On the calculation of dynamic derivatives using computational fluid dynamics

In this thesis, the exploitation of computational fluid dynamics (CFD) methods for the flight dynamics of manoeuvring aircraft is investigated. It is demonstrated that CFD can now be used in a reasonably routine fashion to generate stability and control databases. Different strategies to create CFD-derived simulation models across the flight envelope are explored, ranging from combined low-fidelity/high-fidelity methods to reduced-order modelling. For the representation of the unsteady aerodynamic loads, a model based on aerodynamic derivatives is considered. Static contributions are obtained from steady-state CFD calculations in a routine manner. To more fully account for the aircraft motion, dynamic derivatives are used to update the steady-state predictions with additional contributions. These terms are extracted from small-amplitude oscillatory tests. The numerical simulation of the flow around a moving airframe for the prediction of dynamic derivatives is a computationally expensive task. Results presented are in good agreement with available experimental data for complex geometries. A generic fighter configuration and a transonic cruiser wind tunnel model are the test cases. In the presence of aerodynamic non-linearities, dynamic derivatives exhibit significant dependency on flow and motion parameters, which cannot be reconciled with the model formulation. An approach to evaluate the sensitivity of the non-linear flight simulation model to variations in dynamic derivatives is described. The use of reduced models, based on the manipulation of the full-order model to reduce the cost of calculations, is discussed for the fast prediction of dynamic derivatives. A linearized solution of the unsteady problem, with an attendant loss of generality, is inadequate for studies of flight dynamics because the aircraft may experience large excursions from the reference point. The harmonic balance technique, which approximates the flow solution in a Fourier series sense, retains a more general validity. The model truncation, resolving only a small subset of frequencies typically restricted to include one Fourier mode at the frequency at which dynamic derivatives are desired, provides accurate predictions over a range of two- and three-dimensional test cases. While retaining the high fidelity of the full-order model, the cost of calculations is a fraction of the cost for solving the original unsteady problem. An important consideration is the limitation of the conventional model based on aerodynamic derivatives when applied to conditions of practical interest (transonic speeds and high angles of attack). There is a definite need for models with more realism to be used in flight dynamics. To address this demand, various reduced models based on system-identification methods are investigated for a model case. A non-linear model based on aerodynamic derivatives, a multi-input discrete-time Volterra model, a surrogate-based recurrence-framework model, linear indicial functions and radial basis functions trained with neural networks are evaluated. For the flow conditions considered, predictions based on the conventional model are the least accurate. While requiring similar computational resources, improved predictions are achieved using the alternative models investigated. Furthermore, an approach for the automatic generation of aerodynamic tables using CFD is described. To efficiently reduce the number of high-fidelity (physics-based) analyses required, a kriging-based surrogate model is used. The framework is applied to a variety of test cases, and it is illustrated that the approach proposed can handle changes in aircraft geometry. The aerodynamic tables can also be used in real-time to fly the aircraft through the database. This is representative of the role played by CFD simulations and the potential impact that high-fidelity analyses might have to reduce overall costs and design cycle tim

On the calculation of dynamic derivatives using computational fluid dynamics

In this thesis, the exploitation of computational fluid dynamics (CFD) methods for the flight dynamics of manoeuvring aircraft is investigated. It is demonstrated that CFD can now be used in a reasonably routine fashion to generate stability and control databases. Different strategies to create CFD-derived simulation models across the flight envelope are explored, ranging from combined low-fidelity/high-fidelity methods to reduced-order modelling. For the representation of the unsteady aerodynamic loads, a model based on aerodynamic derivatives is considered. Static contributions are obtained from steady-state CFD calculations in a routine manner. To more fully account for the aircraft motion, dynamic derivatives are used to update the steady-state predictions with additional contributions. These terms are extracted from small-amplitude oscillatory tests. The numerical simulation of the flow around a moving airframe for the prediction of dynamic derivatives is a computationally expensive task. Results presented are in good agreement with available experimental data for complex geometries. A generic fighter configuration and a transonic cruiser wind tunnel model are the test cases. In the presence of aerodynamic non-linearities, dynamic derivatives exhibit significant dependency on flow and motion parameters, which cannot be reconciled with the model formulation. An approach to evaluate the sensitivity of the non-linear flight simulation model to variations in dynamic derivatives is described. The use of reduced models, based on the manipulation of the full-order model to reduce the cost of calculations, is discussed for the fast prediction of dynamic derivatives. A linearized solution of the unsteady problem, with an attendant loss of generality, is inadequate for studies of flight dynamics because the aircraft may experience large excursions from the reference point. The harmonic balance technique, which approximates the flow solution in a Fourier series sense, retains a more general validity. The model truncation, resolving only a small subset of frequencies typically restricted to include one Fourier mode at the frequency at which dynamic derivatives are desired, provides accurate predictions over a range of two- and three-dimensional test cases. While retaining the high fidelity of the full-order model, the cost of calculations is a fraction of the cost for solving the original unsteady problem. An important consideration is the limitation of the conventional model based on aerodynamic derivatives when applied to conditions of practical interest (transonic speeds and high angles of attack). There is a definite need for models with more realism to be used in flight dynamics. To address this demand, various reduced models based on system-identification methods are investigated for a model case. A non-linear model based on aerodynamic derivatives, a multi-input discrete-time Volterra model, a surrogate-based recurrence-framework model, linear indicial functions and radial basis functions trained with neural networks are evaluated. For the flow conditions considered, predictions based on the conventional model are the least accurate. While requiring similar computational resources, improved predictions are achieved using the alternative models investigated. Furthermore, an approach for the automatic generation of aerodynamic tables using CFD is described. To efficiently reduce the number of high-fidelity (physics-based) analyses required, a kriging-based surrogate model is used. The framework is applied to a variety of test cases, and it is illustrated that the approach proposed can handle changes in aircraft geometry. The aerodynamic tables can also be used in real-time to fly the aircraft through the database. This is representative of the role played by CFD simulations and the potential impact that high-fidelity analyses might have to reduce overall costs and design cycle time

