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This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method.

Continuous adjoint method is combined with the S2 surface code.

The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection.

The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method.

The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

The purpose of this paper is to propose the use of the continuous adjoint method as a tool to identify the appropriate location and “type” (suction or blowing) of steady jets used in active flow control systems.

The method is based on continuous adjoint and covers both internal and external aerodynamics. The adjoint equations, including the adjoint to the SpalartAllmaras turbulence model and their boundary conditions are formulated. At the cost of solving the flow and adjoint equations just once, the sensitivity derivatives of the objective function with respect to hypothetical (normal) jet velocities at all wall nodes are computed. Comparisons of the computed sensitivities with finite differences and parametric studies to assess the present method are included.

Though the sensitivities are computed for zero jet velocities, they adequately support decision making on: the recommended location of jet(s), at boundary nodes with high absolute valued sensitivities; and the selection between suction or blowing jets, based on the sign of the computed sensitivities. Regarding adjoint methods, two important findings of this work are: the role of the adjoint pressure which proves to be an excellent sensor in flow control problems; and the prediction accuracy of the proposed adjoint method compared to the commonly made assumption of “frozen turbulence”.

First use of the continuous adjoint method using full differentiation of the turbulence model, in flow control optimization. A low‐cost design tool for recommending some of the most important jet characteristics.

In magnetostatics, topology optimization (TO) addresses the problem of finding the distributions of both current densities and ferromagnetic materials to comply with fixed magnetic specifications. The purpose of this paper is to develop TO in order to design Hall-effect Thrusters (HETs).

In fact, TO problems are known to be large-scale optimization problems. The authors therefore adopt the adjoint method to reduce the computation time required to obtain the gradient information. In this paper, they illustrate the continuous variant of the adjoint method in the context of magnetostatics TO. Herein, the authors propose an implementation of the adjoint method then use it within a gradient-based optimization solver fmincon-MATLAB to solve a HET TO design problem.

By comparison with finite difference method, the authors validate the accuracy of the suggested implementation of the adjoint method. Then, they solve a large-scale HET TO design problem. The resultant design of TO is distinctly original and not intuitive.

In this paper, the authors introduce TO as a tool that has allowed them to explore new and innovative design of a HET. However, although the design presented is original, its manufacture is not feasible. Thus, a discussion section has been included at the end of paper to suggest a possible way to concretize topological solutions.

TO helps to explore more original design possibilities. In this paper, the authors present an implementation of the adjoint method that makes it possible to solve efficiently and in less central processing unit time large-scale TO design problem.

An easy implementation of the adjoint method is presented in magnetostatics TO. This implementation was first validated by comparison with the finite difference method and then used to solve a large-scale design problem. The result of the TO design problem is distinctly original and non-intuitive.

A complete CFD design methodology is presented. The main components of this methodology are a general edge‐based compressible/incompressible flow solver; a continuous adjoint formulation for the gradient computations; a steepest descent technique for the change of design variables; evaluation of the gradient of the discretized flow equations with respect to mesh by finite differences; a CAD‐free pseudo‐shell surface parametrization, allowing every point on the surface to be optimized to be used as a design parameter; and a level type scheme for the movement of the interior points. Several examples are included to demonstrate the methodology developed.

The presented study aims to minimize the energy consumed by a Hall effect thruster (HET) under a constraint which makes it possible to generate a specified magnetic field in a target region of the thruster.

Herein topology optimization (TO) is used to reduce the energy consumption of an HET while keeping its performance unchanged. The design variables are the current densities in the coils and the distribution of materials in the polar pieces of the thruster. Intermediate values of material distribution are penalized using the solid isotropic material with penalization method to favor binary solutions. By means of the adjoint method, this paper provides the derivatives of the objective and constraint functions with respect to material distribution and current density variables.

The TO-based design methodology is developed and validated on a design example involving 2,051 variables. The approach shows its interest and its effectiveness of on a large scale two-criteria problem.

In this paper, TO is presented as a tool that has allowed to explore new and innovative designs. However, although the design presented is original, its fabrication is not feasible. Despite this, the designs found give a good idea of the starting points for shape and parametric optimization tools.

