Semistructured grid generation in three dimensions using a parabolic marching scheme

Abstract

shock impingement point, it was observed that a reduction in  ow separation behind the shock ensued as a result of weakened shock strength. Conclusions The  owŽ eld inside transonic compressors involves high-level  ow physics and is very sensitive to changes in blade geometry. Therefore, the design of an axial compressor blade requires careful maneuvering through complex nonlinear design space. Numerical optimization is attractive in that constraints can be imposed to prevent ill effectsof a design.Constraints,however, limits designspace, and in the case of an axial compressor blade design, a constraint on inletmass  ow rate takes toomuchspaceaway,makingoptimization extremely difŽ cult to perform. This Note shows that incorporating the constraint into an objective function can improve the design results. Also if needed constraints are related to the objective function in someways, it would be possiblethat they all becomea part of the objective function while discouraging the design process from moving into certain directions. The study also shows that the developed design method can improve the adiabatic efŽ ciency of a blade section signiŽ cantly by reducing the losses from the passage shock and the  ow separation. The design method, however, cannot handle three-dimensional effects because it employs quasi-three-dimensional  ow physics and did not produce desired design results for the blade section near the hub region. To ascertain the signiŽ cance of the quasi-threedimensional design results, constructing and evaluating the performance of three-dimensionalblades based on the designed sections will be conducted in the future. References 1Damle, S., Dang, T., Stringham, J., and Razinsky, E., “Practical Use of 3D Inverse Method for Compressor Blade Design,” American Society of Mechanical Engineers, ASME Paper 98-GT-115, June 1998. 2Wang,Z., Cai, R., Chen, H., and Zhang,D., “A FullyThree-Dimensional Inverse Method for Turbomachinery Blading with Navier–Stokes Equations,” American Society of Mechanical Engineers, ASME Paper 98-GT126, June 1998. 3Sorenson, R. L., “A Computer Program to Generate Two-Dimensional Grids About Airfoils and Other Shapes by Use of Poisson’s Equation,” NASA TM-81198, 1980. 4Chima, R. V., “Explicit Multigrid Algorithm for Quasi-ThreeDimensionalViscous Flows in Turbomachinery,”Journalof Propulsion and Power, Vol. 3, No. 5, 1987, pp. 397–405. 5Wilcox, D. C., “Comparison of Two-Equation Turbulence Models for Boundary Layers with Pressure Gradient,” AIAA Journal, Vol. 31, No. 8, 1993, pp. 1414–1421. 6Katsanis, T., andMcNally,W.D., “Revised FORTRANProgramforCalculating Velocities and Streamlines on the Hub-ShroudMidchannel Stream Surface of an Axial-, Radial-, and Mixed-Flow Turbomachine or Annular Duct, Part I—User’s Manual,” NASA TN D-8430, 1977. 7“DOT User’s Manual,” Ver. 3.00, VMA Engineering,Goleta, CA, 1992. 8Hicks, R. M., and Henne, P. A., “Wing Design by Numerical Optimization,” Journal of Aircraft, Vol. 15, No. 7, 1978, pp. 407–412.