Turbo Machinery Dynamics Part 5 pptx

consequence of shock are only a part of the problem, since interaction between the boundary layer and shock waves magnifies the viscous losses (Saravananamuttoo, Rogers, and Cohen, 2001). A damper at part span is required in long and flexible fan blades to control torsional and flexural motion, and also proves advantageous in the event of ingestion of a foreign object during the takeoff roll of the aircraft. However, the performance of the portion of the blade in the proximity of the damping device is diminished, especially if it is located where the Mach number is high. Wide chord fan blade development has eliminated the need for dampers, but improvements in manufacturing and stress analysis techniques have played no small role in bringing about this progress. A fan rotor with integral wide- chord blades machined from a single forging has been developed by some aircraft engine manufacturers. A hollow core with stiffeners helps to cut the weight of some very large fan blades. 6.2 STALL AND SURGE To understand the phenomenon of surging, consider a compressor operating at a constant speed. The machine is connected to a chamber. A throttle valve, placed in the discharge line from the chamber, is gradually opened. As the airflow rate increases, air pressure also rises from the initial point as a result of the built-up energy within the chamber. Maximum efficiency is reached at some point, and further flow leads to a decline in the pressure. With further opening of the valve, the flow rate reaches a point beyond the compressor’s capability. The airflow is not continuous and the efficiency drops off rapidly. In reality, most of the pressure between the initial valve opening and the point of maximum efficiency cannot be delivered because the flow tends to surge. A sudden drop in pressure, accompanied by considerable swings in the flow, rapidly spreads through the compressor during the process. When the compressor is operating at a point where the pressure is still rising, then a decrease in mass flow will cause the pressure also to reduce. If the pressure decline on the downstream side of the compressor occurs after a momentary delay, air will tend to flow back toward the source due to the positive pressure gradient. The pressure ratio then falls quickly. At the same time on the downstream side the pressure also falls, so the flow once again turns around away from the source. When the operating speed and flow rate are at a high level, the frequency at which the flow switches directions will also be high. In an aircraft engine the chamber represents the combustor at the end of the core compressor, and the turbine nozzles take the place of the throttle valve. There are two aspects in the discussion of stability, one pertaining to the flow in the compressor itself, the other of the overall system that includes the compressor. Stability-related issues may be studied FAN AND COMPRESSOR AIRFOILS 143 FIGURE 6.2 Fan airfoil profile for supersonic flow. with the aid of characteristics relating pressure rise with mass flow, and may be divided into separate regions (Fig. 6.3). In the normal operating region the flow is reasonably uniform around the annulus, without the flow separating from the end walls. In a central region of rotating stalls the flow breaks into cells, so some parts of the annulus have nearly normal flow, while others have negligible flow, the pattern turning at a speed less than the rotor’s angular velocity. In the last region flow separation is widespread. In the normal operating regime a positive perturbation in the mass flow results in a lower pressure rise, which results in a deceleration of the flow, correcting the initial excess mass flow and returning the stream back to its stable operating point. Flow perturbation in the central region follows on similar lines in the positive slope portion of the curve, and where the slope is zero the operation may be considered neutrally stable. Once it commences, the instability then develops into a rotating stall. The instability may even start when the slope is slightly neg- ative, possibly due to a nonzero disturbance in the compressor (Kerrebrock, 1992). As the onslaught of instability progresses, mass flow in the unstable embedded cells reaches to a near zero, while in the nonstalled cells it is normal. A single-stage fan or compressor may even experience unstable cells originating in a part of the blade span. With further throttling the cell may propagate to cover the whole blade and spread to