Jan Backhaus

Gradient Enhanced Surrogate Models Based on Adjoint CFD Methods for the Design of a Counter Rotating Turbofan

This paper studies the use of adjoint CFD solvers in combination with surrogate modelling in order to reduce the computational cost of the optimization of complex 3D turbomachinery components. The method is applied to a previously optimized counter rotating turbofan, with a shape parameterized by 104 CAD parameters.Through random changes on the reference design, a small number of design variations are created to serve as training samples for the surrogate models. A steady RANS solver and its discrete adjoint are then used to calculate objective function values and their corresponding sensitivities. Kriging and neural networks are used to build surrogate models from the training data. To study the impact of the additional information provided by the adjoint solver, each model is trained with and without the sensitivity information. The accuracy of the different surrogate model predictions is assessed by comparison against CFD calculations.The results show a considerable improvement of the fitness function approximation when the sensitivity information is taken into account. Through a gradient based optimization on one of the surrogate models, a design with higher isentropic efficiency at the aerodynamic design point is created. This application demonstrates that the improved surrogate models can be used for design and optimization.Copyright

Compressor Leading Edge Sensitivities and Analysis with an Adjoint Flow Solver

Based on the results of a prior study about fan blade degradation, which state a noticeable influence of small geometric changes on the fan performance, an adjoint computational fluid dynamics method is applied to systematically analyze the sensitivities of fan blade performance to changes of the leading edge geometry.As early as during manufacture, blade geometries vary due to fabrication tolerances. Later, when in service, engine operation results in blade degradation which can be reduced but not perfectly fixed by maintenance, repair and overhaul processes. The geometric irregularities involve that it is difficult to predict the blade’s aerodynamic performance. Therefore, the aim of this study is to present a systematic approach for analyzing geometric sensitivities for a fan blade.To demonstrate the potential, two-dimensional optimizations of three airfoil sections at different heights of a transonic fan blade are presented. Although the optimization procedure is limited to the small area of the leading edge, the resulting airfoil sections can be combined to a three-dimensional fan blade with an increased isentropic efficiency compared to the initial blade.Afterwards, an adjoint flow solver is applied to quasi-three-dimensional configurations of an airfoil section in subsonic flow with geometric leading edge variations in orders representative for realistic geometry changes. Validations with non-linear simulation results demonstrate the high quality of the adjoint results for small geometric changes and indicate physical effects in the leading edge region that influence the prediction quality.© 2013 ASME

a code-coupling approach to the implementation of discrete adjoint solvers based on automatic differentiation

We propose a method for selectively applying automatic differentiation (AD) by operator overloading to develop the discrete adjoint of a turbomachinery flow solver. A fully differentiated version of the solver is generated by operator overloading using the tapeless tangent mode of ADOL-C. The differentiated solver is coupled to an undifferentiated version of the same code using message passing. The automatic differentiation is used to calculate derivatives of the flux calculation routines. The flux derivatives depending on inner cell states are sparse, and this sparsity is exploited using analytical differentiation of the spatial discretization scheme. Subsequently the sparse matrix is communicated to the undifferentiated code for solution. Turbomachinery boundary conditions may have dense Jacobians and are therefore only evaluated during the solution process. The solution of the adjoint system of equations is achieved through a preconditioned GMRES, implemented inside the undifferentiated code. A modern three dimensional contra-rotating fan stage with engineering parameterization serves as application example in order to demonstrate the technique and to perform numerical validations. The validation of gradient results is performed by comparing against results from finite differences, and the tangent forward mode.

Adjoint-Based Flow Sensitivity Analyis Using Arbitrary Control Surfaces

This article describes how to extend the dsicrete adjoint method to functionals that are evaluated on arbitrary rotational control surfaces that intersect the flow domain at a position specified by the user, e.g. the pressure loss coefficient of a single blade in a multi-stage configuration. The definition and implementation of the mixed-out states on such surfaces is revisited. The calculation of the corresponding right-hand sides in the adjoint system is explained. These techniques can be used to specify functionals that quantify the deviation of the radial distribution of the flow angles, relative mass flow, etc. from a given target distribution. Sensitivity studies using the conventional approach, i.e. by means of finite differences of many steady solutions, are compared to results based on the adjoint method. The applications demonstrate that the agreement between adjoint and conventional sensitivity predictions is excellent, if the exact definition of the surface functionals is taken into account.Copyright

Forced response sensitivity analysis using an adjoint harmonic balance solver

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values -- e.g. performance data of a component -- themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implementational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

Application of an Algorithmically Differentiated Turbomachinery Flow Solver to the Optimization of a Fan Stage

The adjoint method has already proven its potential to reduce the computational effort for optimizations of turbomachinery components based on flow simulations. However, the transfer of the adjoint-based optimization methods to industrial design problems turns out to pose specific requirements to both the adjoint solver as well as the optimization algorithms which utilize the gradient information. While the construction of the adjoint solver through algorithmic differentiation is described in a parallel publication, we focus here on the robust application of the gradient information in a high-dimensional multi-objective op- timization with several constraints including non-differentiated mechanical constraints. We describe the optimization methods, which comprise the use of gradient-enhanced Kriging meta-models, and subsequently apply these to the design optimization of a contra-rotating fan stage. The results show that through the described combination of methods the adjoint method can be used in practical design optimizations of turbomachinery components.