Marble, F. E., 1964, “Three-Dimensional Flow in Turbomachines,” *High Speed Aerodynamics and Jet Propulsion*X , *Aerodynamics of Turbines and Compressors*. Princeton University Press.

Smith, L. H., Jr, 1969, “Casing Boundary Layers in Multistage Compressors,” *Proc. Symp. Flow Research on Blading*, Dzung, L. S., ed.

Serovy, G. K., 1981, “Axial-Flow Turbomachine Through Flow Calculation Methods,” AGARD Advisory Report No. 175, *Through Flow Calculations in Axial Turbomachines*, Ch. Hirsch and J. D. Denton, eds.

Cumpsty, N. A., 1989, *Compressor Aerodynamics*, Longman Scientific & Technical, Publisher.

Wu, C. H., 1952, “A General Theory of Three-Dimensional Flow in Subsonic or Supersonic Turbomachines of Axial-, Radial-and Mixed-Flow Type,” NACA TN 2604.

Jennions,
I. K., and Stow,
P., 1986, “The Importance of Circumferential Non-uniformities in a Passage-Averaged Quasi-Three-Dimensional Turbomachinery Design System,” ASME J. Eng. Gas Turbines Power, 108, pp. 240–245.

Howard,
M. A., and Gallimore,
S. J., 1993, “Viscous Throughflow Modeling for Multi-Stage Compressor Design,” ASME J. Turbomach., 115, p. 296.

Gallimore,
S. J., 1998a, “Viscous Throughflow Modeling of Axial Compressor Bladerows Using a Tangential Blade Force Hypothesis,” ASME J. Turbomach., 120, p. 662.

Khalid,
S. A., Khalsa,
A. S., Waitz,
I. A., Tan,
C. S., Greitzer,
E. M., Cumpsty,
N. A., Adamczyk,
J. J., and Marble,
F. E., 1999, “Endwall Blockage in Axial Compressors,” ASME J. Turbomach., 121, pp. 499–509.

Van Zante, D. E., Strazisar, A. J., Wood, J. R., Hathaway, M. D., and Okiishi, T. H., 1999, “Recommendations for Achieving Accurate Numerical Simulation of Tip Clearance Flow in Transonic Compressor Rotors,” ASME Paper No. 99-GT-390, accepted for the ASME J. Turbomachinery.

Wellborn,
S. R., Tolchinsky,
I., and Okiishi,
T. H., 2000, “Modeling Shrouded Stator Cavity Flows in Axial-Flow Compressors,” ASME J. Turbomach., 122, pp. 55–61.

Denton, J. D., and Singh, U. K., 1979, “Time Marching Methods for Turbomachinery Flow Calculations,” VKI-LEC-SER-1979-7, VKI.

Dawes,
W. N., 1992, “Toward Improved Throughflow Capability: The Use of Three-Dimensional Viscous Flow Solvers in a Multistage Environment,” ASME J. Turbomach., 114, pp. 8–17.

Denton,
J. D., 1992, “The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines,” ASME J. Turbomach., 114, pp. 18–26.

Hall, E. J., and Delaney, R. A., 1993, “Investigation of Advanced Counter Rotation Blade Configuration Concepts for High Speed Turboprop Systems,” NASA CR 187126.

Gallimore, S. J., 1998b, “Axial Flow Compressor Design,” *The Successful Exploitation of CFD in Turbomachinery Design*, IMechE, HQ, London.

Gallimore, S. J., 1999, Rolls Royce plc, private communication, Compressor Design.

Chen, J. P., Celestina, M. L., and Adamczyk, J. J., 1994, “A New Procedure for Simulating Unsteady Flows Through Turbomachinery Blade Passages,” ASME Paper No. 94-GT-151.

Dorney, D. J., Davis, R. L., Edwards, D. E., and Madavan, N. K., 1990, “Unsteady Analysis of Hot Streak Migration in a Turbine Stage,” AIAA Paper No. 90–2354.

Giles,
M. B., 1990, “Stator/Rotor Interactions in a Transonic Turbine,” AIAA J. Propulsion Power, 6, p. 621.

Gundy-Burlet,
K. L., Rai,
M. M., Stauter,
R. C., and Dring,
R. P., 1991, “Temporally and Spatially Resolved Flow in a Two-Stage Axial Compressor: Part 2—Computational Assessment,” ASME J. Turbomach., 113, No. 2, pp. 219–226.

