IMPELLER AND BLADED DISK Chap. 7 TURBO-MACHINERY DYNAMICS R01-03/11/2013

Transcription

1 UNIVERSITY OF SALENTO SCHOOL OF INDUSTRIAL ENGINEERING DEPT. OF ENGINEERING FOR INNOVATION Lecce-Brindisi (Italy) MASTER OF SCIENCE IN AEROSPACE ENGINEERING PROPULSION AND COMBUSTION IMPELLER AND BLADED DISK Chap. 7 TURBO-MACHINERY DYNAMICS R01-03/11/2013 LECTURE NOTES AVAILABLE ON Prof. Eng. Antonio Ficarella University of Salento - antonio.ficarella@unisalento.it 1

2 INTRODUCTION In a radial stage, on the other hand, the change in the potential energy of the fluid is a direct consequence of the centrifugal force field of the rotor. Consequently, problems arising from the growth of the boundary layer and separation associated with adverse pressure are reduced. Because of this advantage, the centrifugal compressor has been employed to obtain a range of compression ratio and performance efficiency in turbojet engines. Also, centrifugal stages are more rugged than axial blades, thus allowing them to operate at higher tip speeds. The upshot of these beneficial factors is that the pressure ratio may vary from 3.2 for a centrifugal impeller operating at 1.18 tip Mach speed to nearly 14.0 running at 1.86 Mach. The operating efficiency of the centrifugal stage does not degrade as much as in axial stages, dropping from 88.5 percent at the lower speed to about 86 percent at high speed. Stable regions of operation tend to be larger in centrifugal compressor stages. 2

3 From the viewpoint of design configuration the geometry of the diffuser thus becomes quite complex. Vaneless diffusers have been used in the past, the flow velocity reducing naturally in an expanding radial space. But the flow may become unstable due to fluctuations in the velocity. When the flow is split between several diffusing passages, the problem is alleviated. The passages, created by the vanes, reduce the swirl in the flow while providing velocity reduction in a lesser space. The drawback with vanes is that they now become airfoils, and at operation other than the design point, the airflow may occur at a large angle of incidence. In larger impellers one or two splitter blades may also be provided between the adjacent main blades. Splitter blades are used to reduce the pitch spacing between the blades at the outer diameter. Disk burst and low-cycle fatigue are primary causes of failure in turbomachine rotors. 3

4 IMPELLER DESIGN FEATURES pressure gradient in radial direction isentropic condition 4

5 a further pressure rise takes place A higher compression, however, comes at the cost of low-mass flow capacity for a given frontal area. The ratio of the inlet flow area to the frontal area depends on the square of the ratio of the inlet tip radius to the diffuser outlet radius, hence the mass flow capacity is considerably less than for an axial flow compressor of equal dimensions. 5

6 On replacing the axial velocity w3 by the radial velocity v 3 to obtain tangential velocity relative to the impeller at the outlet In the absence of preswirl vanes In the absence of preswirl vanes, the inlet tangential velocity is zero, so β2 = 0 6

7 here it is assumed M3 = M2 Diffusion can be a serious problem for high-pressure ratio radial stages. To take care of this problem, a backward swept impeller with β 3 > 0 and increased tip speed may be employed to achieve the required pressure ratio, while reducing the diffuser inlet Mach number. 7

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9 Applying the concept of diffusion factor to the inducer, and assuming constant flow velocity normal to the passage section, the diffusion factor D may be expressed in terms of flow Mach number at blade tip at inlet M 2, and exit flow Mach number MT, σ is solidity and the ratio of tip radii at inlet and exit re / rt. Mass flow capacity and compression ratio differ with one another, the former reducing when the latter increases. 9

10 Compared to a typical value of 0.5 for an axial flow compressor, the mass flow in a centrifugal stage is substantially less. 10

11 The angular momentum of the flow increases as it progresses through the radial passage, following the contours more closely if the blade spacing is reduced. As the spacing increases, the exit velocity inclines away from the direction of rotor motion (β c = 0), the work done by the impeller decreases and slippage occurs. Slip factor is defined as the ratio of actual tangential velocity to (ωrc u tan β c). 11