Through the HET design problem, TO shows the ability to explore more original design possibilities of a complex magnetostatic design problem and to discover designs that make a HET more efficient with respect to several criteria at the same time.

A new way to reduce the energy consumption of a HET is presented. To achieve this, an adjoint-based TO method is developed and then implemented in a simple way. This approach shows that, for efficiency purposes, TO is a key tool for extending the state of the art of HET designs.

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.

The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.

The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.

The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.

This paper aims to present a dynamically adjusted deflated restarting procedure for the generalized conjugate residual method with an inner orthogonalization (GCRO) method.

The proposed method uses a GCR solver for the outer iteration and the generalized minimal residual (GMRES) with deflated restarting in the inner iteration. Approximate eigenpairs are evaluated at the end of each inner GMRES restart cycle. The approach determines the number of vectors to be deflated from the spectrum based on the number of negative Ritz values, k∗.

The authors show that the approach restores convergence to cases where GMRES with restart failed and compare the approach against standard GMRES with restarts and deflated restarting. Efficiency is demonstrated for a 2D NACA 0012 airfoil and a 3D common research model wing. In addition, numerical experiments confirm the scalability of the solver.

This paper proposes an extension of dynamic deflated restarting into the traditional GCRO method to improve convergence performance with a significant reduction in the memory usage. The novel deflation strategy involves selecting the number of deflated vectors per restart cycle based on the number of negative harmonic Ritz eigenpairs and defaulting to standard restarted GMRES within the inner loop if none, and restricts the deflated vectors to the smallest eigenvalues present in the modified Hessenberg matrix.

The purpose of this paper is to provide a design solution of an engine intake duct suitable for delivering air to the compressor of a gas turbine engine of a general aviation turboprop aircraft, where the initial duct shape suffers a problem of flow distortion due to flow separation at the compressor inlet.

Aerodynamic design uses a three-dimensional inverse-by-optimization approach where the deviation from a desirable target pressure distribution is minimized by means of the adjoint method.

By virtue of a minimization algorithm, the specified target pressure distribution does not necessarily have to be fully realizable to drive the initial pressure distribution towards one with a favourable pressure gradient. The resulting optimized engine intake duct features a deceleration region, in a diverging channel, followed by an acceleration region, in a contracting channel, inhibiting flow separation on the compressor inlet plane.

The flow separation at the compressor inlet has been eliminated allowing proper installation of the engine and flight testing of the aircraft.

Placement and shaping of the intake duct of a turboshaft and turboprop gas turbine engine is a common industrial problem which can be challenging when the available space is limited. The inverse-by-optimization approach based on a reduced flow model, i.e. inviscid flow based on the Euler equations, and a specification of a simple target pressure distribution constitutes an efficient method to overcome the challenge.

The purpose of this paper is to present applications of the topological optimization method dealing with fluid dynamic problems in two- and three dimensions. The main goal is to develop a tool package able to optimize topology in realistic devices (e.g. inlet manifolds) considering the non-linear terms on Navier–Stokes equations.

Using an in-house Fortran code, a Galerkin stabilized finite element is implemented method to solve the three equation systems necessary for the topological optimization method: the direct problem, adjoint problem and topological derivative. The authors address the non-linearity in the equations using an iterative method. Different techniques to create holes into a two-dimensional discrete domain are analyzed.

One technique to create holes produces more accurate and robust results. The authors present several examples of applications in two- and three-dimensional components, which highlight the potential of this method in the optimization of fluid components.

The authors contribute to the methodology and design in engineering.

Engineering fluid flow systems are used in many different industrial applications, e.g. oil flow in pipes; air flow around an airplane wing; sailing submarines; blood flow in synthetic arteries; and thermal and fissure spreading problems. The aim of this work is to create an effective design tool for obtaining efficient engineering structures and devices.

The authors contribute by creating an application of the method to design a tridimensional realistic device, which can be essayed experimentally. Particularly, the authors apply the design tool to an inlet manifold.