fill more of the annulus. Rotating stall cells cover the full blade in multistage compressors. Progression of stall along the blade row may be explained by considering the direction of the flow. With a given passage partially blocked by the stall, flow is diverted to the neighboring passages. This results in an increase in the incidence angle in the next blade in the direction of stagger and a decrease in incidence in the adjacent blade in the opposite direction. This causes the stall region to push in the direction of stagger, propagating at a speed of 40 to 60 percent of the blade tangential velocity. The limit of stability in compressors may be defined by rotating stalls. Further pressure gains result in unsteady flow, causing considerable vibrations in the blades. With the onset of instability as established by the rotating stall due to the pressure rise in the compressor, the system’s behavior largely depends on the interaction with the combustion chamber into which the flow discharges. A parameter based on the time periods to raise the pressure in the combustor from a minimum to the normal operating (∆p min to ∆p design in Fig. 6.3) and for the flow to go through the compressor helps in the understanding (Greitzer, 1976). If V p and V c are flow velocities in the combustor and the compressor, the expressions for the time periods are τ charge = [(∆p/RT)V p ]/Compressor mass flow (6.1) τ flow = ( ρ V c )/Compressor mass flow (6.2) 144 COMPONENT DESIGN FIGURE 6.3 Compressor characteristic (Kerrebrock, 1992). Pressure rise ∆p design ∆p min Unstable Neutrally stable Stable Mass flow 0Q design The ratio of the time periods is (6.3) A detailed study of the problem reveals that the parameter (6.4) identifies the onset of instability, and also indicates if the situation progresses into a stable rotating stall or deteriorates into a full-scale surge. a is a dimensionless flow parameter when ∆p is minimal. Pressure rise depends on r(wr) 2 , hence time ratio t is proportional to B 2 . To understand how t impacts the flow instability establishment, consider operation of the compressor close to a point near the beginning of the stable part of the curve in Fig. 6.3. Unstable operation in the form of a rotating stall initiates at this point, leading to a reduction in pressure buildup. Two extreme cases, t >>1 and t << 1, may be reviewed. In the case of t assuming much larger values than 1, the mass stored in the combustor is considerable, hence flow in the compressor is mostly eliminated and degenerates into a rotating stall. Pressure at the compressor discharge is almost constant, thus flow in the compressor reaches a point of reversing, so the system quickly moves in a time period close to t flow and to a point in the unstable region of Fig. 6.3. Discharge from the combustor takes place over time t charge , to a pressure level that the compressor may be able to support in a rotating stall. Then in another time t flow , the flow rises to a point in the stable region, and the combustor plenum gets replenished in the time period t charge . The cycle becomes repet- itive and sustains itself if corrective action such as reducing fuel flow is not taken. Repeated surging cycles take a heavy toll on the durability of the whole engine system. Reduction in the fuel admitted has a similar effect as permitting more airflow through the combustor and into the turbine, so the compressor returns to the stable operating regime. If t << 1, the time required to enter and exit the combustor chamber is small enough to allow the compressor to provide airflow as the rotating stall develops. As a consequence, the compression process sets into a state where the compressor operates in a rotating stall condition steadily in the neutrally stable region of Fig. 6.3. Flow through the compressor, combustor, and past the turbine nozzle may be mathematically formulated by first-order differential equations using the component’s characteristics, pressures, velocities, and mass flows at the selected locations. The time period required for the rotating stall pattern to settle to a steady form may run over several turns of the rotor. Parameter B plays a substantial role in determining the solution of the equations. Geometric features tend to make the compressor characteristics, and hence the equations, considerably nonlinear. Physical effects of a surge in an aircraft engine’s compressor can be grave. A sudden stoppage in the airflow, with the engine emanating a loud noise, is common during such an event. When repeated a