This paper presents a comparison of reduced order models to predict aerodynamic stability derivatives. The study involved two widely used frameworks for simulating unsteady flows, DoD HPCMP CREATERM-AV/Kestrel and the DLR TAU code. The DLR TAU code contains a linearized version of the discrete unsteady Reynolds-averaged Navier-Stokes equations based on the small perturbation approach which are solved in the frequency domain. This allows a comparison with distinctly different approaches of reduced order aerodynamic modeling. The first approach is based on the linear frequency domain solver which computes stability derivatives directly. Three reduced order models are applied to unsteady simulations to extract stability derivatives from predicted time histories of the force and moment coefficients. The first reduced order model is the stability derivatives method. The second reduced order model is based on the calculated indicial responses to unit step changes in the angle of attack and pitch rate. Furthermore, a system identification approach is applied to the time history of the force and moment coefficients for different training maneuvers to extract the stability derivatives. The weaknesses and strengths of the individual approaches of reduced order models are shown and, in particular, the efficiency of the methods is outlined. The use case is the DLR-F22 ONERA model, a generic research wind tunnel model of a triple delta wing fighter type aircraft configuration, at transonic flow conditions for various angles of attack.

A summary about the DLR results for the Special Session of the AIAA Stability and Control Prediction Workshop regarding the wing section only and wing/tail section of the Common Research model (CRM) is presented. The first prediction workshop revealed a deficit in the accurate determination of the pitching moment coefficient of the Common Research wind tunnel model. Thus, the idea is to perform investigations on a wing only and wing/tail section to improve the prediction accuracy for the pitching moment, and in consequence pitching moment derivatives, to increase the prediction reliability for future workshops. The two-dimensional sections of the CRM wind tunnel model are used to calculate a transonic Mach number sweep for a given lift coefficient to explore mesh-independent solutions. Using aerodynamic coefficients and their partial and total derivatives, and determining the velocity vectors at a defined location provides insight into the different meshing strategies for both airfoils and the wing wake. In addition, DLR also computed the optional test cases by evaluating the lift coefficient range from zero to the maximum for the wing only and the wing/tail case, and evaluating the derivative of the pitching moment coefficient with respect to angle of attack and tail incidence angle for the wing/tail case. The analysis shows that the derivative prediction on the two-dimensional CRM case proves to be very sensitive regarding the grid quality, wing and tail incidence angle as well as the shape of the tail geometry.

Gust load predictions are time-consuming for aircraft design since these are unsteady events and depend not only on the flow conditions but also on many other parameters such as weight and altitude changes. The linear frequency domain solver allows a rapid calculation of gust loads in contrast to a time-accurate method, although the calculation of several harmonics is necessary to reconstruct the equivalent time signal. A further increase in efficiency can be obtained with the use of a Proper Orthogonal Decomposition-Galerkin method for interpolating certain frequencies for the gust time signal for a single operating point of the flight envelope. If several operating points are already known, an interpolation of gust loads between the operating points can be performed on the Grassmann manifold. Considering the flight conditions, subsonic to transonic, of a whole flight envelope, the Proper Orthogonal Decomposition-Galerkin method achieves a good prediction accuracy. For the Grassmann manifold, however, it turns out that it is only suitable in the immediate vicinity of sampled operating points.

A summary about the DLR results from the first AIAA Stability and Control Prediction Workshop is presented. To evaluate and improve the prediction accuracy of stability derivatives of common aerodynamic codes, five test cases, three mandatory and two optional, based on the NASA Common Research Model were set up to perform a validation using the experimental data performed at the ONERA wind tunnel. The first workshop had a strong focus on evaluating longitudinal static stability derivatives and detecting the influence and increments of the wind tunnel sting of the tested Common Research Model. A first step toward lateral static stability derivatives and a β-sweep was included in the optional test cases. At first, investigations should identify solution accuracy and grid convergence behavior with five provided unstructured grids. For the second test case, the impact on the longitudinal static derivatives with respect to a variation of the transonic Mach number was investigated. In comparison to the wind tunnel experiment the numerical simulations thereby underpredicted the drag and pitching moment, especially for Mach numbers greater than 0.83. The last test case was used to determine the increments of the wind tunnel sting. The sting hereby proved to have a great effect on the aerodynamics of the tail plane and lead to a positive shift in the pitching moment. In addition, DLR also computed the optional test cases by evaluating the lateral static derivatives in comparison to finite differences with a frequency domain solver, which is a time-linearized Navier-Stokes method. Ultimately, the effect of the sideslip angle on the aircraft with the wind tunnel sting was investigated.

