scholarly journals Continuous Adjoint-Based Optimization of an Internally Cooled Turbine Blade—Mathematical Development and Application

2021 ◽  
Vol 6 (2) ◽  
pp. 20
Author(s):  
Xenofon Trompoukis ◽  
Konstantinos Tsiakas ◽  
Varvara Asouti ◽  
Marina Kontou ◽  
Kyriakos Giannakoglou
Keyword(s):  
Turbine Blade ◽  
Gas Flow ◽  
Transfer Problem ◽  
Optimization Procedure ◽  
Free Form ◽  
Cooling Channels ◽  
Continuous Adjoint Method ◽  
Internally Cooled ◽  
Continuous Adjoint ◽  
Turbine Blading

This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also includes the adjoint to the turbulence model. Differences in the gradient resulting from making the frozen turbulence assumption are discussed. The developed software was used to optimize both the blade shape of the internally cooled linear C3X turbine blade and the position of cooling channels aiming at (a) minimum total pressure drop of the hot gas flow and (b) minimum highest temperature within the blade. A two-step optimization procedure was used. A free-form parameterization tool, based on volumetric NURBS, controls the blade airfoil contour, while the cooling channels are free to move following changes in the coordinates of their centers. Geometric and flow constraints are included in the performed optimizations, keeping the cooling channels away from the airfoil sides and retaining the turbine inlet capacity and flow turning.

Analysis of a Virtual Prototype First-Stage Rotor Blade Using Integrated Computer-Based Design Tools

2006 ◽  
Author(s):  
Michel Arnal ◽  
Christian Precht ◽  
Thomas Sprunk ◽  
Tobias Danninger ◽  
John Stokes
Keyword(s):  
Heat Transfer ◽  
Gas Flow ◽  
Thermal Loading ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Life Assessment ◽  
Element Analysis ◽  
Pressure Losses ◽  
Cooling Channels ◽  
Internally Cooled

The present paper outlines a practical methodology for improved virtual prototyping, using as an example, the recently re-engineered, internally-cooled 1st stage blade of a 40 MW industrial gas turbine. Using the full 3-D CAD model of the blade, a CFD simulation that includes the hot gas flow around the blade, conjugate heat transfer from the fluid to the solid at the blade surface, heat conduction through the solid, and the coolant flow in the plenum is performed. The pressure losses through and heat transfer to the cooling channels inside the airfoil are captured with a 1-D code and the 1-D results are linked to the three-dimensional CFD analysis. The resultant three-dimensional temperature distribution through the blade provides the required thermal loading for the subsequent structural finite element analysis. The results of this analysis include the thermo-mechanical stress distribution, which is the basis for blade life assessment.

Turbine Blade Aerodynamic Optimization on Unstructured Grids Using a Continuous Adjoint Method

2012 ◽  
Author(s):  
M. Zeinalpour ◽  
K. Mazaheri ◽  
A. Irannejad
Keyword(s):  
Turbine Blade ◽  
Adjoint Method ◽  
Suction Side ◽  
Adjoint Equations ◽  
Inverse Design ◽  
Aerodynamic Optimization ◽  
Design Variables ◽  
Continuous Adjoint Method ◽  
Flow Variables ◽  
Continuous Adjoint

A gradient based optimization using the continuous adjoint method for inverse design of a turbine blade cascade is presented. The advantage of the adjoint method is that the objective function gradients can be evaluated by solving the adjoint equations with coefficients depending on the flow variables. This method is particularly suitable for aerodynamic design optimization for which the number of design variables is large. Bezier polynomials are used to parameterize suction side of the turbine blade. The numerical convective fluxes of both flow and adjoint equations are computed by using a Roe-type approximate Riemann solver. An approximate linearization is applied to simplify the calculation of the numerical flux of adjoint variables on the faces of computational cell. The problem examined is that of the inverse design of NASA C3X blade that reproduces a given pressure distributions over its surfaces. Adjoint results show a good agreement with those obtained by finite-difference method.