number of times, damage to the engine structure may be expected, particularly in the compressor and fan areas. Generally, the aircraft is capable of recovering from the stall and continue to proceed, albeit at a lower speed. If the aircraft is operating above Mach one, the consequences may be more severe. Unusually large pressure generated at the inlet due to the shock wave may result in distortion and damage to the structure. Loss of thrust experienced under such circumstances, although only for a short period of time, may cause the aircraft to go out of control under certain operating conditions. B r a V V p c = ω 2 τ τ τ ρ == charge flow (/)∆pV RTV p c FAN AND COMPRESSOR AIRFOILS 145 6.3 AIRFOIL DESIGN CONSIDERATIONS To understand the energy transfer between moving blades, recall the first two laws of ther- modynamics. For a unit mass, δ e = δ w − p δ (1/ ρ ) where e = internal energy W = mechanical work p = pressure r = density The second law is given by the expression ρ (Du/Dt) =−grad p, where Introducing the enthalpy term h = e + p/r and combining the equations yields the rela- tion (Lieblein, 1965): (6.5) According to this equation, in an inviscid, nonheat conducting limit, the stagnation temperature and pressure of a fluid may only be changed by an unsteady compression or expansion. The energy-transfer process provides a mathematically easier approach. Apply control surfaces on the upstream and downstream sides of a cascade, assume steady flow across these surfaces and identify a tube of stream in the direction of flow. Next, apply the laws of conservation of total fluid energy and of momentum in the direction of blade motion. If wr is the velocity of the blades, power delivered by the blades is P = Fwr, where F = (dm/dt)(v 2 − v 1 ) is the force on the rotor from the tube of stream. Here, the tube mean radius is r 1 , u 1 is the inflow velocity, and the tangential velocity is v 1 on the upstream side of the nozzle vanes. Corresponding parameters r 2 , u 2 , and v 2 are on the downstream of the rotating blades. Torque due to the tube of stream T = (dm/dt)(r 2 v 2 − r 1 v 1 ), so P = wT. Thus, the energy equation takes the form (6.6) This expression based on energy considerations is commonly referred to as the Euler equation for turbines, and relates changes in the enthalpy of the fluid in the rotor. For a per- fect gas c p T t = h + u 2 /2, and for an incompressible fluid r is constant, then the Euler equation takes the form (6.7) Flow past a row of compressor stator vanes and rotor blades may be conveniently represented by a velocity diagram. Figure 6.4 illustrates the scheme to develop the diagram for pp rv rv tt21 22 11 − =− ρ ω () h u h u rv rv 2 2 2 1 1 2 22 11 22 +       −+       =− ω () ρ Dh u Dt p t (/)+ = ∂ ∂ 2 2 D Dt t u= ∂ ∂ +⋅grad 146 COMPONENT DESIGN two nozzle vanes and a single blade stage. Flow velocity angles, denoted by b with a numerical subscript, are measured from the axial direction. A prime indicates the angle is in the moving coordinate system with the rotor. Velocities represented by solid arrows are in the fixed coordinate system, while dashed arrows are in the rotor frame. Hence, the first stator vanes turn the airflow to the angle b 2 , in the process raising the Mach number from M 1 to M 2 . Rotor blades receive the flow at the relative angle b ′ 2 , relative Mach number M′ 2 , turning it to b ′ 3 , and diffusing it to M′ 3 . The stator then receives the flow at angle b 3 and Mach number M 3 , turns it to b 4 and diffuses it to M 4 . Low-pressure ratio compressors can take advantage of the efficiency of one stage by duplicating the geometry in the successive stages by choosing the blading, such that M 4 ≈ M 3 and b 4 ≈ b 3 . The stages may even be identical. High-pressure compressors may require some modifications since Mach numbers tend to decrease with increases in air temperature (Kerrebrock, 1992). A composite velocity diagram for the stator and rotor may also be obtained by combining the data, as shown in the lower part of Fig. 6.4, so the variations in the rotor and stator velocities can be readily observed. The combined diagram indicates that the flow turn introduced by the first stator vanes allows the rotor and stator to be mostly mirror images of each other about the shaft axis, or b ′ 2 ≈ b 3 and b ′ 3 ≈ b 4 . FAN AND COMPRESSOR AIRFOILS 147 FIGURE 6.4 Generation of stage velocity diagram. Mach No. = M 1 Inflow velocity u 1 = v axial1 Stator c s Row 1 s s β 2 β′ 2 β 3 β′ 3 v 2 , M 2 v 2 , M′ 2 c r Rotor Row 1 s r Station # 3 v 3 , M 3 