scholarly journals Turbine Airfoil Optimization Using Quasi-3D Analysis Codes

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Sanjay Goel
Keyword(s):  
Mach Number ◽  
Radial Direction ◽  
Evaluation Criteria ◽  
Inviscid Flow ◽  
Optimization Techniques ◽  
Mathematical Representation ◽  
3D Analysis ◽  
Flow Solver ◽  
Airfoil Optimization ◽  
Geometry Modeling

A new approach to optimize the geometry of a turbine airfoil by simultaneously designing multiple 2D sections of the airfoil is presented in this paper. The complexity of 3D geometry modeling is circumvented by generating multiple 2D airfoil sections and constraining their geometry in the radial direction using first- and second-order polynomials that ensure smoothness in the radial direction. The flow fields of candidate geometries obtained during optimization are evaluated using a quasi-3D, inviscid, CFD analysis code. An inviscid flow solver is used to reduce the execution time of the analysis. Multiple evaluation criteria based on the Mach number profile obtained from the analysis of each airfoil cross-section are used for computing a quality metric. A key contribution of the paper is the development of metrics that emulate the perception of the human designer in visually evaluating the Mach Number distribution. A mathematical representation of the evaluation criteria coupled with a parametric geometry generator enables the use of formal optimization techniques in the design. The proposed approach is implemented in the optimal design of a low-pressure turbine nozzle.

The Extension and Application of Three-Dimensional Time-Marching Analyses to Incompressible Turbomachinery Flows

1990 ◽  
Vol 112 (3) ◽  
pp. 385-390 ◽  
Author(s):  
P. J. Walker ◽  
W. N. Dawes
Keyword(s):  
Mach Number ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Flow Solver ◽  
Flow Equations ◽  
Long Wavelength ◽  
Time Marching ◽  
Wave Boundary

Conventional time-marching flow solvers perform poorly when integrating compressible flow equations at low Mach number levels. This is shown to be due to unfavorable interaction between long-wavelength errors and the inflow and outflow boundaries. Chorin’s method of artificial compressibility is adopted to extend the range of Denton’s inviscid flow solver and Dawes’ three-dimensional Navier–Stokes solver to zero Mach number flows. The paper makes a new contribution by showing how to choose the artificial acoustic speed systematically to optimize convergence rate with regard to the error wave–boundary interactions. Applications to a turbine rotor and generic water pump geometry are presented.

Mach Number Influence on Reduced-Order Models of Inviscid Potential Flows in Turbomachinery

2002 ◽  
Vol 124 (4) ◽  
pp. 977-987 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Mach Number ◽  
Steady Flow ◽  
Inviscid Flow ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Spatial Gradients ◽  
Potential Flows ◽  
Proper Orthogonal Decomposition Technique ◽  
Flow Through ◽  
Phase Angles

An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced-order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced-order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced-order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced-order models.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

1992 ◽  
Vol 114 (3) ◽  
pp. 553-560 ◽  
Author(s):  
O. Le´onard ◽  
R. A. Van den Braembussche
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Pressure Distribution ◽  
Velocity Component ◽  
Design Method ◽  
Normal Velocity ◽  
Flow Solver ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Transonic Cascade

A iterative procedure for blade design, using a time marching procedure to solve the unsteady Euler equations in the blade-to-blade plane, is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a nonzero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.

A Parallel Multiblock Multigrid Flow Solver for Arbitrary Mach Number Applications

2003 ◽  
Author(s):  
Ramesh Pankajakshan ◽  
Lafayette Taylor ◽  
W Briley ◽  
David Whitfield
Keyword(s):  
Mach Number ◽  
Flow Solver

scholarly journals The Use of Optimization Techniques to Design Controlled Diffusion Compressor Blading

1982 ◽  
Author(s):  
N. L. Sanger
Keyword(s):  
Optimization Procedure ◽  
Inviscid Flow ◽  
General Purpose ◽  
Optimization Techniques ◽  
Conjugate Directions ◽  
Surface Boundary ◽  
Controlled Diffusion ◽  
Constrained Problems ◽  
Blade Section ◽  
Stator Blade

