Abstract
This paper introduces a multi-level framework to perform a multi-objective multi-point aerodynamic optimization of the axial compressor blade. This framework results in a considerable speed-up of the design process by reducing both the design parameters and the computational effort. To reduce the computational effort, optimization procedure is working on two levels of sophistication. Fast but approximate prediction methods has been used to find a near-optimum geometry at the firs-level, which is then further verified and refined by a more accurate but expensive Navier–Stokes solver. Surface curvature optimization was carried out in a first-level as a meta-function. Genetic algorithm and gradient-based optimization were used to optimize the parameters of first-level and second-level, respectively. This procedure considers both the aerodynamic and mechanical constraints. An initial blade has been optimized with three different design targets to highlight the ability of the design method and to develop design know-how. Leading-edge shape and curvature distributions of pressure and suction surface had major effects on the design philosophies of the blades. The result shows about −22.5 % reductions in pressure-loss coefficient at design condition and 23.6 % improvement in the allowable incidence-angle range at off-design conditions compared to the initial blade.
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Abbreviations
- b :
-
Bluntness
- c :
-
Cord length (m)
- C :
-
Curvature
- C p :
-
Curvature of pressure side, pressure coefficient
- C s :
-
Curvature of suction side
- C t :
-
Curvature of thickness function
- cl :
-
Lift coefficient
- H :
-
Weight distribution function
- k :
-
Turbulence kinetic energy
- o :
-
Opening (m)
- P :
-
Point, local static pressure (pa)
- P 1 :
-
Inlet static pressure (pa)
- q :
-
Primitive variable (P, u, v, T)
- r :
-
Radius (m)
- s :
-
Tangential spacing of blade (m)
- t :
-
Thickness of blade (m), time (s)
- \({\hat{T}}\) :
-
Eigenvectors corresponding to the eigenvalues
- U i :
-
Velocity components
- V :
-
Inlet flow velocity (m/s)
- Wi :
-
Weight of objective function terms
- x :
-
x Coordinates (m)
- xk i :
-
Locations of maximum height of shape functions
- x j :
-
Coordinates
- y :
-
y Coordinates (m), distance to the nearest wall
- y i :
-
Weight of objective function terms
- Δα :
-
Incidence angle range (deg)
- \({\propto}\) :
-
Incidence angle (deg)
- β :
-
Metal angle (deg)
- \({\omega}\) :
-
Loss coefficient
- γ :
-
Stagger angle (deg)
- \({\varphi}\) :
-
Angle of opening diameter and y axis (deg)
- \({\delta}\) :
-
Leading edge thickness factor (deg)
- ρ :
-
Density (Kg/m3)
- \({\hat{\lambda}}\) :
-
Eigenvalues of the Jacobian matrixdetermined at Roe’s averaged condition
- \({\omega}\) :
-
Turbulent frequency
- \({\delta\omega }\) :
-
Wave amplitude
- \({\xi ,\eta }\) :
-
Coordinate axis in computational domain
- μ t :
-
Turbulent viscosity
- \({\nu _t}\) :
-
Turbulent kinematic viscosity
- 1,2,3:
-
Derivative order
- f:
-
First point of suction and pressure surface
- f_, f_s:
-
First point in pressure and suction surfaces
- fo1, fo2:
-
Point between leading edge and opening in the suction surfaces
- ft1, ft2:
-
Point between leading edge and maximum thickness in the pressure surfaces
- in:
-
Inlet
- l:
-
Leading-edge parameter
- min:
-
Minimum loss
- max:
-
Located at maximum thickness
- o:
-
Locate at opening
- ot1, ot2:
-
Point between opening and trailing edge in the suction surfaces
- out:
-
Outlet
- p:
-
Pressure surface
- ref:
-
Reference value
- s:
-
Suction surface
- s:
-
Parameters related to the thickness
- tt1, tt2:
-
Point between maximum thickness and trailing edge in the pressure surfaces