v′ 3 , M′ 3 Stator Row 2 β 4 Station # 4 v 4 , M 4 v 3 v 4 Composite rotor/stator v 2 v′ 2 v′ 3 velocity diagram wr wr wr wr Station # 1 Station # 2 In closely spaced blades, the angle of the flow exiting the blade is nearly equal to the angle of the trailing edge, the difference referred to as deviation. Blade chord is indicated by c, spacing between the blades by s, and ratio c/s = s is called solidity. Aircraft engine blades mostly have high solidity ratio, approaching 1.0. When the ratio of hub to tip radii is small, blade speed will change considerably from the root to the tip, causing a large effect on the velocity triangles and the corresponding airflow angles. At the same time, variations in pressure (and so density) will cause the velocity vectors to change in magnitude. Thus, velocity triangles at the mean blade height will not be representative of the whole blade. To maximize efficiency, the blade angles must also change over the length of the blade to match the flow angles, and so the blade will take a twisted form (Saravananamuttoo, Rogers, and Cohen, 2001). Inertia forces acting on an element of fluid arising from the whirl and axial flow com- ponents of the velocity are influenced by a number of factors. In the radial direction the forces are generated by: • Centripetal force arising from circumferential flow • Radial component of the centripetal force due to flow along the curved streamline • Linear acceleration along the streamline creating a force with a radial component Design flow conditions that are conducive to satisfying equilibrium in the radial direction may be described as (1) constant specific work, (2) constant axial velocity, and (3) free vortex variation of whirl velocity. Blades using the free vortex concept have a disadvantage arising from variation in the degree of reaction from root to tip, but find widespread usage in axial-flow combustion turbines. Even if the stage has a desirable 50 percent reaction at the mean radius, it is likely to be low at the root and high at the tip for maximized efficiency. A larger diffusion rate is called for at the blade’s root due to the lower tangential speed, so a low reaction rate aggravates the situation, and the problem increases in severity as the blade height increases. The constant specific work concept is helpful in delivering a better distribution of pressure ratio along the blade height. It is also possible to vary parameter values in the constant specific work concept that offers some of the features of the free vortex method, while still satisfying the radial equilibrium condition. In the matter of whirl velocity distribution along the height of the blade, for the first stage, the absence of inlet guide vanes precludes any whirl component as the air enters the compressor, and flow velocity will be constant around the annulus. For the other stages, axial velocity and prior stator outlet angle provide more flexibility in setting the whirl velocity. Air angle distributions for work done by a given stage must next be converted into blade angles along the length of the blade to establish the geometric form. Items to be pre- scribed for the purpose are the angle through which the airflow should turn (b out − b in for the rotor blade and a out − a in for the stator vane). Losses during the diffusion process must be held to a minimum. It is difficult to make the air exit the blade edge at the precise angle, while at the inlet the compressor is required to operate over a range of speed and pressure ratios. Flow angles are determined at design speed and compression pressure, hence it follows that at other operating conditions varying blade speed and flow velocity will change the air angle. The presence of the large array of parameters requiring definition inherently means that experience from a similar compressor will play a role in the selection of values, at least for some items. Correlated experimental and field verification also helps in the process. Cascade tests on rows of blades are now being passed over for results obtained from computational fluid dynamics. Figure 6.5 shows the parameters in a row of blades. Blade camber angle q, chord c, and pitch s are fixed for a given cascade group, and relative air 148 COMPONENT DESIGN inlet and outlet angles a 1 ′ and a 2 ′ are determined by the selected stagger angle z. Angle of incidence i is then determined by a choice of suitable air inlet angle, because i = a 1 − a 1 ′. Deflection of the air stream e = a 1 − a 2 may be obtained from observations on other blades