View Video Presentation: https://doi.org/10.2514/6.2022-3899.vid From aircraft design to certification a huge amount of aerodynamic data is needed for the entire flight envelope including pressure and shear stress distributions, global coefficients as well as derivatives. The goal of data-driven methods is to provide aerodynamic data based on various data-sources but with lower evaluation time and storage than the original models. These data-sources might include flight tests, wind tunnel experiments or numerical simulations, and they are often available at various levels of fidelity, ranging from simple hand book methods over high-fidelity numerical simulations to in-flight measurements. Within the past few years, the demand for efficient exploitation and exploration of these data sets became evident to further enhance existing designs and approaches, evaluate new technical capabilities and foster the availability of high-fidelity aerodynamic data in closely related disciplines. The German Aerospace Center is continuously developing the Surrogate Modeling for Aero-Data Toolbox in python (SMARTy) with the aim of providing state-of-the-art data-driven techniques for both, developers and practical engineers. SMARTy is designed following an Application Programming Interface approach that enables easy combination of different modules into larger, complex applications. Moreover, integration into multi-disciplinary analysis and optimization workflows is possible relying on the FlowSimulator. The SMARTy capabilities are highlighted herein by means of several application cases. This includes surrogate modeling, multi-fidelity modeling, data fusion, reduced order modeling, deep learning as well as highly integrated tasks such as surrogate-based robust design, intrusive reduced order modeling for unsteady responses or data-driven turbulence modeling.

In modern aircraft design the accurate prediction of dynamic control surface deflections is crucial for the evaluation and application of new load alleviation techniques. Time-marching approaches, such as the unsteady Reynolds-averaged Navier-Stokes equations, do provide a complete modeling of the aerodynamic flowfield; however, they are extremely time-consuming and still too expensive for design applications. In this paper a model is presented, which enables the fast and accurate prediction of aerodynamic responses for arbitrary control surface deflections. The model hereby reflects the time signal of the control surface deflection as a superposition of frequency components and computes the dynamic response behavior of the control surface using the linear frequency domain. The frequency responses are precomputed in a surrogate model for a wide parameter space of Mach number, Reynolds number, angle of attack and flap chord ratio, so that a frequency response for a new flight condition can be computed by mere interpolation. After building the surrogate model, the method achieves reduction in computational time of up to six orders of magnitude in comparison to time-marching simulations, while still covering the viscous and unsteady aerodynamic effects in the flow.

A method is presented, that is able to mitigate gust loads on an airfoil induced by an incoming gust velocity field. It thereby computes the lift coefficient response to a specified arbitrary gust velocity profile and predicts the required time-accurate control surface deflection. The method uses the linear frequency domain solver to predict frequency responses for the gust and control surface derivative of the lift coefficient efficiently. The frequency responses are computed and then subsequently filled as samples into a surrogate model. For a new flight condition the surrogate model predicts the frequency response by mere interpolation. Because the aerodynamic response on the gust and the behavior of the control surface are known, the aerodynamic lift response and the required flap deflection for alleviation can both be predicted from a given gust velocity field. The method is thereby able to predict the aerodynamic response and a time-accurate deflection for any flight condition in the design space within milliseconds. Results of the method are shown and analyzed on a 2D profile of a transonic airfoil with an implemented plain flap. The parameter studies were made in low speed with variation of Mach number, Reynolds number, angle of attack, flap chord size and initial flap deflection. In comparison to unsteady Reynoldsaveraged Navier-Stokes computations, the presented method can predict the aerodynamic responses with the same accuracy and it saves more than 6 orders of magnitude in computation time. Using the linear frequency domain solver it is also able to predict the arising unsteady aerodynamic behavior and still cover the viscous effects in the flow.

Simulations of periodic fluidic excitations in the context of active flow control are per- formed using a frequency domain solver for the efficient prediction of global air loads. Frequency domain methods have become a viable choice whenever the disturbance of the flow is small and periodic, and can reduce the computational effort substantially in compar- ison to time-accurate unsteady simulations. Although time-accurate unsteady simulations resolve the entire spectrum of the flow, they suffer from a long transient phase and thus require an extensive use of computational resources. The goal is to extend the time- linearized frequency domain method of the DLR TAU-code toward load control by blowing fluidic actuators. This paper presents the set of discretized unsteady equations and as- sociated boundary conditions for both the time accurate and frequency domain method. The applied time-linearized frequency method decouples each harmonic, forming a linear approach, which renders the sequential calculation of the individual harmonics to evaluate the time response of air loads. At first, blowing actuation for a two-dimensional airfoil with a single slot is considered for which constant as well as periodic excitations are used for validation and investigation purposes of air loads between the time-accurate and nonlinear frequency domain method. In addition, a 2-element high-lift wing with a flow separation on the trailing edge flap is simulated that demonstrates the good prediction quality of air load derivatives with the frequency domain method.

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.

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.

