il..f.:, n it; :-..-.:::7!.. 4,7,,... -,,..,,i., I.,...-:,--.. -t,. ' THE AMERICAN SOCIETY OF MECHANICALENGINEERS 5, MS E 47tti St.,L._ Ma:Yogic, _ N.Y. 100,17 1-1.-.4.,!,rt. -;-± -` -416.1%44 # 1.,, i,..., i ;. for statimenticor:opinione advanced in p rapers or 'discussion at Meetings of the &sciatic; Of its DMsiens'Or The. Society shall not be Sections, or printed in Its Publications. Discussion is printed only It paper, is published' in an AgalE Journal. Authorization to photocopy. materiel for Infernal or rpersonal use under circumstance not failing within the ft:tiros* provisions of the Copyright Act Is 'greeted by ASME to libraries and other uteri registered with the Copyright Clearance Ceetef(CdC) Transactional Reporting Service provided that the base fee of $0.3.0. I: per page is paid directly to the CPC, 27 Congress Street.Sithin. MA 01970. Requests for special penniaslon or bulk reproduction should be addressed to the'asme Technical Putilshing Department ' u- '..;. - CopyrIgh10 1997 by ASME All'Alghts Fie served I "Printed In U.S.A. PHYSICS OF AIRFOIL CLOCKING_ IN AXIAL COMPRESSORS Karen L. Gundy-Burlet NASA Ames Research Center Moffett Field, CA 94035-1000 1111 11111111111 11 1111 11 Daniel J. Dorney Pratt St Whitney East Hartford, CT 06108 Abstract Axial compressors have inherently unsteady flow fields because of relative motion between rotor and stator airfoils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead to progressively more complex wake/wake and wake/airfoil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. The current study uses an unsteady, twodimensional thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of stator clocking in a lowspeed 2i-stage compressor. Relative motion between rotors and stators is made possible by the use of systems of patched and overlaid grids. Results include surface pressures instantaneous forces and efficiencies for a 21-stage compressor configuration. Nomenclature Cp Pressure coefficient, Cp Cr Force coefficient, Cr Tri or, r Force Number of iterations per airfoil passing period Pressure Pr, Compressor inlet total Pressure Dynamic pressure based on 1.4, U. Wheel speed at midspan Introduction Efficiency Density Pitch Subscripts Inlet Circumferential component Axial component The operating environment in a multistage turbomachine is inherently unsteady, with interactions occuring between rotor and stator airfoils. These interactions are both viscous and inviscid in nature. The potential field of each airfoil is inviscid in nature, and mainly affects adjacent airfoil tows. The viscous field is much more complex, with wakes from upstream airfoils convecting many chords downstream to interact with airfoils and other wakes. The effects of airfoil clocking (or indexing) on turbine performance has been investigated by Huber et al. (1995), Griffin et al. (1995) and Dorney and Sharma (1996). The studies showed changes in efficiency on order of 0.5% as the stators were clocked. The highest efficiencies occured when the first-stage stator wake impinged on the second-stage stator while the lowest occured when the first-stage stator wake convected through the middle of the second-stage stator passage. Very little work has been published on the subject of airfoil clocking in compressors though. Wake/wake and wake/airfoil interactions were investigated for a two-dimensional 2}-stage compressor configuration in Gundy-Burlet (1991). The effect of axial gap on the unsteady Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Downloaded From: http://proceedings.asmedigitalcollection.asme.org Orlando, on 10/11/2018 Florida Terms of Use: June http://www.asme.org/about-asme/terms-of-use 2-5, 1997
flow within the compressor was studied. It was expected that reducing the axial gap between successive airfoils would result in increased unsteady forces on the airfoils because of the stronger potential interaction. However, the results indicated that the amplitude and frequency of the unsteady forces could also be dependent on the interactions between the convected wakes and the airfoils. The wake structures could either increase or decrease the amplitude and frequency on the downstream airfoils. The purpose of this study is to determine if airfoil clocking (or indexing) strategies can be used to alter the steady and unsteady characteristics of the flow in a multistage compressor. An unsteady, two-dimensional thin-layer Navier-Stokes zonal approach is used for a parametric investigation of the effects of stator clocking on the unsteady flow in a 2}-stage compressor. Results include time-averaged pressures and pressure amplitudes, force polars and compressor efficiency.. Algorithm The current work is based on an extension of an approach developed by Rai and is discussed in detail in Rai (1987) and Rai, Madavan and Gaya (1993). The approach is reviewed in brief here. The flow field is divided into two basic types of zones. Inner "0" grids are used to resolve the flowfield near the airfoils. These "0" grids are overlaid on outer "H" grids which are used to resolve the flowfield in the passages between airfoils. The "H" grids are allowed to slip relative