- t_p, t_s:
-
Last point at pressure and suction surfaces
- t:
-
Thickness
- W, E, N, S:
-
West, East, North, South
- L:
-
left
- R:
-
right
- ′:
-
First order derivative
References
Dunham, J.: A parametric method of turbine blade profile design. American Society of Mechanical Engineers, No 74-GT-119 (1974)
Corral, R.; Pastor, G.: Parametric design of turbomachinery airfoils using highly differentiable splines. J. Propuls. Power 20(2) (2004)
Keshin, A.; Dutta, A.K.; Bestle, D.: Modern compressor aerodynamic blading process using multi-objective optimization. ASME Turbo Expo, No.GT2006-90206 (2006)
Bonnaiuti, D.; Zangeneh, M.: On the coupling of inverse design and optimization techniques for the multiobjective, multipoint design of turbomachinery blades. J. Turbomach. 131(021014) (2009)
Korakiantis, T.: Hierarchical development of three direct-design methods for two-dimensional axial-turbomachinery cascades. J. Turbomach. 115(021014), 314–324 (1993)
Sonoda, T.; Yamaghuci, Y.; Arima, T.; Sendhoff, B.; Schreiber, H.: Advanced High Turning Compressor Airfoils for Low Reynolds Number Condition. ASME Paper, No.GT2003-38458 (2003)
Shahpar, S.; Radford, D.: Application of the FAITH Linear Design System to a Compressor Blade. Proceedings of ISAABE Conference, No. 99–7045 (1999)
Kammerer, S.; Mayer, J.F.; Paffrath, M.; Wever, U.; Jung, A.R.: Three-Dimensional Optimization of Turbomachinery Blading Using Sensitivity Analysis. ASME Paper, No. GT2003-38037 (2003)
Buche, D.; Guidati, G.; Stoll, P.: Automated Design Optimization of Compressor Blades for Stationary, Large-Scale Turbomachinery. ASME Paper No. 2003-38421 (2003)
Benini, E.; Tourlidakis, A.: Design Optimization of Vanned Diffusers of Centrifugal Compressors Using Genetic Algorithms. AIAA Paper No. 2001-2583 (2001)
Bonaiuti, D.; Pediroda, V.: Aerodynamic optimization of an industrial centrifugal compressor impeller using genetic algorithms. Proc. Eurogen (2001)
Samad, A.; Kim, K.Y.: Shape optimization of an axial compressor blade by multi-objective genetic algorithm. Proc. Inst. Mech. Eng. A J. Power Energy 222(6599-61) (2008)
Ju, Y.P.; Zhang, C.H.: Multi-point and multi-objective optimization design method for industrial axial compressor cascades. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 225(1481–1496) (2011)
Pierret, S.; Van den Braembussche, R.A.: Turbomachinery blading design using Navier Stokes solver and artificial neural network. ASME J. Turbomach. 121, 326–332 (1999)
Korakiantis, T.: Prescribed-curvature-distribution airfoils for the preliminary geometric design of axial- turbomachinery cascades. J. Turbomach. 115(JTM000325), 325–333 (1993)
Koller, U.; Mönig, R.; Küsters, B.; Schreiber, H.A.: Development of advanced compressor airfoils for heavy-duty gas turbines—part i: design and optimization. J. Turbomach. 122(JTM000397), 397–405 (2000)
Kermani, M.J.; Plett, E.G.: Roe Scheme in Generalized Coordinates; Part I- Formulations. American Institute of Aeronautics and Astronautics Paper 2001-0086 (2001)
Van Leer, B.: Towards the ultimate conservation difference scheme, V, a second order sequel to Godunov’s method. J. Comput. Phys. 32, 110–136 (1979)
Schreiber, H.A.; Starken, H.: Experimental Cascade Analysis of a Transonic Compressor Rotor Blade Section. West Germany ASME 288 (1984)
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Fathi, A., Shadaram, A. Multi-Level Multi-Objective Multi-Point Optimization System for Axial Flow Compressor 2D Blade Design. Arab J Sci Eng 38, 351–364 (2013). https://doi.org/10.1007/s13369-012-0435-7
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DOI: https://doi.org/10.1007/s13369-012-0435-7