribution of velocities on the blade surfaces are different from the distributions predicted theoretically. It is likely that the discrepancies between theoretical and experimental results are due to secondary flows from pressure losses and boundary-layer separation in the blade passages. High-performance impellers should be designed, when possible, with the aid of theoretical methods for determining the velocity distributions on the blade surfaces. 232 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 233 ± [219±274/56] 29.10.2001 3:59PM Examples of the theoretical velocity distributions in the impeller blades of a centrifugal compressor are shown in Figure 6-18. The blades should be designed to eliminate large decelerations or accelerations of flow in the impeller that lead to high losses and separation of the flow. Potential flow solutions predict the flow well in regions away from the blades where Figure 6-15. Two-dimensional surface for a flow analysis. Figure 6-16. Flow map of impeller plane. Centrifugal Compressors 233 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 234 ± [219±274/56] 29.10.2001 3:59PM boundary-layer effects are negligible. In a centrifugal impeller the viscous shearing forces create a boundary layer with reduced kinetic energy. If the kinetic energy is reduced below a certain limit, the flow in this layer becomes stagnant, then it reverses. Figure 6-17. Flow map as seen in meridional plane. 234 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 235 ± [219±274/56] 29.10.2001 3:59PM Figure 6-18. Velocity profiles through a centrifugal compressor. Centrifugal Compressors 235 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 236 ± [219±274/56] 29.10.2001 3:59PM Inducer The function of an inducer is to increase the fluid's angular momentum without increasing its radius of rotation. In an inducer section the blades bend toward the direction of rotation as shown in Figure 6-19. The inducer is an axial rotor and changes the flow direction from the inlet flow angle to the axial direction. It has the largest relative velocity in the impeller and, if not properly designed, can lead to choking conditions at its throat as shown in Figure 6-19. There are three forms of inducer camber lines in the axial direction. These are circular arc, parabolic arc, and elliptical arc. Circular arc camber lines are used in compressors with low pressure ratios, while the elliptical arc produces good performance at high pressure ratios where the flow has transonic mach numbers. Figure 6-19. Inducer centrifugal compressor. 236 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 237 ± [219±274/56] 29.10.2001 3:59PM Because of choking conditions in the inducer, many compressors incor- porate a splitter-blade design. The flow pattern in such an inducer section is shown in Figure 6-20a. This flow pattern indicates a separation on the suction side of the splitter blade. Other designs include tandem inducers. In tandem inducers the inducer section is slightly rotated as shown in Figure 6-20b. This modification gives additional kinetic energy to the boundary, which is otherwise likely to separate. Centrifugal Section of an Impeller The flow in this section of the impeller enters from the inducer section and leaves the impeller in the radial direction. The flow in this section is not com- pletely guided by the blades, and hence the effective fluid outlet angle does not equal the blade outlet angle. To account for flow deviation (which is similar to the effect accounted for by the deviation angle in axial-flow machines), the slip factor is used:   V 2 V 2I 6-8 (a) (b) Figure 6-20. Impeller channel flow. Centrifugal Compressors 237 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 238 ± [219±274/56] 29.10.2001 3:59PM where V 2 is the tangential component of the absolute exit velocity with a finite number of blades, and V 2I is the tangential component of the absolute exit velocity, if the impeller were to have an infinite number of blades (no slipping back of the relative velocity at outlet). With radial blades at the exit,   V 2 U 2 6-9 Flow in a rotating impeller channel (blade passage) will be a vector sum of flow with the impeller stationary and the flow due to rotation of the impeller as seen in Figure 6-21. In a stationary impeller, the flow is expected to follow the blade shape and exit tangentially to it. A high adverse pressure gradient along the blade passage and subsequent flow separation are not considered to be general possibilities. Inertia and centrifugal forces cause the fluid elements to move closer to and along the leading surface of the blade toward the exit. Once out of the blade passage, where there is no positive impelling action present, these fluid elements slow down. Causes of Slip in an Impeller The definite cause of the slip phenomenon that occurs within an impeller is not known. However, some general reasons can be used to explain why the flow is changed. Figure 6-21. Forces and flow characteristics in a centrifugal compressor. 238 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 239 ± [219±274/56] 29.10.2001 3:59PM Coriolis circulation. Because of the pressure gradient between the walls of two adjacent blades, the Coriolis forces, the centrifugal forces, and the fluid follow the Helmholtz vorticity law. The combined gradient that results causes a fluid movement from one wall to the other and vice versa. This movement sets up circulation within the passage as seen in Figure 6-22. Because of this circulation, a velocity gradient results at the impeller exit with a net change in the exit angle. Boundary-layer development. The boundary layer that develops within an impeller passage causes the flowing fluid to experience a smaller exit area as shown in Figure 6-23. This smaller exit is due to small flow (if any) within the boundary layer. For the fluid to exit this smaller area, its velocity must increase. This increase gives a higher relative exit velocity. Figure 6-22. Coriolis circulation. Figure 6-23. Boundary-layer development. Centrifugal Compressors 239 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 240 ± [219±274/56] 29.10.2001 3:59PM Since the meridional velocity remains constant, the increase in relative velocity must be accompanied with a decrease in absolute velocity. Although it is not a new approach, boundary-layer control is being used more than ever before. It has been used with success on airfoil designs when it has delayed separation, thus giving a larger usable angle of attack. Control of the flow over an airfoil has been accomplished in two ways: by using slots through the airfoil and by injecting a stream of fast-moving air. Separation regions are also encountered in the centrifugal impeller as shown previously. Applying the same concept (separation causes a loss in efficiency and power) reduces and delays their formation. Diverting the slow- moving fluid away lets the separation regions be occupied by a faster stream of fluid, which reduces boundary-layer build-up and thus decreases separation. To control the boundary layer in the centrifugal impeller, slots in the impeller blading at the point of separation are used. To realize the full capability of this system, these slots should be directional and converging in a cross-sectional area from the pressure to the suction sides as seen in Figure 6-24. The fluid diverted by these slots increases in velocity and attaches itself to the suction sides of the blades. This results in moving the separation region closer to the tip of the impeller, thus reducing slip and losses encountered by the formation of large boundary-layer regions. The slots must be located at the point of flow separation from the blades. Experi- mental results indicate improvement in the pressure ratio, efficiency, and surge characteristics of the impeller as seen in Figure 6-24. Leakage. Fluid flow from one side of a blade to the other side is referred to as leakage. Leakage reduces the energy transfer from impeller to fluid and decreases the exit velocity angle. Number of vanes. The greater the number of vanes, the lower the vane loading, and the closer the fluid follows the vanes. With higher vane load- ings, the flow tends to group up on the pressure surfaces and introduces a velocity gradient at the exit. Vane thickness. Because of manufacturing problems and physical necessity, impeller vanes are thick. When fluid exits the impeller, the vanes no longer contain the flow, and the velocity is immediately slowed. Because it is the meridional velocity that decreases, both the relative and absolute velocities decrease, changing the exit angle of the fluid. A backward-curved impeller blade combines all these effects. The exit velocity triangle for this impeller with the different slip phenomenon changes is shown in Figure 6-25. This triangle shows that actual operating conditions are far removed from the projected design condition. 240 Gas Turbine Engineering Handbook [...]... //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 242 ± [219±2 74/ 56] 29.10.2001 3:59PM 242 Gas Turbine Engineering Handbook Figure 6-25 Effect on exit velocity triangles by various parameters Figure 6-26 Various slip factors as a function of the flow coefficient //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 243 ± [219±2 74/ 56] 29.10.2001 3:59PM Centrifugal Compressors 243 impeller channels would rotate with... efficiency of centrifugal compressor components has been steadily improved by advancing their performance However, significant //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 244 ± [219±2 74/ 56] 29.10.2001 3:59PM 244 Gas Turbine Engineering Handbook further improvement in efficiency will be gained only by improving the pressure recovery characteristics of the diffusing elements of these machines, since... vaneless space behind the rotor It is minimized in a diffuser, which is symmetric around the axis of rotation //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 2 54 ± [219±2 74/ 56] 29.10.2001 3:59PM 2 54 Gas Turbine Engineering Handbook Figure 6- 34 Recirculating loss Vaneless diffuser loss This loss is experienced in the vaneless diffuser and results from friction and the absolute flow angle Vaned diffuser... energy is reduced below a certain limit, the flow in this layer becomes stagnant and then reverses This flow reversal causes //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 246 ± [219±2 74/ 56] 29.10.2001 3:59PM 246 Gas Turbine Engineering Handbook Figure 6-29 Jet-wake flow distribution from an impeller separation in a diffuser passage, which results in eddy losses, mixing losses, and changed-flow angles... volute, it is better to have the volute width larger than the impeller width This enlargement results in the flow from the //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 248 ± [219±2 74/ 56] 29.10.2001 3:59PM 248 Gas Turbine Engineering Handbook Figure 6-30 Flow patterns in volute impeller being bounded by the vortex generated from the gap between the impeller and the casing At flows different from...//INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 241 ± [219±2 74/ 56] 29.10.2001 3:59PM Centrifugal Compressors 241 Figure 6- 24 Percent design flowÐlaminar flow control in a centrifugal compressor Several empirical equations have been derived for the slip factor (see Figure 6-26) These empirical... geometry, inlet flow conditions, and exit flow conditions Figure 6-27 Figure 6-27 Geometric classification of diffusers //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 245 ± [219±2 74/ 56] 29.10.2001 3:59PM Centrifugal Compressors 245 Figure 6-28 Flow regions of the vaned diffuser shows typical diffusers classified by their geometry The selection of an optimum channel diffuser for a particular task... design conditions, there exists a circumferential pressure gradient at the impeller tip and in the volute at a given radius //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 249 ± [219±2 74/ 56] 29.10.2001 3:59PM Centrifugal Compressors 249 At low flows, the pressure rises with the peripheral distance from the volute tongue At high flows, the pressure falls with distance from the tongue This condition results... measured occurrence of backflow from the collector through the impeller during the period between the two sudden changes //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 247 ± [219±2 74/ 56] 29.10.2001 3:59PM Centrifugal Compressors 247 Scroll or Volute The purpose of the volute is to collect the fluid leaving the impeller or diffuser, and deliver it to the compressor outlet pipe The volute has an important... pressure gradient that a compressor normally works against increases the chances of separation and causes significant loss //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 252 ± [219±2 74/ 56] 29.10.2001 3:59PM 252 Gas Turbine Engineering Handbook Figure 6-32 Secondary flow at the back of an impeller Clearance loss When a fluid particle has a translatory motion relative to a noninertial rotating coordinate . 6-27. Geometric classification of diffusers. 244 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 245 ± [219±2 74/ 56] 29.10.2001 3:59PM shows typical diffusers. the Figure 6- 24. Percent design flowÐlaminar flow control in a centrifugal com- pressor. Centrifugal Compressors 241 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 242 ± [219±2 74/ 56] 29.10.2001. factors as a function of the flow coefficient. 242 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 243 ± [219±2 74/ 56] 29.10.2001 3:59PM impeller channels would