to one another to simulate the relative motion between rotors and stators. The thin-layer Navier-Stokes equations are solved in the inner zones where viscous effects are important. The Euler equations are used in the outer zones where viscous effects are weak. The governing equations are cast in the strong conservation form. A fully implicit, finite-difference 'method is used to advance the solution of the governing equations in time. A Newton-Raphson subiteration scheme is used to reduce the linearization and factorization errors at each time step. The convective terms are evaluated using a third-order-accurate upwind-biased Roe scheme. The viscous terms are evaluated using second-order accurate central differences. The Baldwin-Lomax (1978) turbulence model is used to compute the turbulent eddy viscosity. Details of the turbulence model, zonal and natural boundary conditions, grid configuration, bookkeeping system, and database management systems are discussed in Gundy-Burlet et al. (1989). Geometry and Grid The 21-stage compressor geometry used in this study models the midspan geometry of an experiment by Dring (AGARD, 1989) and is identical to the 50% axial gap configuration of Gundy-Burlet (1991). The experimental configuration consists of an inlet guide vane (IGV) followed by two rotor/stator pairs. There are 48 IGVs while each of the other rotor and stator blade rows contain 44 airfoils. It would be prohibitively expensive to compute the flow through the entire 224 airfoil system, so for this computation, the number of IGVs has been reduced to 44. The IGNrs have been resealed by a factor of 48/44 in order to maintain the same blockage as in the experiment. The flow has been computed only through one passage and periodicity has been used to model the other 43 passages. Note, scaling the IGV blade count in itself represents a form of airfoil clocking because the locations of IGV wakes are modified with respect to the first stator. The axial gaps between airfoil rows in the experimental and computational configurations are approximately 50% of the average axial chord. The circumferential positions of the first-stage rotor (rotor-1) relative to the second-stage rotor (rotor-2) and the first-stage stator (stator-1) relative to the second-stage stator (stator-2) were not documented in the experiment. For the calculations, the rotors were circumferentially aligned. The full computational model with all 8 separate stator displacements in terms of percentage of pitch is shown in Fig. 1. The zero displacement position was defined as the one in which the stators were circumferentially aligned. The other positions were evenly spaced at 12.5% of pitch apart. A zonal grid system is used to discretize the flowfield within the 2}-stage compressor. Figure 2 shows the zonal grid system used for the 0% displacement case. In Fig. 2, every other point in the grid has been plotted for clarity. There are two grids associated with each airfoil. An inner, body-centered "0" grid is used to resolve the flow near the airfoil. The thin-layer Navier- Stokes equations are solved on the inner grids. The grid points of the inner grids are clustered near the airfoil to resolve the viscous terms. The Euler equations are solved on the outer sheared cartesian "H" grids. The rotor and stator grids are allowed to slip past each other to simulate the relative motion between rotor and stator airfoils. In addition to the two grids used for each airfoil, there is also an inlet and an exit grid, for a total of 12 grids. Fine grids are used to obtain detailed data regarding the steady and unsteady flow structure in the compressor. The inner grids are dimensioned 214 x 44 (streamwise x tangential). The average value of y+, the non-dimensional distance of the first grid point above the surface, was approximately equal to 1.0 for all five blade rows. The outer grids have an average of 110 points in the axial direction, but they all have 87 points in the circumferential direction. The inlet and outlet grids have 40 and 42 points in the axial direction respectively, for a total of 102064 points in the grid. Results The results reported in this section are for the 21-stage compressor described above. These results were all computed at an inlet Mach number of 0.07, an inlet Reynolds number (based on the first-stage rotor chord) of 39,370 per cm, and a pressure rise of C 1.11. Several approximations should be considered when interpreting the following results. The flow in the compressor is three-dimensional with end-wall boundary layer growth, hub corner stall and tip leakage effects. Because STAGE-2 is a two-dimensional code, it is unable to compute these three-dimensional effects. Stream-tube contraction terms have not been implemented in the code, so the effect of the end-wall boundary layer growth is not modeled. For these computations, 2 sub-iterations per time-step and 2
Inlet Guide Vane First- Stage Rotor First- Stage Stator Second- Stage 87.5% Stator 75.0% 62.5% 50.0% Second- Stage Rotor 12.5% 0.0% c::,... Figural. 2112 stage compressor geometry with second-stage stator clocking positions. Figure 2. Zonal grid topology.