A method is presented for automating compressor blade design using numerical optimization, and is applied to the design of a controlled diffusion stator blade row. A general purpose optimization procedure is employed, which is based on conjugate directions for locally unconstrained problems and on feasible directions for locally constrained problems. Coupled to the optimizer is an analysis package consisting of three analysis programs which calculate blade geometry, inviscid flow, and blade surface boundary layers. The optimization concepts are briefly discussed. Selection of design objective and constraints is described. The procedure for automating the design of a two-dimensional blade section is discussed, and design results are presented.

scholarly journals Data-Efficient Design Exploration through Surrogate-Assisted Illumination

2018 ◽  
Vol 26 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Adam Gaier ◽  
Alexander Asteroth ◽  
Jean-Baptiste Mouret
Keyword(s):  
Three Dimensional ◽  
Flow Simulation ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Efficient Design ◽  
Design Exploration ◽  
High Performing ◽  
Airfoil Optimization ◽  
Modeling Techniques ◽  
Illumination Algorithms

Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization algorithms because they produce diverse, high-quality solutions in a single run, instead of only a single near-optimal solution. Unfortunately, these algorithms currently require a large number of function evaluations, limiting their applicability. In this article, we introduce a new illumination algorithm, Surrogate-Assisted Illumination (SAIL), that leverages surrogate modeling techniques to create a map of the design space according to user-defined features while minimizing the number of fitness evaluations. On a two-dimensional airfoil optimization problem, SAIL produces hundreds of diverse but high-performing designs with several orders of magnitude fewer evaluations than MAP-Elites or CMA-ES. We demonstrate that SAIL is also capable of producing maps of high-performing designs in realistic three-dimensional aerodynamic tasks with an accurate flow simulation. Data-efficient design exploration with SAIL can help designers understand what is possible, beyond what is optimal, by considering more than pure objective-based optimization.

The Maximum Intensity of Tropical Cyclones in Axisymmetric Numerical Model Simulations

2009 ◽  
Vol 137 (6) ◽  
pp. 1770-1789 ◽  
Author(s):  
George H. Bryan ◽  
Richard Rotunno
Keyword(s):  
Numerical Model ◽  
Tropical Cyclones ◽  
Radial Direction ◽  
Initial Conditions ◽  
Azimuthal Velocity ◽  
Inviscid Flow ◽  
Small Radius ◽  
Grid Spacing ◽  
Fall Velocity ◽  
New Model

Abstract An axisymmetric numerical model is used to evaluate the maximum possible intensity of tropical cyclones. As compared with traditionally formulated nonhydrostatic models, this new model has improved mass and energy conservation in saturated conditions. In comparison with the axisymmetric model developed by Rotunno and Emanuel, the new model produces weaker cyclones (by ∼10%, in terms of maximum azimuthal velocity); the difference is attributable to several approximations in the Rotunno–Emanuel model. Then, using a single specification for initial conditions (with a sea surface temperature of 26°C), the authors conduct model sensitivity tests to determine the sensitivity of maximum azimuthal velocity (υmax) to uncertain aspects of the modeling system. For fixed mixing lengths in the turbulence parameterization, a converged value of υmax is achieved for radial grid spacing of order 1 km and vertical grid spacing of order 250 m. The fall velocity of condensate (Vt) changes υmax by up to 60%, and the largest υmax occurs for pseudoadiabatic thermodynamics (i.e., for Vt > 10 m s−1). The sensitivity of υmax to the ratio of surface exchange coefficients for entropy and momentum (CE/CD) matches the theoretical result, υmax ∼ (CE/CD)1/2, for nearly inviscid flow, but simulations with increasing turbulence intensity show less dependence on CE/CD; this result suggests that the effect of CE/CD is less important than has been argued previously. The authors find that υmax is most sensitive to the intensity of turbulence in the radial direction. However, some settings, such as inviscid flow, yield clearly unnatural structures; for example, υmax exceeds 110 m s−1, despite a maximum observed intensity of ∼70 m s−1 for this environment. The authors show that turbulence in the radial direction limits maximum axisymmetric intensity by weakening the radial gradients of angular momentum (which prevents environmental air from being drawn to small radius) and of entropy (which is consistent with weaker intensity by consideration of thermal wind balance). It is also argued that future studies should consider parameterized turbulence as an important factor in simulated tropical cyclone intensity.

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