This paper presents a multidisciplinary design optimization of a turbocharger radial turbine for automotive applications with the aim to improve two major manufacturer requirements: the total-to-static efficiency and the moment of inertia of the radial turbine impeller. The search for the best design is constrained by mechanical stress limitations, by the mass flow and power, and by aerodynamic constraints related to the isentropic Mach number distribution on the rotor blade. The optimization of the radial turbine is performed with a two-level optimization algorithm developed at the von Karman Institute for Fluid Dynamics. The system makes use of a differential evolution algorithm, an artificial neural network (ANN), and a database as a compromise between accuracy and computational cost. The ANN performance predictions are periodically validated by means of accurate steady state 3D Navier-Stokes and centrifugal stress computations. The results show that it is possible to improve the efficiency and the moment of inertia only in a few numbers of iterations while limiting the stresses to a maximum value. Based on the large number of evaluated designs during the optimization, this paper provides design recommendations of a turbocharger radial turbine at least for a good preliminary design.

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.

The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD) workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP) algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier–Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.

This paper presents a gradient-based design optimization of a turbocharger radial turbine for automotive applications. The aim is to improve both the total-to-static efficiency and the moment of inertia of the turbine wheel. The search for the optimal designs is accomplished by a high-fidelity adjoint-based optimization framework using a fast sequential quadratic programming algorithm. The proposed method is able to produce improved Pareto-optimal designs, which are trade-offs between the two competing objectives, in only a few iterations. This is realized by redesigning the blade shape and the meridional flow channel for the respective target while satisfying imposed aerodynamic constraints. Furthermore, a comparative study with an evolutionary algorithm suggests that the gradient-based method has found the global Pareto front at a computational cost which is about one order of magnitude lower.

The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for computational fluid dynamics (CFD) validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents a sound methodology to design and optimize the LS89 using computer-aided design (CAD) at design conditions. The novelty of the study resides in the parametrization of design space, which is done at the CAD level, and the detailed analysis of the aerodynamic performance of the optimized design. Higher level constraints are imposed on the shape, such as the trailing edge thickness, the axial chord length, and G2 geometric continuity between the suction side and pressure side at the leading edge. The gradients used for the optimization are obtained by applying algorithmic differentiation to the CAD kernel and grid generator and the discrete adjoint method to the CFD solver. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced while keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The flow is governed by the Reynolds-averaged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case.

A sensitivity calculation using adjoint method has a feature of low calculation cost because sensitivity information of all computational grid points can be calculated by only one numerical simulation. From this feature, it has been utilized as a calculation method of sensitivity information for a gradient-based optimization and this optimization procedure with adjoint method can be one of suitable ways for centrifugal compressor impeller which has a lot of design parameters such as meridional shape, blade angle and thickness. During the gradient-based optimization, mesh morphing, which moves the computational grid directly based on sensitivity information, is generally used for shape deformation. However, the mesh morphing is difficult to implement due to shape constraints which is particularly required for rotating blades, such as minimum blade thickness and rotationally axisymmetric shape. In this study, in order to avoid these problems, sensitivity information of each grid point was converted into that of conventional design parameters, and optimization was carried out. In order to verify the effectiveness of this method, two different optimizations were carried out for centrifugal compressor impeller. In the single-point optimization which focuses on efficiency improvement, maximum efficiency was increased by 3.5% compared to a baseline impeller. While, multi-points optimization which considers balance between flow capacity and efficiency showed that the maximum efficiency was improved by 0.6% compared to the baseline impeller while maintaining the same flow capacity.