Aerodynamic design optimization of a hypersonic rocket sled deflector using the free-form deformation technique

2021 ◽  
pp. 095441002199498
Author(s):  
Tianjiao Dang ◽  
Bingfei Li ◽  
Dike Hu ◽  
Yachuan Sun ◽  
Zhen Liu
Keyword(s):  
Design Optimization ◽  
Optimization Method ◽  
Free Form ◽  
Aerodynamic Design ◽  
Aerodynamic Shape ◽  
Aerodynamic Design Optimization ◽  
Continuous Adjoint Method ◽  
Free Form Deformation ◽  
Shape Parameterization ◽  
Continuous Adjoint

An aerodynamic design optimization of a hypersonic rocket sled deflector is presented using the free-form deformation (FFD) technique. The objective is to optimize the aerodynamic shape of the hypersonic rocket sled deflector to increase its negative lift and enhance the motion stability of the rocket sled. The FFD technique is selected as the aerodynamic shape parameterization method, and the continuous adjoint method based on the gradient method is used to search the optimization in the geometric shape parameter space; the computational fluid dynamics method for a hypersonic rocket sled is employed. An automatic design optimization method for the deflector is carried out based on the aerodynamic requirements of the rocket sled. The optimization results show that the optimized deflector meets the design requirement of increasing the negative lift under the constraint of drag. By improving the pressure distribution on the surface of the deflector, the negative lift is increased by 7.39%, which confirms the effectiveness of the proposed method.

scholarly journals The Influence of Rotation on the Internal Flow of a Cooled Turbine Blade With Serpentine-Shaped Cooling Channels

1997 ◽  
Author(s):  
Y. Otsuki ◽  
T. Sugimoto ◽  
R. Tanaka ◽  
D. E. Bonn ◽  
V. J. Becker ◽  
...  
Keyword(s):  
Turbine Blade ◽  
Gas Flow ◽  
Stokes Equations ◽  
Internal Flow ◽  
Computer Code ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
3 Dimensional ◽  
Cooling Channels ◽  
Blade Cooling

Numerical 3-D investigations have been carried out in order to analyze the cooling gas flow pattern inside a turbine blade configuration. The blade is not an actual industrial configuration but is representative for contemporary configurations. The cooling gas enters the serpentine cooling channels through the blade foot. The cooling gas mass flow is divided into two serpentine flows. One covers the front part of the blade and is ejected at the tip, the other serves the rear region and is ejected through a slot in the trailing edge. Internal turbulence promoters are neglected. Boundary conditions typical for front stage blade cooling gas states were chosen. The computations have been performed with the modern CHTFlow computer code, which solves the fully compressible 3-dimensional Navier-Stokes equations. First the influence of the diffusive transport mechanisms is investigated and shown to be quite important. Through comparison of computation in a fixed and rotating frame of reference, the significant influence of rotation is demonstrated.

scholarly journals Two view NURBS reconstruction based on GACO model

2021 ◽  
Author(s):  
Deepika Saini ◽  
Sanoj Kumar ◽  
Manoj K. Singh ◽  
Musrrat Ali
Keyword(s):  
Optimization Algorithms ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Least Square ◽  
Ant Colony ◽  
Free Form ◽  
Reconstruction Process ◽  
Nurbs Curve ◽  
Data Points ◽  
Ant Colony Optimization Algorithms

AbstractThe key job here in the presented work is to investigate the performance of Generalized Ant Colony Optimizer (GACO) model in order to evolve the shape of three dimensional free-form Non Uniform Rational B-Spline (NURBS) curve using stereo (two) views. GACO model is a blend of two well known meta-heuristic optimization algorithms known as Simple Ant Colony and Global Ant Colony Optimization algorithms. Basically, the work talks about the solution of NURBS-fitting based reconstruction process. Therefore, GACO model is used to optimize the NURBS parameters (control points and weights) by minimizing the weighted least-square errors between the data points and the fitted NURBS curve. The algorithm is applied by first assuming some pre-fixed values of NURBS parameters. The experiments clearly show that the optimization procedure is a better option in a case where good initial locations of parameters are selected. A detailed experimental analysis is given in support of our algorithm. The implemented error analysis shows that the proposed methodology perform better as compared to the conventional methods.

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

A chemical plant layout for the production of syngas from renewable power, H2O and biogas, is presented to ensure a steady productivity of syngas with a constant H2-to-CO ratio under time-dependent electricity provision. An electrolyzer supplies H2 to the reverse water-gas shift reactor. The system compensates for a drop in electricity supply by gradually operating a tri-reforming reactor, fed with pure O2 directly from the electrolyzer or from an intermediate generic buffering device. After the introduction of modeling assumptions and governing equations, suitable reactor parameters are identified. Finally, two optimal control problems are investigated, where computationally expensive model evaluations are lifted viaparareal and necessary objective derivatives are calculated via the continuous adjoint method. For the first time, modeling, simulation, and optimal control are applied to a combination of the reverse water-gas shift and tri-reforming reactor, exploring a promising pathway in the conversion of renewable power into chemicals.

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