See discussions, stats, and author profiles for thispublication at:http://www.researchgate.net/publication/226415242Design optimization of axial flowcompressor blades with three-dimensional Navier-Stokes solverARTICLE in JOURNAL OF MECHANICAL SCIENCE ANDTECHNOLOGY APRIL 2012Impact Factor: 0.84 DOI: 10.1007/BF03185803CITATIONS READS23 7032 AUTHORS, INCLUDING: Kwang-Yong Kim Inha University 322 PUBLICATIONS 1,535 CITATIONS SEE PROFILE Availablefrom: Kwang-Yong Kim Retrieved on: 11 October 2015 KSME International Journal, Vol. 14, No.9, pp. 1005-1012, 2000 1005 Design Optimization of Axial Flow Compressor Blades with Three-Dimensional Navier-Stokes Solver Sang-Yun Lee, Kwang-Yong Kim* School of Mechanical, Aerospace and Automation Engineering, lnha University Numerical optimization techniques combined with a three-dimensional thin-layer Navier- Stokes solver are presented to find an optimum shape of a stator blade in an axial compressor through calculations of single stage rotor-stator flow. Governing differential equations are discretized using an explicit finite difference method and solved by a multi-stage Runge-Kutta scheme. Baldwin-Lomax model is chosen to describe turbulence. A spatially-varying time-step and an implicit residual smoothing are used to accelerate convergence. A steady mixing approach is used to pass information between stator and rotor blades. For numerical optimiza- tion, searching direction is found by the steepest decent and conjugate direction methods, and the golden section method is used to determine optimum moving distance along the searching direction. The object of present optimization is to maximize efficiency. An optimum stacking line is found to design a custom-tailored 3-dimensional blade for maximum efficiency with the other parameters fixed. Key Words: Numerical Optimization, Axial Compressor, Blade, Thin-Layer Navier-Stokes Equations, Stacking Line design and use of shock free, controlled diffusion 1. Introduction airfoils (CDA) for high-speed compressor appli- cations have been successfully completed. The Turbomachines have complicated flow phe- new designs use custom-tailored airfoils rathernomena such as separation, turbulent wakes, than the standard series of blade profiles such assecondary flows, and tip clearance vortices. Thus, NACA 400, NACA 65/circular are, and doubleaccurate flow analysis is essential for designing circular arc (Lakshminarayana, 1996). The CDAefficient aerodynamic blade shapes that reduce profiles minimize loss sources by diffusing theloss. Recently, with the development of sophisti- flow from supersonic to subsonic velocities with-cated measuring instruments and technology, out a shock wave, and by delaying boundaryprecise measurement of turbomachinery flow layer separation.fields are being obtained. This trend, coupled Hobbs and Weingold (1984) analyticallywith rapid CFD development and the use of CFD developed a series of controlled diffusion airfoilsin the design process, has led to the design of to be shock-free and to avoid surface boundarymore efficient fluid machinery. layer separation. In experimental cascade testing, Within the past 15 years, research into the the CDA profile demonstrated the capability of achieving low loss and increased incidence range Corresponding Author, at elevated Mach numbers, high loading levels, E-mail: kykim@inha.ac.kr and thicker leading and trailing edges, without TEL: +82-32-872-3096; FAX: +82-32-868-1716 performance penalty. School of Mechanical, Aerospace and Automation Engineering, Inha University, 253 Yonghyuri-dong, The CDA performance was compared with that Nam-ku, Incheon 402-751, Korea. (Manuscript of conventional NACA 65 airfoils by Rechter, et Received February 15, 2000 ; Revised May 24, 2000) al (1985). Two alternative sets of stator blades1006 Sang- Yun Lee and Kwang- Yong Kimwere designed and built, each having the same An H-type grid for the inlet flow region anddesign condition. Cascade and compressor tests, C-type grids around the rotor and stator are used.under the same flow conditions, revealed the Grids are overlapped by one cell at the interfacesuperiority of the CDA profile for axial compres- between two adjacent grid blocks because of thesors over NACA 65 airfoils. node-centered finite-difference scheme used in However, the capability of these modern airfoil the solver. At the interface, the solutions next toprofiles to realize their peak aerodynamic poten- the boundary are integrated circumferentially attial is limited by three-dimensional flow effects. each spanwise location and then they are storedThis is a result of these technical advances being for use as boundary conditions for the neighbor-built on the basis of a two-dimensional compress- ing grids.ible potential flow code combined with an im-proved boundary layer code. To design a full- 3. Compressor Blade Design Approachspan blade shape, Behlke (1986) used an integrat-ed corejendwall vortex design model to apply Although compressor blades are typicallyCDA technology to the blade sections near the designed on stream surfaces, coordinates of bladeend walls. sections are actually determined on a surface In this paper, optimization of the three-dimen- normal to the radial direction for the conveniencesional shape of a stator through the use of a single of construction.stage rotor-stator calculation is described. The There are some general rules for compressorflow field is treated as three-dimensional and blade design. Diffusion rates on the blade surfacesviscous. The airfoil stacking line is chosen as the should be reduced as much as possible. Thevariable to be optimized. This line is difficult to three-dimensional blade shape must be consistentoptimize using conventional design methods. The with the operating condition which varies alongairfoil stacking line is also an important variable the span. In addition some aerodynamic charac-in the determination of the 3-D blade shape. teristic variables must be insensitive over a wide operating range. As shown in the case of CDA 2. Flow Analysis airfoil shapes, efforts to reduce loss by controlling diffusion on the surface of a blade section have Three-dimensional Navier-Stokes equations been relatively successful. However, these designand energy equation are solved on body-fitted methods have not been developed sufficiently togrids using an explicit finite-difference scheme. allow design of full-span blade shapes that satisfyViscous terms in the stream wise direction are the complicated three-dimensional flowfield inneglected using a thin-layer approximation, and turbomachinery. Therefore, in this work, to takethose in other directions are calculated. The account for the effects of three-dimensional flowBaldwin-Lomax model is chosen as the turbu- structure in the design, stacking line optimizationlence model. An explicit Runge-Kutta scheme is of the stator was the main design objective.used to march from the initial to steady state with The stacking line determines the relative cir-a spatially varying time step to accelerate conver- cumferential coordinates of blades being stackedgence. Artificial dissipation terms are added to in the radial direction. A leaned and skewedresolve shocks. Mach numbers in each direction, blade can decrease the total energy loss throughtotal pressure, and total temperature are given at reduced secondary flow and diffusion in the bladethe inlet. At the exit, the hub static pressure ratio passages. For example, in a turbine application,is specified, and the radial equilibrium equation leaned, positively curved, and negatively curvedis solved along the blade span. A periodic tip blade cascades were tested experimentally by Hanclearance model is used to calculate rotor tip and et al (1994). In the case of the negatively curvedstator hub tip clearance flows. A no-slip and an blade, the secondary vortical losses were greatlyadiabatic wall conditions are used. reduced, and the efficiency was raised. Similarly,PDF File Count = 60019881