of similar type, from computations or from cascade tests. Nominal values of e are mostly dependent on the pitch spacing to chord ratio, s/c, and air outlet angle a 2 . The impact on the deflection e due to other factors such as camber angle is not significant. Figure 6.6 provides representative values for nominal deflection values. These data are of consequence in the design process if two of the parameters are known, so the third item can then be established. The procedure is good for both stator vanes and rotating blades. Deviation in the flow at the blade exit angle may be calculated from the empirical rule d = mq√(s/c), where m = 0.23(2a/c) 2 + 0.1(a 2 /50), a is the point of maximum camber from the leading edge of the blade. If a circular arc is selected for the mean camber line, then 2a/c = 1. This set of information is now mostly adequate to establish the primary geometric parameters for the rotor blade. Blade chord may be placed relative to the axial direction by the stagger angle z. Particular details concerning the specification of the base profile are provided in Probs. 6.1 to 6.4. The National Advisory Committee for Aeronautics (NACA) series of blade profiles are extensively used in the turbine industry. FAN AND COMPRESSOR AIRFOILS 149 FIGURE 6.6 Airflow deflection curves (Saravananamuttoo, Rogers, and Cohen, 2001). FIGURE 6.5 Airfoil parameter identification. 6.4 UNSTEADY VISCOUS FLOW Unsteady turbomachinery flow computations are necessitated for the understanding and pre- diction of aeroelasticity phenomena, such as blade flutter and forced response. Nonlinear unsteady flow evaluation by the time marching method is useful for gaining insight into phenomena associated with finite amplitude excitation, boundary layer displacement, and large shock excursion, but become prohibitively expensive for large models. Methods based on nonlinear aerodynamics do not meet the immediate needs in turbomachinery design, where computationally efficient procedures for routine parametric calculations are the norm. A good compromise is offered by the linearized frequency domain procedure. A two- dimensional steady-state flow is obtained from the nonlinear potential equations. Three- dimensional effects are introduced by adding the stream tube thickness and changes in radius, then resolved by the linearized Euler method. When correctly formulated, shock capturing schemes become simpler to implement in three dimensions. Viscous flow effects are important in shock-boundary layer interaction, flow separation, and recirculation. Such flows are important for unsteady flow, since the investigations are conducted at off-design conditions. Generally speaking, fan blades encounter flutter at part speed, where the behavior of the flow is dominated by viscous effects. For a three- dimensional blade row the unsteady compressible Favre-averaged Navier-Stokes equation can be cast in absolute velocity, but solved in a relative non-newtonian reference frame rotating with the blade. The governing equations are linearized around the steady-state solution by expressing the conservative variables and the coordinates as a sum of a mean steady-state value and a small perturbation. The system of equations is linear in the sense that all coefficients of the unsteady flow terms depend on the steady-state flow and geometric properties, but not on time. Five different boundary conditions may be considered. Flow tangency at the solid walls is expressed by the requirement that there is no flow through the surface of the moving wall, hence the local fluid velocity relative to the wall has no component normal to it. No slip- page at the solid walls calls for the local fluid velocity relative to the moving wall to be zero. Periodic boundary conditions are somewhat more complicated. In a flutter application, the blade may oscillate with a nonzero phase shift in reference to its neighbors. Similarly, in an interaction between wake and rotor there is a phase shift in the unsteady pressure distribution experienced by the rotating blades if there is no one-to-one correspondence between the wakes and the blades. Unsteady flow computations require nonreflecting boundary conditions to prevent spurious inward reflections of outgoing waves at inflowing and outflow- ing boundaries. Single frequency nonreflecting boundary conditions may be used here (Giles, 1990). Consistent numerical implementation for the viscous and nonviscous fluxes requires linearization of the artificial dissipation and of the turbulence model. Artificial