1000 time-steps per cycle have proven sufficient to provide both time-accuracy and stability. Here, a cycle is defined as the time it takes a rotor to travel a distance equal to 2atn/N, where r is the radius at midspan, n is the number of rotor blades being modelled and N is the number of rotor blades in the actual machine. Each simulation was run in excess of 100 cycles to ensure time-periodicity. The computations were performed on a Silicon Graphics PowerChallenge Array with 8 compute nodes each comprised of between 2 and 8 R8000 cpns. Shell scripts were used to automate the process. Eight separate clocking positions were chosen in this study in order to make optimal parallel use of an 8 cpu compute node. Each individual computation required 102p-secs per iteration per grid point and ran at 46 Mflops. Because of the parallelization, the combined throughput is 8 times these figures. Results will be presented for stator-2 only in this paper. For other detailed comparisons with experiment of the flow through the compressor, please see Gundy-Burlet, et al. (1991). Timeaveraged surface pressures have been compared with experimental data in Fig. 3 for stator-2. The time-averaged pressures are obtained by averaging the instantaneous static pressure over one cycle. The pressures are then non-dimensionalized and plotted with respect to axial distance. Time-averaged pressure for each of the 8 different stator positions is plotted here. No attempt has been made to distinguish between the different cases because the time-averaged pressures are quite similar to each other. Minor differences do not affect the overall good comparison with the experimental data. Simple time-averaged pressure plots do not adequately elucidate the effects of clocking. An unsteady analysis is required to investigate airfoil docking in ttubomachines. Force Polar plots are used to investigate both the frequendes and amplitudes associated with the unsteadiness.. These plots are generated by integrating the instantaneous surface pressure field and resolving the resultant force into its axial and tangential components. The two force components are plotted as a function of time. Because of the reflective boundary conditions and non-blade-passing-frequency shedding by the IGV, cycle-to-cycle periodicity cannot be obtained for the more sensitive variables, like forces or efficiencies. The forces are therefore ensemble averaged over 10 cycles. The reflective boundary conditions, which are applied 25 chords upstream of the IGV and downstream of the second stator, are used because non-reflecting boundary conditions do not maintain mass-flow rate. The tangential force is then plotted against the axial force. The symbol on each of the plots indicates the time average of the force over 10 cycles. Figures 4 through 10 show the force polars for the 0.0% through 87.5% displacements respectively. Each of the force polar plots has some characteristics in common. The average force appears to be the same for each displacement. There is a large excursion from the time-averaged force corresponding to the interaction of stator-2 with the rotor-2 wake. The interaction of stator-2 with wakes from upstream airfoils results in several small force variations. There are, however, large differences in the total amplitude of the forces about the time-averaged values. The smallest amplitude is for the 12.5% displacement case followed by 62.5% displacement case. The 25.0% and 37.5% displacements are similar to each other and have slightly larger amplitudes than the 12.5% and 62.5% cases. The 50.0%, 75.0% and 87.5% cases all have similar but slightly higher amplitudes yet again, and the largest amplitude case (0.0% displacement) has an amplitude of a little more than double that of the 12.5% displacement case. This variation occurs because of the differing interactions between stator-2 and the convected wakes from upstream airfoils. Stator clocking can also be seen to have an effect on the compressor efficiency. Using the definition from Oates (1984), compressor efficiency is given by Tit - 1.0 Note, the average efficiency is calculated using the time-average of the area-averaged total pressure and total temperature. The efficiency is temporally and spatially averaged over ten rotor blade-passing cycles at a position approximately 1.5 cm (17% of the rotor axial chord) aft of the second-stator trailing edge. Ensemble averaging over multiple cycles is used to average out small variations in efficiency due to the reflective boundary conditions used for this computation, as well as off-frequency shedding by