12 DIFFUSER FOR INDUSTRIAL GAS TURBINE 12

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15 INTERACTION BETWEEN IMPELLER AND VOLUTE Lack of symmetry about the rotor axis of this component results in a circumferential distortion of the flow in the region where the impeller discharges and enters the volute. An unsteady impeller flow results in modifying conditions at the volute inlet. Simulation of this interaction requires the simultaneous solution of unsteady Navier-Stokes equations in both the impeller and the volute. 15

16 Assuming a subsonic and radially outward flow in the diffuser, one boundary condition is needed at the impeller exit and four at the volute inlet. On the impeller side of the boundary circumferential and spanwise variation of static pressure resulting from the volute calculations is imposed. 16

17 On the volute side of the boundary the spatial variation of four timeaveraged flow quantities, mass flux, energy flux, and tangential and axial momentum flux must be imposed. Because of the periodic nature of the impeller s flow, time averaging is limited to a period τ/n (where τ is the period of rotation, N is the number of blades) corresponding to the passing of one blade passage past a point in the volute. 17

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20 pressure and temperature distributions at midspan the Strouhal number of 0.25 permits waves to travel twice back and forth during each shaft rotation, and explains the presence of twin peaks in the pressure and temperature traces. St = fl/v 20

21 FLOW CHARACTERISTICS IN VANED DIFFUSER Modern impeller designs reach absolute discharge Mach numbers between 0.9 and 1.3, so at least transonic diffuser inlet conditions will prevail. The distorted impeller discharge will mark the flow field in the diffuser inlet by strong velocity and flow angle fluctuations in the circumferential and axial directions. Compressors with vaned diffusers pose interesting problems because the region between the impeller exit and diffuser inlet is characterized by unsteady flow, by interaction between impeller and diffuser and between boundary and shock layers. These features are not independent of each other in their action and extent. An increase in the radial gap, for instance, leads to a reduction in the interaction between the impeller and diffuser and a more uniform flow into the diffuser, but will also lead to growth in the boundary layer thickness. 21

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23 Surge investigation is conducted using pressure transducers mounted flush in the diffuser front wall at the impeller s suction and discharge and at the diffuser throat and exit. The axial motion of the shaft is also recorded to obtain an estimate of mechanical loading during surge. The compressor is initially prethrottled with a slide valve on the pressure side, then adjusted in a slow stepwise closing for further throttling up to the surge limit. 23

24 Figure shows the course of the unsteady pressure signals. Prior to the first surge cycle, pressure signals at impeller exit and at diffuser throat indicate a distinct alteration. At the threshold of reversed flow a slight pressure drop is noticed at the diffuser exit, but the remaining probes show a steep pressure rise. Simultaneously, the rotor is observed to move abruptly toward the shroud, imposing a heavy load on the thrust bearing and an explicit danger of contact at the shroud. During the reversed flow both the impeller exit and diffuser throat transducers show strong pressure oscillations, reducing to a near normal. 24

25 RADIAL INFLOW TURBINE 25

26 Flow angles for the three different tip flow regimes are plotted. Over the first 20 percent of the meridional length the flow in the clearance is mostly inclined in the streamwise direction, with part of the flow moving from the suction to the pressure side. The distortion of the casing causes the fluid to recirculate over the tip. In the midsection the flow is nearly perpendicular to the blade, with the tip flow driven mainly by the pressure difference over the tip. Downstream of 60 percent meridional length the streamlines over the tip are inclined in the streamwise direction while diverging toward the trailing edge. Changes in blade loading near 26 the tip are responsible for this flow pattern.