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 a standard transonic airfoil and a high-aspect-ratio-wing dynamic test case using rigid pitch modes. The response data obtained from the linear frequency domain are in good agreement with the experiment for a two-dimensional case. For the three-dimensional case, there are larger differences. More important, the linear-frequency-domain method is in excellent agreement to time-accurate Reynolds-averaged Navier-Stokes simulations. Depending on the linear-frequency-domain-employed-solution scheme, reductions in computational costs well beyond an order of magnitude are obtained. In addition, the limits of the so-called frozen-eddy-viscosity approach are established.

Dynamic derivatives are used to represent the influence of the aircraft motion rates on the aerodynamic forces and moments needed for studies of flight dynamics. The use of computational fluid dynamics has potential to supplement costly wind-tunnel testing. The paper considers the problem of the fast computation of forced periodic motions using the Euler equations. Three methods are evaluated. The first is computation in the time domain, which provides the benchmark solution in the sense that the time-accurate solution is obtained. Two acceleration techniques in the frequency domain are compared. The first uses a harmonic solution of the linearized problem, referred to as the linear frequency-domain approach. The second uses the harmonic balance method, which approximates the nonlinear problem using a number of Fourier modes. These approaches are compared for the ability to predict dynamic derivatives and for computational cost. The NACA 0012 aerofoil and the DLR-F12 passenger jet wind-tunnel model are the test cases. Compared to time-domain simulations, an order of magnitude reduction in computational costs is achieved and satisfactory predictions are obtained for cases with a narrow frequency spectrum and moderate amplitudes using the frequency-domain methods.

A major design requirement for transport aircraft is efficient cruise flight in the transonic region. From the aerodynamic viewpoint, this is achieved by favorable lift-to-drag ratio of the aircraft, both at the main design point and at off-design conditions. We therefore present a method to efficiently perform a multi-point optimization of a representative wing-body configuration. Designs are evaluated with RANS CFD simulations, the wing is parametrized using 40 free-form deformation control points, and a gradient-based method is used to drive the optimization. The gradient of cost functions is computed with a discrete adjoint approach, in which flow and mesh adjoint equations are solved. Compared to single-point optimization, with multi-point optimization we obtain a design with slightly lower best lift-to-drag ratio, but which has improved lift-to-drag polar over the whole range of practical lift coefficients compared to the baseline design.

The adjoint approach - which allows fast and accurate evaluations of the gradients with respect to the design parameters - is seen as a promising strategy in numerical shape optimization based on high fidelity methods. After describing the theory of the viscous discrete adjoint method and its implementation within the unstructured RANS solver TAU, the presentation shows all major applications conducted at DLR for solving 2D and 3D aerodynamic shape optimization problems. The latest extention toward wing flight shape optimisations is also presented. On all cases presented, optimizations were successfully performed within a limited number of flows evaluations, confirming the efficiency of the strategy.

During flutter analysis of a new aircraft a huge number of unsteady aerodynamic simulations is necessary in the parameter space consisting of Mach number, aeroelastic trim state, structural mode shape and frequency. For subsonic flow conditions fast potential methods like the Doublet Lattice Method can be applied. In the transonic regime unsteady flow perturbations depend on the mean flow state and CFD methods have to be employed. However, solving the nonlinear unsteady RANS equations for thousands of parameter combinations is not applicable. Hence, faster CFD methods are needed to reduce the computational costs. Assuming small time-harmonic perturbations, the RANS equations can be linearized around the steady mean solution. The latter are preferably solved in the frequency domain. This results in a large, sparse linear system for the perturbation of the fluid unknowns. In this paper an efficient time-linearized solver (LFD-TAU) is presented with special focus on 2-d external flows with strong shock-induced separation. The results are compared to small-amplitude pulse response and single-frequency RANS simulations, demonstrating good agreement over a wide frequency range. Even under pre-buffet flow conditions, showing aerodynamic resonance peaks, the resonance frequency is captured well, while the amplitudes are overestimated.

Structural loads for full aircraft configurations can be represented by evaluating dynamic derivatives over a wide parameter space mainly including different mode shapes, an- gle of attack and Mach numbers. Traditionally, these values are determined by wind tunnel tests applying forced periodic motions to aircraft models. The ability of numerical simula- tions provide an excellent addendum to wind tunnel tests. Instead of time-accurate unsteady Reynolds-averaged Navier-Stokes (URANS) solvers which are recognized as extremely compu- tational expensive this paper considers a linearized frequency domain solver (LFD). With this approach the unsteady simulation reduces to a single steady state computation and a single linear simulation in the frequency domain. By the assumption of small perturbations and har- monic oscillations dynamic derivatives can be computed efficiently within a wide parameter space. In addition, the theoretical background for the LFD will be presented. Based on the linearization of the RANS equations and modeling of small perturbations with Fourier series a complex valued linear system has to be solved.