Power-to-Syngas: A Parareal Optimal Control Approach

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.

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

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.

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

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.

A complexity-driven framework for waveform tomography with discrete adjoints

Summary We develop a new approach for computing Fréchet sensitivity kernels in full waveform inversion by using the discrete adjoint approach in addition to the widely used continuous adjoint approach for seismic waveform inversion. This method is particularly well suited for the forward solver AxiSEM3D, a combination of the spectral-element method (SEM) and a Fourier pseudo-spectral method, which allows for a sparse azimuthal wavefield parametrization adaptive to wavefield complexity, leading to lower computational costs and better frequency scaling than conventional 3-D solvers. We implement the continuous adjoint method to serve as a benchmark, additionally allowing for simulating off-axis sources in axisymmetric or 3-D models. The kernels generated by both methods are compared to each other, and benchmarked against theoretical predictions based on linearized Born theory, providing an excellent fit to this independent reference solution. Our verification benchmarks show that the discrete adjoint method can produce exact kernels, largely identical to continuous kernels. While using the continuous adjoint method we lose the computational advantage and fall back on a full-3-D frequency scaling, using the discrete adjoint retains the speedup offered by AxiSEM3D. We also discuss the creation of a data-coverage based mesh to run the simulations on during the inversion process, which would allow to exploit the flexibility of the Fourier parametrization and thus the speedup offered by our method.

An Iterative Method for Shape Optimal Design of Stokes–Brinkman Equations with Heat Transfer Model

This work is concerned with the shape optimal design of an obstacle immersed in the Stokes–Brinkman fluid, which is also coupled with a thermal model in the bounded domain. The shape optimal problem is formulated and analyzed based on the framework of the continuous adjoint method, with the advantage that the computing cost of the gradients and sensitivities is independent of the number of design variables. Then, the velocity method is utilized to describe the domain deformation, and the Eulerian derivative for the cost functional is established by applying the differentiability of a minimax problem based on the function space parametrization technique. Moreover, an iterative algorithm is proposed to optimize the boundary of the obstacle in order to reduce the total dissipation energy. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of our method.

Shape Optimization of a Two-Fluid Mixing Device Using Continuous Adjoint

In this paper, the continuous adjoint method is used for the optimization of a static mixing device. The CFD model used is suitable for the flow simulation of the two miscible fluids that enter the device. The formulation of the adjoint equations, which allow the computation of the sensitivity derivatives is briefly demonstrated. A detailed analysis of the geometry parameterization is presented and a set of different parameterization scenarios are investigated. In detail, two different parameterizations are combined into a two-stage optimization algorithm which targets maximum mixture uniformity at the exit of the mixer and minimum total pressure losses. All parameterizations are in conformity with specific manufacturability constraints of the final shape. The non-dominated front of optimal solutions is obtained by using the weighted sum of the two objective functions and executing a set of optimization runs. The effectiveness of the proposed synthetic parameterization schemes is assessed and discussed in detail. Finally, a reduced length mixer is optimized to study the impact of the length of the tube on the device’s performance.