Gas Turbine Engineering Handbook 2 Episode 6 pps

//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 ± 241 ± [219±274/56] 29.10.2001 3:59PM Several empirical equations have been derived for the slip factor (see Figure 6-26). These empirical equations are limited. Two of the more common slip factors are presented here. Stodola Slip Factor The second Helmholtz law states that the vorticity of a frictionless fluid does not change with time. Hence, if the flow at the inlet to an impeller is irrotational, the absolute flow must remain irrotational throughout the impeller. As the impeller has an angular velocity !, the fluid must have an angular velocityÐ! relative to the impeller. This fluid motion is called the relative eddy. If there were no flow through the impeller, the fluid in 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±274/56] 29.10.2001 3:59PM Figure 6-25. Effect on exit velocity triangles by various parameters. Figure 6-26. Various slip 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±274/56] 29.10.2001 3:59PM impeller channels would rotate with an angular velocity equal and opposite to the impeller's angular velocity. To approximate the flow, Stodola's theory assumes that the slip is due to the relative eddy. The relative eddy is considered as a rotation of a cylinder of fluid at the end of the blade passage at an angular velocity ofÐ! about its own axis. The Stodola slip factor is given by   1 À  Z 1 À sin  2 V m2 cot  2 U 2 P T T R Q U U S 6-10 where:  2  the blade angle Z  the number of blades V m2  the meridional velocity U 2  blade tip speed. Calculations using this equation have been found to be lower than experi- mental values. Stanitz Slip Factor Stanitz calculated blade-to-blade solutions for eight impellers and concluded that for the range of conditions covered by the solutions, U is a function of the number of blades (Z), and the blade exit angle ( 2 )is approximately the same whether the flow is compressible or incompressible   1 À 0:63 Z 1 À 1 W m2 U 2 cot  2 P R Q S 6-11 Stanitz's solutions were for =4 < 2 <=2. This equation compares well with experimental results for radial or near-radial blades. Diffusers Diffusing passages have always played a vital role in obtaining good performance from turbomachines. Their role is to recover the maximum possible kinetic energy leaving the impeller with a minimum loss in total pressure. The efficiency of centrifugal compressor components has been steadily improved by advancing their performance. However, significant Centrifugal Compressors 243 //INTEGRA/B&H/GTE/FINAL (26-10-01)/CHAPTER 6.3D ± 244 ± [219±274/56] 29.10.2001 3:59PM further improvement in efficiency will be gained only by improving the pressure recovery characteristics of the diffusing elements of these machines, since these elements have the lowest efficiency. The performance characteristics of a diffuser are complicated functions of diffuser geometry, inlet flow conditions, and exit flow conditions. Figure 6-27 Figure 6-27. Geometric classification of diffusers. 244 Gas Turbine Engineering Handbook [...]... the curve for heavy gas: 1 2 3 4 The flow at surge is higher The stage produces slightly more head than that corresponding to medium gas The right-hand side of the curve turns downward (approaches stonewall) more rapidly The curve is flatter in the operating stage //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 26 2 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 26 2 Gas Turbine Engineering Handbook DESIGN SU PO... in Figure 6- 37 appears to have a more gentle slope than either the middle or upper curve This //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 25 8 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 25 8 Gas Turbine Engineering Handbook 2 >90° 2 < 90° Backward Leaning Blade SU RG E Radial Blade Impeller Efficiency Forward Leaning Blade 2 >90° HEAD EFFICIENCY Forward Leaning Blade 2 = 90° Radial Blade 2 = 90° Backward... aerodynamic instability, although it is possible that the system arrangement could be capable of augmenting this instability Figure 6- 36 shows a typical //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 25 6 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 25 6 Gas Turbine Engineering Handbook Figure 6- 36 Typical compressor performance map performance map for a centrifugal compressor with efficiency islands and constant aerodynamic... 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 ± 25 2 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 25 2 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... 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 ± 24 6 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 24 6 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... Conversely, as flow increases beyond the rated point, excessive negative //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 26 0 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 26 0 Gas Turbine Engineering Handbook Design Air Angle α Good Flow Path Small Air Angle α Surge Condition α α α Large Air Angle α Stone Wall Condition Figure 6- 39 Vaned diffuser incidence can cause stonewall Despite its narrowing effect on the usable... diffuser are complicated functions of diffuser 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 ± 24 5 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM Centrifugal Compressors 24 5 Figure 6 -28 Flow regions of the vaned diffuser shows typical diffusers classified by their geometry The selection of an... encountered in the flow passage (Áqsf ) qia ˆ qth À Áqin À Áqsh À Áqbl À Áqc À Áqsf 6- 18† //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 25 0 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 25 0 Gas Turbine Engineering Handbook Therefore, the adiabatic efficiency in the impeller is imp ˆ qia qtot 6- 19† The calculation of the overall stage efficiency must also include losses encountered in the diffuser Thus, the... 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 ± 24 8 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 24 8 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... The 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 ± 24 4 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM 24 4 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, . conditions. Figure 6 -27 Figure 6 -27 . Geometric classification of diffusers. 24 4 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 24 5 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM shows. changes. Figure 6 -29 . Jet-wake flow distribution from an impeller. 24 6 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 24 7 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM Scroll. equations. Figure 6- 32. Secondary flow at the back of an impeller. 25 2 Gas Turbine Engineering Handbook //INTEGRA/B&H/GTE/FINAL ( 26 -10-01)/CHAPTER 6. 3D ± 25 3 ± [21 9 27 4/ 56] 29 .10 .20 01 3:59PM Stator