Hodson,
H. P., and Dawes,
W. N., 1998, “On the Interpretation of Measured Profile Losses in Unsteady Wake-Turbine Blade Interaction Studies,” ASME J. Turbomach., 120, p. 276.

Rai, M. M., and Dring, R. P., 1987, “Navier–Stokes Analysis of the Redistribution of Inlet Temperature Distortion in a Turbine,” AIAA Paper No. 87–2146.

Sharma,
O. P., Pickett,
G. F., and Ni,
R. H., 1992, “Assessment of Unsteady Flows in Turbines,” ASME J. Turbomach., 114, pp. 79–90.

Hall, E. J., 1997, “Aerodynamic Modeling of Multistage Compressor Flowfields,” ASME Papers No. 97-GT-344 and 97-GT-345.

Adamczyk, J. J., 1985, “Model Equation for Simulating Flows in Multistage Turbomachines,” ASME Paper No. 85-GT-226.

LeJambre,
C. R., Zacharias,
R. M., Biederman,
B. P., Gleixner,
A. J., and Yetka,
C. J., 1998, “Development and Application of a Multistage Navier–Stokes Flow Solver: Part II—Application to a High-Pressure Compressor Design,” ASME J. Turbomach., 120, p. 215.

Mansour, M., 1999, AlliedSignal Engines, private communication, Multistage Compressor Simulations.

Wellborn, S. R., 1999, Rolls-Royce Allison, private communication, Multistage Compressor Simulations.

Reid, L., and Moore, R., 1978, “Design and Overall Performance of Four Highly Loaded, High-Speed Inlet Stages for an Advanced High-Pressure Ratio Core Compressor,” NASA TP 1337.

Denton, J., 1996, “Lessons Learned From Rotor 37,” presented at the Third International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows (ISAIF).

Adamczyk,
J. J., Mulac,
R. A., and Celestina,
M. L., 1986, “A Model for Closing the Inviscid Form of the Average-Passage Equation System,” ASME J. Turbomach., 108, p. 180.

Kirtley, K. R., Turner, M. G., and Saeidi, S., 1999, “An Average-Passage Closure Model for General Meshes,” ASME Paper No. 99-GT-077.

Rhie,
C. M., Gleixner,
A. J., Spear,
D. A., Fischberg,
C. J., and Zacharias,
R. M., 1998, “Development and Application of a Multistage Navier–Stokes Solver: Part 1—Multistage Modeling Using Body Forces and Deterministic Stresses,” ASME J. Turbomach., 120, p. 205.

Adamczyk, J. J., 1991, “A Mathematical Constraint Placed Upon Inter-Blade Row Boundary Conditions Used in The Simulation of Multistage Turbomachinery Flows,” AGARD Conf. Proc. 510, *CFD Techniques for Propulsion Applications*.

Adkins,
G. G., and Smith,
L. H., 1982, “Span-wise Mixing in Multistage Axial Flow Compressors,” ASME J. Eng. Power, , 104, p. 97.

Lewis,
K. L., 1993, “Spanwise Transport in Axial-Flow Turbines: Part 1—The Multistage Environment,” ASME J. Turbomach., 116, pp. 179–186.

Lewis,
K. L., 1994, “Spanwise Transport in Axial-Flow Turbines: Part 2—Throughflow Calculations,” ASME J. Turbomach., 116, pp. 187–193.

Butler, T. L., Sharma, O. P., Joslyn, H. D., and Dring R. P., 1989, “Redistribution of an Inlet Temperature Distortion in an Axial Flow Turbine Stage,” AIAA J. Propulsion Power, 5.

Graham, R. W., 1979, “Fundamental Mechanisms That Influence the Estimate of Heat Transfer to Gas Turbine Blades,” ASME Paper No. 79-GT-43.

Kerrebrock,
J. L., and Mikolajczak,
A. A., 1970, “Intra-Stator Transport of Rotor Wakes and Its Effect on Compressor Performance,” ASME J. Eng. Power, 92, p. 359.

Kirtley, K. R., Celestina, M. L., and Adamczyk, J. J., 1993, “The Effect of Unsteadiness on the Time-Mean Thermal Loads in a Turbine Stage,” SAE Paper No. 931375.

