scholarly journals Continuous adjoint complement to the Blasius equation

2021 ◽  
Vol 33 (3) ◽  
pp. 033608
Author(s):  
Niklas Kühl ◽  
Peter Marvin Müller ◽  
Thomas Rung
Keyword(s):  
Blasius Equation ◽  
Continuous Adjoint

Continuous adjoint aerodynamic optimization design for multi-stage gas turbine with cooling air

2017 ◽  
Vol 89 (3) ◽  
pp. 444-456
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Gas Turbine ◽  
Optimization Design ◽  
Adjoint Method ◽  
Air Injection ◽  
Aerodynamic Optimization ◽  
Content Type ◽  
Multi Stage ◽  
Surface Code ◽  
Cooling Air ◽  
Continuous Adjoint

Purpose 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. Design/methodology/approach Continuous adjoint method is combined with the S2 surface code. Findings 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. Practical implications The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method. Originality/value 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.

scholarly journals A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 1: Offline forward and adjoint transport models

2017 ◽  
Vol 10 (3) ◽  
pp. 1157-1174 ◽  
Author(s):  
Yosuke Niwa ◽  
Hirofumi Tomita ◽  
Masaki Satoh ◽  
Ryoichi Imasu ◽  
Yousuke Sawa ◽  
...  
Keyword(s):  
Temporal Resolution ◽  
Meteorological Data ◽  
Forward Model ◽  
High Temporal Resolution ◽  
Tracer Transport ◽  
Adjoint Model ◽  
Transport Models ◽  
Flux Limiter ◽  
Adjoint Transport ◽  
Continuous Adjoint

Abstract. A four-dimensional variational (4D-Var) method is a popular algorithm for inverting atmospheric greenhouse gas (GHG) measurements. In order to meet the computationally intense 4D-Var iterative calculation, offline forward and adjoint transport models are developed based on the Nonhydrostatic ICosahedral Atmospheric Model (NICAM). By introducing flexibility into the temporal resolution of the input meteorological data, the forward model developed in this study is not only computationally efficient, it is also found to nearly match the transport performance of the online model. In a transport simulation of atmospheric carbon dioxide (CO2), the data-thinning error (error resulting from reduction in the time resolution of the meteorological data used to drive the offline transport model) is minimized by employing high temporal resolution data of the vertical diffusion coefficient; with a low 6-hourly temporal resolution, significant concentration biases near the surface are introduced. The new adjoint model can be run in discrete or continuous adjoint mode for the advection process. The discrete adjoint is characterized by perfect adjoint relationship with the forward model that switches off the flux limiter, while the continuous adjoint is characterized by an imperfect but reasonable adjoint relationship with its corresponding forward model. In the latter case, both the forward and adjoint models use the flux limiter to ensure the monotonicity of tracer concentrations and sensitivities. Trajectory analysis for high CO2 concentration events are performed to test adjoint sensitivities. We also demonstrate the potential usefulness of our adjoint model for diagnosing tracer transport. Both the offline forward and adjoint models have computational efficiency about 10 times higher than the online model. A description of our new 4D-Var system that includes an optimization method, along with its application in an atmospheric CO2 inversion and the effects of using either the discrete or continuous adjoint method, is presented in an accompanying paper Niwa et al.(2016).

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

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.

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