Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method

Ahmadpour

Applied Thermal Engineering

et al. 2017

Highlights• CFD-based shape optimization of a nozzle and a turbine blade regarding nucleating steam flow is performed.• Nucleation rate and droplet radius are the best suited objective functions for the optimization p rocess.• Maximum 34% reduction in entropy generation rate is reported for turbine cascade.• A maximum 10% reduction in Baumann factor and a maximum 2.1% increase in efficiency is achieved for a turbine cascade. Abstract:In this study CFD-based shape optimization of a 3D nozzle and a 2D turbine blade cascade is undertaken in the presence of non-equilibrium condensation within the considered flow channels.A two-fluid formulation is used for the simulation of unsteady, turbulent, supersonic and compressible flow of wet steam accounting for relevant phase interaction between nucleated liquid droplets and continuous vapor phase. An in-house CFD code is developed to solve the governing equations of the two phase flow and was validated against available experimental

Section: Comparison Between Optimization In Dry and Wet Conditionsmentioning

confidence: 99%

Section: Comparison Between Optimization In Dry and Wet Conditionsmentioning

confidence: 99%

See 1 more Smart Citation

CFD-based shape optimization of steam turbine blade cascade in transonic two phase flows

Ahmadpour

Applied Thermal Engineering

et al. 2017

Journal of Turbomachinery

“…A gradient-based local algorithm together with the adjoint method can therefore handle a large number of design variables, needed to generate sophisticated industrial configurations. This global framework of shape optimization with adjoint method is widely used in turbomachinery [3][4][5][6][7][8], ranging from two-dimensional single-point cascade optimization to three-dimensional multipoint multistage optimization, and from steady to unsteady flows.…”

Section: Introductionmentioning

confidence: 99%

Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

Montanelli

Montagnac

Gallard³

2015

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

Volume 8: Turbomachinery, Parts A, B, and C

“…Euler equations Both the flow and adjoint solvers only account for the inviscid flow effects. The argument being that, in some external flows, such as in clean aircraft configurations, and in some internal flows, such as in some turbine blades, the viscous effects can be neglected since there are no regions of flow separation [9]. RANS with algebraic turbulence models The adjoint solver is consistent with the flow solver, but a simplistic turbulence model is used to expedite the developement of the former solver.…”

Section: Introductionmentioning

confidence: 99%

Interpretation of Adjoint Solutions for Turbomachinery Flows

Shankaran

Marta

Venugopal

et al. 2012

While the mathematical derivation of the adjoint equations and their numerical implementation is well established, there is a scant discussion on the understanding of the adjoint solution by itself. As this is a field solution of similar resolution of the flow-field, there is a wealth of data that can be used for design guidance. This paper addressess this specific topic. In particular, we take representative cases from turbomachinery aerodynamic problems and use the adjoint solution to identify the “physical insight” it provides. We aim to tie the adjoint solution to the flow-field which has physical properties. Towards this end, we first look at three problems 1) a fan, 2) a compressor rotor and stator, 3) a low pressure turbine. In all three of them, we focus on changes related to geometry, but one can also realize the changes using other inputs to the flow solver (eg. boundary conditions). We show how the adjoint counter-part of the density, the velocity fields and the turbulence quantities can be used to provide insights into the nature of changes the designer can induce to cause improvement in the performance metric of interest. We also discuss how to use adjoint solutions for problems with constraints to further refine the changes. Finally, we use a problem where it is not immediately apparent what geometry changes need to be used for further evaluation with optimization algorithms. In this problem, we use the adjoint and flow solution on a turbine strut, to determine the kind of end-wall treatments that reduce the loss. These changes are then implemented to show that the loss is reduced by close to 8%.