Orkwis, P. D., and Turner, M. G., 1999, “An Eulerian/Lagrangian Approach for Analyzing Temperature Segregation Effects in High Pressure Turbines,” to be published.

Valkov,
T., and Tan,
C. S., 1993, “Control of the Unsteady Flow in a Stator Blade Row Interacting With Upstream Moving Wakes,” ASME J. Turbomach., 117, pp. 97–105.

Valkov,
T. V., and Tan,
C. S., 1998, “Effect of Upstream Rotor Vortical Disturbances on the Time-Average Performance of Axial Compressor Stators: Part 1—Framework of Technical Approach and Wake-Stator Blade Interactions,” ASME J. Turbomach., 121, pp. 377–386.

Valkov,
T. V., and Tan,
C. S., 1999, “Effect of Upstream Rotor Vortical Disturbances on the Time-Average Performance of Axial Compressor Stators: Part 2—Rotor Tip Vortex/Streamwise Vortex-Stator Blade Interactions,” ASME J. Turbomach., 121, pp. 386–396.

Dawes, W. N., 1994, “A Numerical Study of the Interaction of a Transonic Compressor Rotor Over-tip Leakage Vortex With the Following Stator Blade Row,” ASME Paper No. 94-GT-156.

Fritsch,
G., and Giles,
M. B., 1993, “An Asymptotic Analysis of Mixing Loss,” ASME J. Turbomach., 117, pp. 367–374.

Smith,
L. H., 1996, “Wake Dispersion in Turbomachines,” ASME J. Basic Eng., 88 , No. 3.

Adamczyk, J. J., 1996, “Wake Mixing in Axial Flow Compressors,” ASME Paper No. 98-GT-29.

Batchelor, G. K., 1967, *An Introduction to Fluid Dynamics*, Cambridge University Press.

Deregel, P., and Tan, C. S., 1996, “Impact of Rotor Wakes on Steady State Performance of Compressor,” ASME Paper No. 96-GT-253.

Van Zante, D. E., Adamczyk, J. J., Strazisar, A. J., and Okiishi, T. H., 1997, “Wake Recovery Performance Benefit in a High-Speed Axial Flow Compressor,” ASME Paper No. 97-GT-535.

van de Wall, A. G., 1999, “A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions,” Ph. D Thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University.

Smith, L. H., Jr., 1996, Discussion of ASME Paper No. 96-GT-029 and ASME Paper No. 96-GT-253, Birmingham, United Kingdom.

Barankiewicz, W. S., and Hathaway, M. D., 1997, “Effects of Stator Indexing on Performance in a Low Speed Multistage Axial Compressor,” ASME Paper No. 97-GT-496.

Arndt,
N., 1993, “Blade Row Interaction in a Multistage Low-Pressure Turbine,” ASME J. Turbomach., 115, pp. 137–146.

Sharma, O. P., Stetson, G. M., Daniels, W. A., Greitzer, E. D., Blair, M. F., and Dring, R. P., 1997, “Impact of Periodic Unsteadiness on Performance and Heat Load in Axial Flow Turbomachines,” NASA Contractor Report No. 202319.

Wellborn, S. R., and Okiishi, T. H., 1996, “Effects of Shrouded Stator Cavity Flows on Multistage Compressor Aerodynamic Performance,” NASA CR 198536.

Adamczyk, J. J., Hathaway, M. D., Shabbir, A., and Wellborn, S. R., 1998, “Numerical Simulation of Multi-Stage Turbomachinery Flows,” presented at the Applied Vehicle Technology Symposium on Design Principles and Methods for Aircraft Gas Turbine Engines, Toulouse, France, May 11–15.

Cline, S. J., Fesler, W., Liu, H. T., Lovell, R. C., and Shaffer, S. J., 1977, “Energy Efficient Engine, High Pressure Compressor Component Performance Report,” NASA CR-168245.

Wisler, D. C., Koch, C. C., Smith, L. H., Jr., 1977, “Energy Efficient Engine, Preliminary Design Study of Advanced Multistage Axial Flow Core Compressors,” NASA CR 135133.

Smith, L. H., Jr., 1999, GE Aircraft Engines, private communication, CAFMIX II Development.