27 details of tip leakage flow characteristics at 46 percent meridional length 27

28 Because turbine components are exposed to high-temperature gas while attaining targeted aerodynamic performance, ceramic applications in the turbine are of considerable significance. 28

29 burst capability of the rotor 29

30 To determine the vibratory strength of the blades, resonant point vibration stresses are measured by strain gages bonded in the vicinity of stress peak points. 30

31 STRESSES IN ROTATING DISK A turbine disk is subjected to loads arising from the centrifugal force of attached blades, and due to radial forces caused by its own spinning motion. In addition, the disk also provides a load path for attached shafts. Steady and transient thermal gradients imposed on the disk create additional stresses in the disk. Disk material characteristics such as Young s modulus and thermal coefficient of expansion will play a major role in determining stresses throughout the geometry, as also the load-carrying capability. 31

32 hoop load is given by the expression Pc = [rω2r2arim/g] hoop stress is given by σt = [rω2r2/g] Since the rim is also subjected to Frim due to the mass of the blades, the total tangential stress in the rim is given by σt = [rω2r2/g] + Frim/(2πArim) 32

33 distribution of elastic stress in a uniform disk with a center bore 33

34 TWIN WEB DISK 34

35 The weight of a turbine rotor system can be minimized by using the concept of disks with twin webs. Single-web geometry disks made of nickel alloys that can better withstand loads represented by the turbine annulus area and speed squared (AN 2) have reached a limit where further gains in their load carrying capability cannot be obtained. The twin-web disk, developed by the U.S. Air Force has the potential to provide this breakthrough. Mismatch in the thermal properties between ceramic matrix composite (CMC) and nickel-base alloys at higher operating temperatures precludes use of a composite ring reinforced metal disk. The additional temperature causes the higher expansion rate nickel bore to grow too much relative to the CMC ring, resulting in excessive axial bending. Consequently, a design comparison has been completed between the composite ring reinforced and the twin-web disk design without the CMC ring. 35

36 Several different processing methods are available for producing the turbine disk. As the twin-web design emerged as the concept of choice, new bond process requirements have been developed. The procedure utilizes features of both transient liquid phase and forge joining to produce high-quality metallurgical bonds while imparting low distortion. 36

37 DISK BURST CAPABILITY Finite element analysis is required for obtaining stresses in a disk, especially if there are holes and scallops near the rim. An alternate method suitable for preliminary design uses the concept of dividing the disk into a number of constant thickness rings. Stresses are computed iteratively while ensuring that deformation at both radii of the ring is compatible with those in the neighboring rings. Thermal gradients due to steady state or transient conditions may also be included in the model. 37

38 Axial and shearing stresses are not of significance. Rim and body loads are axisymmetric in character, so tangential stress does not vary around the circumference and is a function of the radius. Thus, only tangential stress σt and radial stress σr need to be determined, and only two differential equations relating to equilibrium and compatibility are required. The equilibrium equation requires algebraic summation of all forces (stress multiplied by element area) in the radial direction. The relation between stresses and strains is provided by Hooke s law, with the strain terms having provision for thermal growth, aδt, where a represents the material coefficient of thermal expansion and ΔT is metal temperature less base temperature. 38

39 Two differential equations are obtained, calling for two boundary conditions to determine the constants of integration. To understand the phenomenon of disk burst, as the spin speed increases, yield strength is first reached in the bore where stress level is highest. Plasticity characteristics of the material cause redistribution of the stresses, first in the bore then toward the rim as the hoop stresses become more uniformly distributed. An approximation of the maximum burst speed can be made by equating the hoop stress integrated over the cross section along the diameter with the centrifugal force of the disk and attached blades on half the disk. The disk will yield when average tangential stress equals the ultimate tensile strength of the assumed ideally ductile material. 39

40 Burst failures rarely take place across the diameter. It might also be noted that burst from overspeed condition may not be the only mode of failure; burst due to low-cycle fatigue after a number of accumulated operating cycles is many times the case since it renders the component sensitive to cyclic inelastic strain. 40

