Markus Widhalm

Linear-Frequency-Domain Predictions of Dynamic-Response Data for Viscous Transonic Flows

Determining the flutter boundaries for full aircraft configurations by time-accurately solving the Reynolds-averaged Navier–Stokes equations is prohibitive with respect to computational expense, as the unsteady aerodynamic loading must be predicted for a wide range of flight conditions, frequencies, and structural mode shapes. Nonetheless, there is an increasing demand to accurately predict flutter boundaries in the viscous transonic regime—a demand, which, until recently, could only be satisfied by high-fidelity Reynolds-averaged Navier–Stokes methods. Brought to application readiness over the last years, time-linearized/small-disturbance methods, however, have been shown to satisfy this demand as well. They retain the Reynolds-averaged Navier–Stokes method’s fidelity to a high degree, at a substantially reduced computational expense. Such a method is presented here on the basis of the TAU–Reynolds-averaged Navier–Stokes method. Denoted as the TAU linear-frequency-domain method, it is validated for both ...

Investigation on Adjoint Based Gradient Computations for Realistic 3d Aero-Optimization

A discrete adjoint method for e�ciently computing gradients for aerodynamic shape op- timizations is presented. The chain itself involves an unstructured mesh Reynolds-Averaged Navier-Stokes solver, and is suitable for the optimization of complex geometries in three dimensions. In addition to the discrete ow adjoint the method introduces a second ad- joint equation for the mesh deformation. Using the adjoint chain it is possible to evaluate the gradients of a cost function for the cost of one adjoint ow solution and one adjoint volume mesh deformation, without performing any (forward) mesh deformation. By choos- ing a suitable mesh deformation operator, like linear elasticity, the chain may be readily constructed by hand. Furthermore, this adjoint chain can be subsequently used with pa- rameterized surface grids. The accuracy and the computational savings of the resulting procedure is examined for the gradient-based shape optimization of a wing in inviscid ow.

Non-uniform rational B-splines-based aerodynamic shape design optimization with the DLR TAU code

With the improving capabilities of computational fluid dynamics (CFD) for the prediction of aerodynamic performance, CFD tools are now being increasingly used for aerodynamic design optimization in the aerospace industry. In this article, an automated optimization framework is presented to address inviscid aerodynamic design problems. Key aspects of this framework include the use of the continuous adjoint methodology to make the computational requirements independent of the number of design variables, and computer-aided design-based shape parameterization, which uses the flexibility of non-uniform rational B-splines to handle complex configurations.

Algorithmic Developments in TAU

The paper describes a selection of algorithmic developments which have been implemented in the hybrid Navier-Stokes solver TAU during the MEGAFLOW II project. The paper concentrates on algorithms that help to improve the performance, the accuracy as well as the functionality. The algorithms presented are implicit MAPS-smoothing, low Mach number preconditioning, least square reconstruction in combination with a cell centered approach, the actuator disk boundary condition and a formulation for moving coordinate systems enabling steady solutions in a rotating frame. Results are presented in comparison to earlier versions of the TAU code, highlighting the improvements with respect to performance and/or accuracy. Comparisons with experimental data and results obtained with the FLOWer code are used to validate the new functionalities.

Achieving High Speed CFD simulations: Optimization, Parallelization, and FPGA Acceleration for the unstructured DLR TAU Code

Today, large scale parallel simulations are fundamental tools to handle complex problems. The number of processors in current computation platforms has been recently increased and therefore it is necessary to optimize the application performance and to enhance the scalability of massively-parallel systems. In addition, new heterogeneous architectures, combining conventional processors with specific hardware, like FPGAs, to accelerate the most time consuming functions are considered as a strong alternative to boost the performance. In this paper, the performance of the DLR TAU code is analyzed and optimized. The improvement of the code efficiency is addressed through three key activities: Optimization, parallelization and hardware acceleration. At first, a profiling analysis of the most time-consuming processes of the Reynolds Averaged Navier Stokes flow solver on a three-dimensional unstructured mesh is performed. Then, a study of the code scalability with new partitioning algorithms are tested to show the most suitable partitioning algorithms for the selected applications. Finally, a feasibility study on the application of FPGAs and GPUs for the hardware acceleration of CFD simulations is presented.

Aerodynamic Optimization for Cruise and High-Lift Configurations

Within the next few years, numerical shape optimization based on high fidelity methods is likely to play a strategic role in future aircraft design. In this context, suitable tools have to be developed for solving aerodynamic shape optimization problems, and the adjoint approach – which allows fast and accurate evaluations of the gradients with respect to the design parameters – is seen as a promising strategy. Based on the unstructured RANS solver TAU, a continuous as well as a discrete adjoint have been developed and applied to cruise and high-lift configuration optimization problems. This paper describes investigations of planform optimizations for a flying wing transport aircraft with an Euler continuous adjoint method, the wing design of the DLR-F6 wing-body aircraft configuration and the flap and slat settings of the DLR-F11 high-lift wing-body aircraft with a viscous discrete adjoint method.

Lagrangian Trajectory Simulation of Rotating Regular Shaped Ice Particles

This paper focuses on the numerical simulation of the motion of regular shaped ice particles under the forces and torques generated by aerodynamic loading. Ice particles can occur during landing and take-off of aircraft at ground level up to the lower bound of the stratosphere at cruising altitude. It may be expected that the particle Reynolds number is high because the flow around the aircraft is in certain regions characterized by strong acceleration and deceleration of the flow. In combination with this flow pattern, the rotation of particles becomes important. Applicable translational and rotational equations of motion combined with a drag correlation taking into account rotation will be derived for a Lagrangian type particle tracking. Orientation is described with quaternions to prevent the singularities associated with the description by Euler angles. The influence of regular shaped particles on collection efficiencies is investigated. Test cases are the flow past a cylinder, a NACA0012 airfoil and a NHLP L1/T2 three element airfoil. Due to the increased computational effort compared to the purely translational approach, observed trajectory simulation times are reported.

Efficient Evaluation of Dynamic Response Data with aLinearized Frequency Domain Solver at TransonicSeparated Flow Conditions

Each perturbation of an aircraft state in trim induces aerodynamic loads on wings, con- trol surfaces and other parts of an aircraft. These loads have to be quantified for a wide range of flight states covering the flight envelope. Small disturbance approaches based on the Reynolds-averaged Navier Stokes equations fulfil the requirements of efficiently predict- ing accurate dynamic response data. These time-linearized methods have been successfully applied in flight dynamic and aeroelastic analyses for moderate flight conditions. Small disturbance approaches on the basis of Navier-Stokes solvers have become most often the right choice, for example in flight dynamic and aeroelastic analysis, to combine efficiency and accuracy for predicting dynamic response data. However, in complex flows exhibiting shock-induced separations, deficits in robustness of the iterative solution methods often lead to simplifications of the equations and thus reducing the quality of the computed results. The presented linearized frequency domain solver has shown accurate results compared to nonlinear time-accurate unsteady simulations for attached flow conditions. The area of application is extended to separated transonic flows demonstrating the method’s capability to accurately capture strong shock-boundary interactions. Deriving the exact linearization of the turbulence model as well as implementing a robust method to solve the stiff linear systems are key tasks to achieve this target. Results are presented for the LANN wing undergoing rigid body motions comparing dynamic derivatives of lift and moment coeffi- cients between the linearized frequency domain solver and its time-domain counterpart. In addition, local surface pressure and skin friction coefficients are analysed at two span sta- tions. The presented linearized frequency domain solver (TAU-LFD) has shown accurate results in comparison to fully time-accurate unsteady simulations at separated transonic flow conditions.