dissipation is a blend of second- and fourth-order differences to damp numerical oscillations in the vicinity of the discontinuities and to ensure stability of the scheme in smooth regions of the flow. Viscous fluxes contain contributions due to gradients of the unsteady flow velocity and temperature at constant viscosity, while also accounting for the variation of the unsteady viscosity. The evaluation requires linearization of the turbulence model used in the steady flow solver, but if it is neglected, the linearized viscous terms may still be represented using mean flow values for the eddy viscosity, sometimes called the frozen turbulence approach. A number of integration approaches are available when solving linearized equations using time marching algorithms. Marshall and Giles, (1997) use an explicit Runge-Kutta technique with a local time stepping. Montgomery and Verdon, (1997) propose a two-point backward implicit difference and expansion of the residual about the nth time level. 150 COMPONENT DESIGN The process is illustrated for flow over a transonic turbine blade, referred to as the 11th International Standard Configuration. A subsonic attached flow and a transonic flow exhibiting a separation bubble on the suction surface are considered. Figure 6.7 shows the computational grid used for the viscous calculations. Quadrilateral elements are deleted in the boundary layer for inviscid calculations. For the subsonic case the inlet flow angle is −15.2°, outlet isentropic Mach number is 0.69, and inlet Reynolds number based on blade chord is 650,000 (Sbardella and Imregun, 2001). On the suction surface both viscous and inviscid calculations overpredict the Mach number distribution in the midchord region, but the steady flow is captured adequately to initiate the linearized unsteady flow. The isentropic Mach number distribution along the chord is shown in Fig. 6.8. For the transonic off-design case the inlet flow angle is 34°, outlet isentropic Mach number is 0.99, and inlet Reynolds number based on chord length is 860,000. A noteworthy feature of the flow, the recirculation bubble on the suction surface, is indicated in Fig. 6.9. Because of the significant viscous features, the Navier-Stokes analysis shows good agreement with measured data reported by Fransson et al. (1999), with the exception of behavior at the trailing edge. However, the differences noticed in the steady-state flow lead to major discrepancies for unsteady flow predictions. Unsteadiness arising from the bending of the blade normal to the chord serves as a good example. The reduced frequency is 0.21 for the subsonic case and 0.15 for the transonic case. The amplitude of the pressure distribution for the subsonic case is in good agreement with the measured data, although deviations are noticeable in the phase. A similar comparison for the transonic case overpredicts the unsteady pressure coefficient on the suction side in the 0 to 30 percent chord region and around the trailing edge. Thus, the linearized viscous flow approach for the turbine blade provides useful data for the subsonic case, but discrepancies are evident in the transonic condition. FAN AND COMPRESSOR AIRFOILS 151 FIGURE 6.7 Computational grid (Sbardella and Imregun, 2001). 6.5 FLOW CHARACTERISTICS AT STALL INCEPTION The inception of two forms of rotating stalls has been observed in axial compressors. One of them, called modal stall, is characterized by waves with length scale on the order of the compressor’s circumference, and propagates at a speed of one-fourth to one-half the speed of the rotor (Haynes, Hendricks, and Epstein, 1994; Tryfonidis, 1995). Another considerably different rotating stall is characterized by disturbances with a dominant length scale much shorter than the circumference, on the order of several blade pitches, and a propagation speed of 70 to 80 percent of the rotor speed. In contrast to the inception of a modal stall, mechanistic description of this phenomenon is difficult due to the shorter length, and may best be referred to as spikes. Experiments indicate that this rotating stall inception possesses a radial structure (ref: Silkowsky, 1995), 152 COMPONENT DESIGN FIGURE 6.8 Isentropic Mach number distribution—subsonic case (Sbardella and Imregun, 2001). FIGURE 6.9 Transonic case separation bubble (Sbardella and Imregun, 2001). [...]... 25. 