Adjoint-Based Optimization of a Modern Jet-Engine Fan Blade

A Multi-point Approximation Method (MAM) coupled with adjoint is presented to increase the efficiency of a modern jet-engine fan blade. The study performed makes use of Rolls-Royce in-house suite of codes and its discrete adjoint capability. The adjoint gradient is used along with MAM to create a Design Of Experiment to enhance the optimization process. A generalized Free-Form Deformation (FFD) technique is used to parametrize the geometry, creating a design space of 180 parameters. The resulting optimum blade at design conditions is then evaluated at off-design conditions to produce the characteristic curve, which is compared with real test data. Finally, a preliminary Active Design Subspace (ADS) representing the fan efficiency is created to evaluate the robustness of the objective function in respect to the most significant design parameters. The ADS allows to collapse a large design space of the order of hundreds parameters to the few most important variables, measuring their contribution. This map is valuable in many respects to the fan designers and manufacture engineers to identify any ridges where the performance may deteriorate rapidly, hence a more robust part of the design space can easily be visualized and identified.

The Adjoint Gradient Method for Time-Optimal Control of a Moon Landing: Ascent, Descent, and Abort

This article illustrates a novel approach for the determination of time-optimal controls for dynamic systems under observance of end conditions. Such problems arise in robotics, e.g. if the control of a robot has to be designed such that the time for a rest-to-rest maneuver becomes a minimum. So far, such problems have been considered as two-point boundary value problems, which are hard to solve and require an initial guess close to the optimal solution. The aim of this contribution is the development of an iterative, gradient based solution strategy for solving such problems. As an example, a Moon-landing as in the Apollo program, will be considered. In detail, we discuss the ascent, descent and abort maneuvers of the Apollo Lunar Excursion Module (LEM) to and from the Moon’s surface in minimum time. The goal is to find the control of the thrust nozzle of the LEM to minimize the final time.

An Adaptive Hierarchical Multiscale Algorithm for Estimation of Optimal Well Controls

Summary In determining the optimal well controls by maximizing net present value (NPV) for the remaining life of a reservoir, one typically defines the length of the control steps a priori. Moreover, these control steps are often the same for all wells. We provide a scale-splitting/merging method for adaptively selecting the number and the lengths of control steps as the overall optimization proceeds. We start with a reasonably small number of control steps and find the associated optimal controls by maximizing NPV. Both the adjoint-gradient-based steepest-ascent method and ensemble-based optimization (EnOpt) are considered as optimization algorithms. Because the correlation length used to generate the ad hoc covariance matrix indigenous to EnOpt affects the results, we implement a simple method to reduce the correlation length as the optimization proceeds. This enables EnOpt to generate a good approximation for well-control problems in which the optimal solution is bang-bang. The adaptive approach is applied to two example problems, and the results are compared with those obtained with a predetermined number of control steps.