Turner, M. G., 1999, private communication, Blockage Estimates.

Liu, H. T., 1999, GE Aircraft Engines, private communication, Compressor Stall.

Shabbir, A., Celestina, M. L., Adamczyk, J. J., and Strazisar, A. J., 1997, “The Effect of Hub Leakage Flow on Two High Speed Axial Flow Compressor Rotors,” ASME Paper No. 97-GT-346.

Escuret, J. F., and Veysseyre, P. H., 1997, “Effect of a Mismatch Between the Buttons of Variable Stator Vanes and the Flowpath in a Highly Loaded Transonic Compressor Stage,” ASME Paper No. 97-GT-471.

Wellborn,
S. R., and Okiishi,
T. H., 1998, “The Influence of Shrouded Stator Cavity Flows on Multistage Compressor Performance,” ASME J. Turbomach., 121, pp. 486–497.

Shang,
T., Epstein,
A. H., Giles,
M. B., and Sehra,
A., 1993, “Blade Row Interaction Effects on Compressor Measurements,” AIAA J. Propulsion Power, 9, No. 4, p. 569.

Giles, M. B., 1992, “An Approach for Multi-stage Calculations Incorporating Unsteadiness,” ASME Paper No. 92-GT-282.

Cumpsty, N. A., Dong, Y., and Li, Y. S., 1995, “Compressor Blade Boundary Layers in the Presence of Wakes,” ASME Paper No. 95-GT-443.

Halstead,
D. E., Wisler,
D. C., Okiishi,
T. H., Walker,
G. J., Hodson,
H. P., and Shin,
H., 1997, “Boundary Layer Development in Axial Compressors and Turbines: Part 1 of 4—Composite Picture,” ASME J. Turbomach., 119, p. 114.

Hodson,
H. P., 1990, “Modeling Unsteady Transition and Its Effects on Profile Loss,” ASME J. Turbomach., 112, pp. 691–701.

Walker, G. J., 1974, “The Unsteady Nature of Boundary Layer Transition on an Axial Flow Compressor,” ASME Paper No. 74-GT-135.

Harvey, N. W., Schulte, V. S., Howell, R. J., and Hodson, H. P., 1999, “The Role of Research in the Aerodynamic Design of an Advanced Low Pressure Turbine,” Proc. 3rd European Conf. on Turbomachinery, IMechE, London, Mar.

Launder,
B. E., and Spalding,
D. B., 1974, “The Numerical Computation of Turbulent Flows,” Comp. Math. Appl. Mech., 3, p. 269.

Shih,
T. H., Liou,
W. W., Shabbir,
A., Zhu,
J., and Yang,
Z., 1995, “A New k–ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows,” Comp. Fluids, 23, No. 3, p. 227.

Hathaway,
M. D., Gertz,
J. B., Epstein,
A. H., and Strazisar,
A. J., 1986, “Rotor Wake Characteristics of a Transonic Axial-Flow Fan,” AIAA J., 24, No. 11, p. 1802.

Kotidis,
P. A., and Epstein,
A. H., 1991, “Unsteady Radial Transport in a Transonic Compressor Stage,” ASME J. Turbomach., 113, pp. 207–218.

Binder,
A., Foster,
W., Kruse,
H., and Rogge,
H., 1985, “An Experimental Investigation Into the Effect of Wakes on the Unsteady Turbine Rotor Flow,” ASME J. Eng. Mater. Technol., 107, p. 458.

van de Wall, A. G., Kadambi, J. R., Boyle, R. J., and Adamczyk, J. J., 1995, “The Transport of Vorticies Through a Turbine Cascade,” ASME Paper No. 95-GT-240.

Zierke, W. C., Straka, W. A., and Taylor, T. D., 1993, “The High Reynolds Number Flow Through an Axial Flow Pump,” Applied Research Lab. Penn. State Univ. T. R. 93-12.

Graf,
M. B., Greitzer,
E. M., Marble,
F. E., and Sharma,
O. P., 1999, “Effects of Stator Pressure Field on Upstream Rotor Performance”, ASME J. Turbomach., 122, this issue, pp. XXX–000.

Lighthill, M. J., 1964, “Introduction to Fourier Analysis and Generalized Functions,” Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press.