35 kg/s, and Mach number at inlet midspan is 0.22 The instrumented row has 63 blades of 110-mm chord length at midspan and 116-mm at the tip, solidity of 1 .55 at the tip, and stagger angle of 40 .5 Nominal clearance at the tip is 1 .55 mm The stator has 83 vanes with a chord length of 89 mm Signs of instability for the nominal clearance were not observed, hence it was enlarged to 2.3, 3 .5, and 5. 0... of the disturbance, the upstream velocity near the tip is shown in Fig 6.12 for the computations and for the experiment conducted by Silkowsky (19 95) on the E3 154 COMPONENT DESIGN 2 .5 θ = 2π Inlet axial velocity 2 1 .5 1 0 .5 θ=0 0 A −0 .5 −10 B C 5 D 0 5 Time (periods) FIGURE 6.10 Traces of inlet axial velocity (Hoying et al., 1998) compressor at 20 percent immersion The origin of the time scale is... boundary layer Stalling static 177 FAN AND COMPRESSOR AIRFOILS 3 .5 Wind tunnel Rotating rig Representative 95% confidence interval AbCos(be)/tc 3.0 2 .5 t = Tip clearance height 2.0 c = Chord length 1 .5 b = Relative flow angle Ab = Blocked area 1.0 0 .5 0 0.4 0 .5 0.6 0.7 0.8 Difference in static and total defect pressure coefficients FIGURE 6. 35 0.9 Blockage of flow area vs blade pressure loading (Khalid... location stall from the DRA compressor is shown in Fig 6.23 164 COMPONENT DESIGN Pressure at 5 circumferential positions 70% speed Probe # 5 Probe # 4 Probe # 3 Emerging stall cell Probe # 2 Speed 51 % Probe # 1 0 8 Speed 33% 16 24 Time, rotor revolutions 32 40 Pressure at 5 circumferential positions 85% speed Probe # 5 Probe # 4 Probe # 3 Modal activity Probe # 2 Probe # 1 666 FIGURE 6.21 668 670 672 674... layer thickness between zero and 3 .5 clearance heights, blade stagger angles between 35 and 65 , clearances between 1.4 and 3 .5 percent of chord, solidities of 1.1 and 1.6, and jet pressure coefficient varying from free stream to 60 percent of free stream When the inlet displacement thickness is changed from 0 to 3 .5 clearance heights, normalized blockage increases from 0.8 to 1.2 of the datum value... straighteners, the rotor has 51 controlled diffusion blades with tip chord = 119 mm, tip solidity = 1.26, tip camber = 25. 4°, and hub-to-tip ratio = 0.8 Inlet guide vanes are 3.2 rotor chords upstream of the rotor leading edge to impart swirl to the flow, but permit circumferential nonuniformities due to the wakes Data are collected primarily with a slant hot wire traversed radially 15 percent chord downstream... clearance leakage angle decrease The combined effect of the two is a reduction in the exit plane blockage as the stagger angle increases For a 50 -percent increase in solidity the blockage is reduced by 5 to 30 percent for stagger angles ranging from 35 to 65 Increased solidity decreases blade loading for the same overall passage pressure rise, reducing the leakage jet angle and clearance mass flux... bending and torsion in a blade mode The plot of imag2 2 2 inary part of the spanwise blade mode number p = (l 0 − w b)/w 0 and the complex number l 0 are shown as a function of the real part of p Here l and w are the reduced and circular frequencies of vibration Three sets of calculations are made for a fixed frequency parameter l = 0. 15 and varying amounts of bending and torsion loads Either method... acquired signals permit correlation between various sensors The first indication of unstable operation occurs with a tip clearance of 3 .5 mm, and a more complete development appears with a 5. 00-mm clearance The signs are observed at a number of speed points between 50 and 100 percent Figure 6.13 provides details of the compressor characteristics At the 0.87 mass flow rate point, a narrow band of indications... spectrum at casing wall (Mailach, Lehman, and Vogler, 2000) 158 COMPONENT DESIGN + Maximum pressure − Minimum pressure FIGURE 6. 15 2000) Propagation of rotating instabilities in blade tip region (Mailach, Lehman, and Vogler, spectrum measured at the casing wall for an operating point near the stability limit; the blade tip clearance is 5. 0 mm, the machine is operating at design speed, and the mass . inception and development. 154 COMPONENT DESIGN FIGURE 6.10 Traces of inlet axial velocity (Hoying et al., 1998). 2 .5 2 1 .5 0 .5 −0 .5 0 1 Inlet axial velocity −10 50 5 Time (periods) AB C D θ =. rpm, mass flow is 25. 35 kg/s, and Mach number at inlet midspan is 0.22. The instrumented row has 63 blades of 110-mm chord length at midspan and 116-mm at the tip, solidity of 1 .55 at the tip, and. curves (Saravananamuttoo, Rogers, and Cohen, 2001). FIGURE 6 .5 Airfoil parameter identification. 6.4 UNSTEADY VISCOUS FLOW Unsteady turbomachinery flow computations are necessitated for the understanding

Định dạng
Số trang	40
Dung lượng	906,43 KB