the IGV. The efficiencies for the 8 separate displacements are shown in Table 1, along with the deviation from the average value.. With the exception of the low efficiency at 37.5% displacement, the efficiency roughly forms a sign wave with a peak value of 97.81% at 25.0% displacement and a minimum value of 97.20% at 87.5% displacement. The lower efficiency at the 37.5% displacement occurs because the wake of the first stator (in a time-averaged sense) begins to impact the suction surface of the second-stage stator, instead of the pressure surface. The relative impact point of the first-stator wake on the second stator has a significant effect on the unsteady potential field of the second stator. The wake also influences the angle of attack which the second stator experiences. In general, it was observed that higher efficiencies are observed when the firststator wake is located on the pressure side of the second-stator passage. A difference of approximately 0.6% in efficiency is consistent with estimates of efficiency gains of between 0.5% and 1.0% when turbine airfoils are clocked (Huber et al. 1995, Griffin et al. 1995). One interesting point is that the minimum amplitude on stator-2 (12.5% displacement) has an efficiency that is close to the peak value. Appropriate timing of this compressor could provide both higher efficiency as well as lower time-varying forces on stator-2. Displacement, %pitch 77 Aq 0.0 97.34-0.15 12.5 97.60 +0.11 25.0 97.81 +0.32 37.5 97.33-0.16 50.0 97.70 +0.21 62.5 97.53 +0.04 75.0 97.43-0.06 87.5 97.20-0.29 Table. 1. Compressor efficiency. - P' 1.0 (1) 4
32 34 36 38 40 42 44 Axial Distance, In. Figure 3. Time-averaged surface pressures The interactions between the convected wakes and the airfoils are visualized through the use of entropy contours. Blue indicates a lower level of entropy and red signifies a higher entropy region. In the interests of brevity, contours for a few illustrative cases are shown. Contours for the 12.5%, 37.5%, 62.5% and 87.5% displacements are shown in Figs. 12 through 15, respectively. The viscous flow field upstream of the second-stage stator is not significantly affected by the position of the stator. There are several important flow features whose convection paths need to be followed in order to understand the changes in amplitude and efficiency. The rotor-i wake convects downstream and is cut by stator-1. The faster convection rate along the suction surface (relative to the pressure surface) of stator-1 causes the cut ends of the rotor-1 wake to be displaced from each other about 40% of average chord. Rotor-2 then cuts the stator-2 wake, and the relative positions of the rotors causes one end of the rotor-1 wake to convect along the pressure surface of rotor-2. Thus, ahead of stator-2 for each case, there is a strong rotor-2 wake which has a complex grouping of interacting wakes on its pressure side and a single stator-1 wake intersecting its suction side. This group of wakes is circled near the trailing edge of rotor-2 in each of Figs. 12 through 15. It should be noted that clocking rotor-2 with rotor-i and stator-1 with the IGV would change the geometry and characteristics of these convected wake forms. The 12.5% displacement case (Fig. 12) is characterized by both high efficiency and low force amplitudes. It can be seen that stator-2 cuts the rotor-2 wake where it intersects with the "isolated" leg of the stator-1 wake. The 'isolated" leg of the stator-1 wake convects relatively quickly just off the suction surface of stator-2. Most of the circled wake grouping convects relatively slowly down the pressure surface of stator-2. The buildup of the wakes on the pressure surface of stator-2 is quite evident in Fig. 12. This stable arrangement interacts with the stator- 2 llovrfield to cause a slightly larger pressure difference between the pressure and suction surfaces which results in lower losses and force amplitudes on stator-2. For the 37.5% displacement case (Fig. 13), the circled gronping of wakes convects almost entirely along the suction surface of stator-2. The low-energy fluid sitting near the suction surface reduces the pressure difference from the pressure to suction surfaces of stator-2 thereby reducing the efficiency of the stator. A slight displacement of the stator-1 wake off the surface of stator-2 results in an efficiency improvement. The 62.5% case (Fig. 14) had a moderate efficiency and the second-lowest force amplitude. The circled grouping of wakes convects through the stator-2 passage well off the suction surface of stator-2. The 87.5% case (Fig. 15) shows the