41 FLUID-FLOW FORCES IN WHIRLING IMPELLER Fluid dynamic forces play a major role in single- and multistage centrifugal compressors, and the source and mechanism of the destabilizing forces arising from the secondary flow passages need to be understood using computational fluid dynamics theory. The Reynolds averaged Navier-Stokes equation may also be solved in a strong conservative form using an algebraic solver, where both compressible and incompressible flow fields may be modeled using the k ε turbulence model. The turbulent Reynolds stresses are approximated using the eddy viscosity principle, with the eddy viscosity related to the turbulent kinetic energy k and the dissipation rate e. Accuracy of shear stresses at the boundaries may be maintained by ensuring that grid points near the wall are placed in the proper logarithmic range. A full three-dimensional combined primary/secondary flow model may be built using a multiblock body-fitted mesh, then solved by performing a multiple frame of reference solution using different reference frames in various domain regions. A sliding interface is required at the boundaries between the regions, and may be placed across the primary flow just up- and downstream of the impeller 41

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45 To capture small and linear motion characteristics, eccentricity may be kept at 10 percent of the shroud clearance. 45

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47 UNCONTAINED FAILURE FROM FRACTURE OF FAN HUB In July 1996, a McDonnell Douglas MD-88 experienced an engine failure during the takeoff roll (NTSB AAR-98/01, 1998). The titanium fan hub had accumulated 16,542 h and 13,835 operating cycles at the time of the accident. The service life of the fan hub is limited to 20,000 cycles. 47

48 details of the fan hub The hub fractured through a tie-rod hole and blade slot. 48

49 One radial fracture contained a fatigue crack that originated at two locations on the inboard side of a tie-rod hole. Outside the fatigue region the fracture features were consistent with an overstressed separation. Metallurgical examination of the surface of the hole wall revealed an area in which the surface finish was darker than the surrounding area at each fracture origin, displaying evidence of circumferential machining marks consistent with machining marks associated with boring operation performed during manufacture. A magnified examination of the dark areas of the hole surface also showed a number of small parallel surface cracks aligned with the axis of the hole. A scanning electron microscope examination of the fracture face in the origin areas showed evidence of overstress to a depth of in, followed by an area about in deep that contained fracture features consistent with a fast-propagating fatigue crack. The marks were deemed to meet manufacturing standards, and were accepted. As a life-limited part, the fan hub must be inspected by the airline operator if the part was removed during engine overhaul using visual and fluorescent penetrant inspection procedures. 49

50 COMPRESSOR DISK FAILURE INVESTIGATION Rupture in a compressor disk during engine operation can result in disastrous consequences. An incident in June 1995 involving a Douglas DC-9 airplane during takeoff highlights this point (NTSB Report # AAR-96/03, 1996). Shrapnel from the right engine penetrated the fuselage and the main fuel line, the engine caught fire and spread to the cabin, the takeoff was rejected, and the aircraft stopped on the runway. The National Transportation Safety Board determined the probable cause was failure from rupture of the seventh-stage high-pressure compressor disk. A crack was not detected by maintenance and inspection personnel, and allowed the crack to grow to a length at which the disk ruptured under normal operating conditions. 50

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52 Maintenance records indicated that the failed disk had accumulated about 24,000 h and 6300 cycles, and had a life limit of 30,000 h or 18,900 cycles. The larger piece of the disk was fractured circumferentially (see arrows c ), which is typical of overstress. A radial fracture of the disk bore (position indicated by arrows h1 and h2 in the figure) had occurred. 52

53 Figure shows the aft face of the two recovered segments placed relative to each other by matching the fracture faces. Stress distribution holes are indicated by the arrows 1 through 9 and

54 Examination in a scanning electron microscope established that fatigue cracking originated from numerous pits in the hole wall and progressed radially toward the center of the disk from hole no. 1. Energy dissipative x-ray analysis of the pits on the hole surface revealed cadmium rich deposits with some nickel. The original manufacturing process calls for the disk to be plated with a Ni-Cad coating for corrosion protection. Fatigue striation development was noted to continue 0.88 in from the first hole. Secondary cracks originated at welldefined corrosion pits in the hole wall, with evidence of nickel and cadmium deposits. 54

55 The 12th-stage compressor disk from the accident engine, undamaged in the incident, was examined by safety board and manufacturer metallurgists. Several tie-rod holes in the disk had corrosion pits with nickel and cadmium plated on the pitted surface. 55