Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels—Part I: Numerical Method

Verstraete, Tom; Coletti, Filippo; Bulle, Je ́re ́my; Vanderwielen, Timothe ́e; Arts, Tony

doi:10.1115/1.4023030

Cited by 52 publications

(12 citation statements)

References 19 publications

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“…The sensitivities of the objective function with respect to all control points of the tri-variate B-spline are given by Equation (16). The design variables in this test case are limited to the control points on the skin of the U-bend, i.e., the surface that is allowed to change, thus excluding the long inlet and outlet legs (see Figure 2).…”

Section: Computation Of the Design Variable Sensitivitiesmentioning

confidence: 99%

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Verstraete

Müller

2017

IJTPP

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Abstract:The success of shape optimisation depends significantly on the parametrisation of the shape. Ideally, it defines a very rich variation in shape, allows for rapid grid generation of high quality, and expresses the shape in a standard Computer Aided Design (CAD) representation. While most existing parametrisation methods fail at least one of these criteria, this work introduces a novel parametrisation method, which satisfies all three. A tri-variate B-spline volume is used to define the volume to be optimised. The position of the external control points are used as design parameters, while the internal control points are repositioned to ensure regularity of the transformation. The grid generation process transforms a Cartesian grid (defined in parametric space) to the physical space using the tri-variate net of control points. This process guarantees a high grid quality even for large deformations, and has extremely low computational cost as it only involves a transformation from parameter space to physical space. This allows the computation of the grid sensitivities with respect to the design variables at a fraction of the cost of a Computational Fluid Dynamics (CFD) iteration, therefore allowing the use of one-shot methods. This novel parametrisation is applied to the shape optimisation of a U-bend passage of a turbine-blade serpentine-cooling channel with the objective to minimise pressure losses. A steady state, Reynolds-Averaged, density-based Navier-Stokes solver is used to predict the pressure losses at a Reynolds number of 40,000. The sensitivities of the objective function with respect to the control points are computed using a hand-derived adjoint solver and geometry generation system. A one-shot approach is used to simultaneously converge flow, gradient and design, resulting in a rapid design approach with a design time equivalent to approximately 10 normal CFD runs, while still maintaining a CAD representation of the geometry. A large reduction in pressure loss is obtained, and the flow in the optimal geometry is analysed in detail.

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Section: Computation Of the Design Variable Sensitivitiesmentioning

confidence: 99%

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Verstraete

Müller

2017

IJTPP

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“…This paper is the extension of the 2D style variation of inner surface to a 3D inner surface variation and the final optimum design was validated by the experiment using streolithography models. Recently, Verstraete et al 2 published similar U-bend optimisation study including inner and outer surface but these authors constrained their study to use 2D variation of the inner surface.…”

Section: Introductionmentioning

confidence: 96%

Optimisation of a 180° U-shaped bend shape for a turbine blade cooling passage leading to a pressure loss coefficient of approximately 0.6

Namgoong

Ireland

Son

2015

Proceedings of the Institution of Mechanical Engineers, Part G:

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The U-bend which turns flow through 180 is encountered in many applications in mechanical and aerospace engineering systems. One important example occurs in modern turbine blade cooling systems, where the internal cooling passages is threaded radially outwards and inwards to form a multi-pass arrangement where straight passages are connected with U-bends. The main purpose of the present investigation was to focus on finding a 3D U-bend configuration with minimum pressure loss using the 3D CAD-based surface parameterisation method. The design of experiment technique and surrogate design space model were successfully applied by the authors, as opposed to direct numerical optimisation, to reduce the computational cost. A standard Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics method with the Spalart-Allmaras one equation turbulence model was selected for. Even though the simple RANS with the one equation turbulence model cannot simulate the highly complex U-bend flow physics precisely, the optimisation process was able to identify an optimum U-bend configuration which achieved a 63.3% pressure loss reduction, relative to the datum configuration, yielding the lowest loss U-bend in the literature. The authors also performed careful experiments to confirm their predictions and the performance of the optimum U-bend configuration identified by this work was validated.

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“…Shape design involving fluid flow means determining a flow geometry that will satisfy the governing flow equations and boundary conditions while simultaneously meeting one or more design criteria, such as achieving the desired shape of an aerofoil, flow split in a T-junction or pressure loss in a return bend (Ashrafizadeh, Raithby, and Stubley 2004;Dulikravich 1992;Verstraete et al 2013). When the specified target is achieved by seeking an appropriate shape of the flow domain, the problem is known as inverse shape design.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of flow split ducting elements using an improved Box complex method

Srinivasan

Balamurugan

Jayanti

2016

Engineering Optimization

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Iterative search methods, such as the Box complex method, can be used for inverse shape design problems. In the present article, an improved version of the Box complex method is proposed specifically for computational fluid dynamics-based optimization of fluid flow ducting elements. The original Box complex method is improved by (1) assigning non-uniform weights for the estimation of the centroid, (2) using a reduced reflection factor for accelerated convergence, and (3) introducing measures to prevent premature breakdown of the iterative process. The success of the improved Box complex method over the original Box complex method is demonstrated on two benchmark functions and by applying it to two fluid flow problems of engineering. The improved method is shown to substantially accelerate the convergence with approximately 50% reduction in computational effort for the T-junction and manifold problems. ARTICLE HISTORYInverse shape design; internal flow; computational fluid dynamics; search algorithms; Box complex method; computational efficiency

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Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels—Part I: Numerical Method

Cited by 52 publications

References 19 publications

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Adjoint-Based Design Optimisation of an Internal Cooling Channel U-Bend for Minimised Pressure Losses

Optimisation of a 180° U-shaped bend shape for a turbine blade cooling passage leading to a pressure loss coefficient of approximately 0.6

Shape optimization of flow split ducting elements using an improved Box complex method

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