A modified airfoil-based piezoaeroelastic energy harvester with double plunge degrees of freedom

In this letter, a piezoaeroelastic energy harvester based on an airfoil with double plunge degrees of freedom is proposed to additionally take advantage of the vibrational energy of the airfoil pitch motion. An analytical model of the proposed energy harvesting system is built and compared with an equivalent model using the well-explored pitch-plunge configuration. The dynamic response and average power output of the harvester are numerically studied as the flow velocity exceeds the cut-in speed (flutter speed). It is found that the harvester with double-plunge configuration generates 4%–10% more power with varying flow velocities while reducing 6% of the cut-in speed than its counterpart

Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow

Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3≤ Ma≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. Firstly, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state-of-the-art computational fluid dynamics solvers as cross-validated benchmarks. Indicial functions are calculated for a step change in the angle of attack and for a sharp-edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following an encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories

Adaptive design of experiments for efficient and accurate estimation of aerodynamic loads

Aerodynamic design, which aims at developing the outer shape of the aircraft while meeting several contrasting requirements, demands an accurate and reliable aerodynamic database. Computing forces and moments with the highest level of ?fidelity is a prerequisite, but practically limited by wall clock time and available computing resources. An e?fficient and robust approach is therefore sought after. This study investigates two design of experiments algorithms in combination with surrogate modelling. In traditional design of experiments, the samples are selected a priori before running the numerical explorative campaign. It is well-?known that this may result in either poor prediction capabilities or high computational costs. The second strategy employs an adaptive design of experiments algorithm. As opposed to the former, this is a self?-learning technique that iteratively: i) identi?fies the regions of the design space that are characterised by stronger non?linearities; and ii) select the new samples in order to maximise the information contentassociated with the simulations to be performed during the next iteration. In this work, the Reynolds?-averaged Navier-?Stokes equations are solved around a complete aircraft confi?guration. A representative ?flight envelope is created taking the angle of attack and Mach number as design parameters. The adaptive strategy is found to perform better than the traditional counterpart. This is quantifi?ed in terms of the sum of the squared error between the surrogate model predictions and CFD results. For the pitch moment coe?fficient, which shows strong non?linearities, the error metric using the adaptive strategy is reduced by about one order of magnitude compared to the traditional approach. Furthermore, the proposed adaptive methodology, which is employed on a high performance computing facility, requires no extra costs or complications than a traditional methodolog

Experimental Nonlinear Control for Flutter Suppression in a Nonlinear Aeroelastic System

Experimental implementation of input–output feedback linearization in controlling the dynamics of a nonlinear pitch–plunge aeroelastic system is presented. The control objective is to linearize the system dynamics and assign the poles of the pitch mode of the resulting linear system. The implementation 1) addresses experimentally the general case where feedback linearization-based control is applied using as the output a degree of freedom other than that where the physical nonlinearity is located, using a single trailing-edge control surface, to stabilize the entire system; 2) includes the unsteady effects of the airfoil’s aerodynamic behavior; 3) includes the embedding of a tuned numerical model of the aeroelastic system into the control scheme in real time; and 4) uses pole placement as the linear control objective, providing the user with flexibility in determining the nature of the controlled response. When implemented experimentally, the controller is capable of not only delaying the onset of limit-cycle oscillation but also successfully eliminating a previously established limit-cycle oscillation. The assignment of higher levels of damping results in notable reductions in limit-cycle oscillation decay times in the closed-loop response, indicating good controllability of the aeroelastic system and effectiveness of the pole-placement objective. The closed-loop response is further improved by incorporating adaptation so that assumed system parameters are updated with time. The use of an optimum adaptation parameter results in reduced response decay times

Harmonic balance Navier–Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

Multi–megawatt horizontal axis wind turbines often operate in yawed wind transients in which the resulting periodic loads acting on blades, drive–train, tower and foundation adversely impact on fatigue life. Accurately predicting yawed wind turbine aerodynamics and resulting structural loads can be challenging, and would require the use of computationally expensive high–fidelity unsteady Navier–Stokes Computational Fluid Dynamics. The high computational cost of this approach can be significantly reduced by using a frequency–domain framework. The paper summarizes the main features of the COSA Harmonic Balance Navier–Stokes solver for the analysis of open rotor periodic flows, presents initial validation results based on the analysis of the NREL Phase VI experiment, and it also provides a sample application to the analysis of a multi–megawatt turbine in yawed wind. The reported analyses indicate that the harmonic balance solver determines the considered periodic flows from 30 to 50 times faster than the conventional time–domain approach with negligible accuracy penalty to the latter. Copyright c2017 John Wiley & Sons, Ltd