Abstract

Modern fluid mechanics examines understanding, predicting and directing of fluids in the fluid structures. But new computational methods need to find out the optimal solution of each hydraulic system because of minimization of power losses. Consequently, this article looks through the shape optimization of hydraulic parts using adjoint optimization method. It is most used gradient-based method. This approach enables to calculate the objective function sensitivities in consideration of the design variables (Kyriakos and Papadimitriou, 2008). Many producers talk about the optimized solutions, but only small part from them use all possibilities for finding the best one. It is motivation why in this paper the shape optimization of the hydraulic valve component with respect to minimization of pressure losses is presented.

Abstract

Abstract

This paper presents the Multi-Disciplinary Optimization (MDO) of a business jet including static aeroelastic effects. Two different CFD tools (AETHER by Dassault Aviation and PUMA by NTUA) are coupled with a CSM model (VPS software by ESI). Single discipline as well as coupled multi-disciplinary sensitivity derivatives (SDs) are computed by means of adjoint methods. Both a purely discrete and a hybrid continuous(fluid)/discrete(structure) adjoint formulations are presented. The computed SDs are verified against finite differences.

Abstract

Abstract

Abstract

Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape. In this work, an adaptive NSPCC method is proposed where the optimisation begins with a coarser design space and adapts to finer parametrisation during the design process where more shape control is needed. The refinement sensor is based on a comparison of smoothed node-based sensitivity compared to its projection onto the shape modes of the current parametrisation. Both static and adaptive parametrisation methods are coupled in the adjoint-based shape optimisation process to reduce the total pressure loss of a turbine blade internal cooling channel. The discrete adjoint flow solver STAMPS is used to compute the flow fields and their derivatives w.r.t. surface node displacements. The shape derivatives for gradient-based optimisation are obtained by application of reverse mode AD to the NSPCC CAD kernel. Since a CAD model is kept inside the design loop, the resulting optimal shape is directly available in CAD for further analysis or manufacturing. Based on the analysis regarding quality of the optima and rate of convergence of the design process adaptive NSPCC method outperforms static NSPCC approach.

Abstract

In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting observed noisy data into the given dynamical system. Also we explain in detail the advantage of using the adjoint equation method to compute the derivatives or gradients, which are needed for the application of gradient methods and quasi-Newton algorithms to find the minimum of the cost function. In particular we consider two classic iterative algorithms: the conjugate gradient (CG) algorithm and the BFGS algorithm. For educational purposes we try to explain several numerical and computational issues with some detail and illustrate them with the SEIRD epidemiological model.