lowest efficiency of any stator-2 displacement. In this case, stator-2 cuts through the center of the circled wake/wake interaction region. The stator-1 wake convects down the pressure-side of the stator-2 passage without coming in contact with stator-2 while a large portion of the circled wakes convect down the suction surface. Small changes in the relative position of the second-stage stator with the upstream stator wake can have large non-linear effects on efficiency and force amplitudes. Summary A third-order accurate, upwind-biased, thin-layer Navier- Stokes zonal code (STAGE-2) has been used to investigate stator clocking in a multistage compressor. The effects of stator clocking on the unsteady flow within a low-speed 24-stage compressor have been investigated. The results indicate that clocking in multistage compressors is a complex, non-linear phenomenon which warrants further study. In particular, Variations in efficiency, force amplitudes and frequencies are functions of the relative position of the clocked airfoil and convected wake groupings. The optimal combination of high efficiency and low force amplitude occured when the stator-1 wake convected along the pressure surface of stator-2. A slight movement of the stator-1 wake to the suction surface of stator-2 resulted in a distinct loss in efficiency and higher amplitude unsteadiness. 5
When performing parametric studies of airfoil clocking, one must be careful in choosing the parameter variation in order not to overlook these effects. Acknowledgements The authors would like to acknowledge the High Performance Computing and Communications Program for computer time in support of this project. Bibliography AGARD, 1989, '"Test Cases for Computation of Internal Flows in Aero Engine Components", AGARD Propulsion and Energetics Panel, Working Group 18, AGARD-AR-275. B. S. Baldwin and H. Lomax, 1978, 'Thin layer approximation and algebraic model for separated turbulent Bow", AIAA Paper 78-257, January. Dorney, D. J., Sharma, 0. P., 1996, "A Study of Turbine Performance Increases Through Airfoil Clocking", AIAA Paper 96-2816, Lake Buena Vista, FL. Griffin, L. W., Huber, F. W., and Sharma, 0. P., 1995, 'Performance Improvement Through Indexing of Turbine Airfoils: Part II - Numerical Simulation,' ASME Paper 95-GT-28, Houston, TX, also to appear in the J. of Turbomachinery Gundy-Burlet, K. L., Rai, M. M., and Dring, R. P., 1989, "Two-Dimensional Computations of Multistage Compressor Flows Using a Zonal Approach", AIAA Paper 89-2452, Monterey, Calif., July. Gundy-Burlet, K. L., 1991, "Computations of Unsteady Multistage Compressor Flows in a Workstation Environment" ASME Paper 91-GT-336. Gundy-Burlet, K. L., Rai, M. M., Stauter, R. C., and Dung, R. P., 1991, "Temporally and Spatially Resolved Flow in a Two- Stage Axial Compressor, Part 2 - Computational Assessment", J. Turbomachinery, Vol. 113, No. 2, Apr., pp. 227-232. Huber, F. W., Johnson, P. D., Sharma, 0. P., Staubach, J. B., and Gaddis, S. W., 1995, "Performance Improvement Through Indexing of Turbine Airfoils: Part I - Experimental Investigation," ASME Paper 95-GT-27, Houston, TX, also to appear in the J. of Turbomachinery. Oates, G. C., 1984, "Aerothermodynamics of Gas Turbine and Rocket Propulsion", AIAA Educational Series. Rai, M. M., 1987, "Navier-Stokes Simulations of Rotor/Stator Interactions Using Patched and Overlaid Grids", J. Propulsion Power, Vol. 3, No. 5, Sept., pp.387-396. Rai, M. M., Madavan, N. K. and Gayali, S., 1993, "Multipassage Navier-Stokes Simulations of Turbine Rotor-Stator Interaction", J. Propulsion and Power, Vol. 9, No. 3, May-June, pp. 389-396. 6
-0.34-0.34-0.36-0.36 E5-0.38-0.40-0.38 15-0.40 0.28 0.30 0.32 0.34 0.36 0.38 Figure 4. Force Polars, 0.0% Displacement -0.34 0.28 0.30 0.32 0.31 CF.-' 0.36 0.38 Figure 8. Force Polars, 50.0% Displacement -036 - -038' -0.40 N. 0.28 0.30 0.32 0.34 0.36 0.38 Figure 5. Force Polars, 12.5% Displacement -0.34-034 032 0.34 Figure 9. Force Polars, 62,5% Displacement -036-036 -038-0.38-0.40 0.28 0.30 0.32 034 0.16 0.38 Figure 6. Force Polars, 25.0% Displacement -0.34-041 0.28 0.30 Figure 10. 0.32 0.34 0.36 0.38 CE-' Force Polars, 75.0% Displacement -0.36-038 -0.40 0.28 0.30 0.32 031 0.36 0.38 Figure 7. Force Polars, 37.5% Displacement 032 0.34 036 0.38 Figure 11. Force Polars, 87.5% Displacement 7
Iii.,sure. 12. Entropy Contours, Stator 2 displaced 1231% of pit( h. e figure Ii Entropy Oiniours..Siainr 2 displaced 27.5\% of pi!ch.. 4.1tAx lip's: 14. Ent topy Contouts, Stalin 2 displaced 62.5)% of pitch ilgure 15. hitt opy Construes, Stains 2 displaced 87.5% of pitch. 8