Efficient aerodynamic derivative calculation in three-dimensional transonic flow

ABSTRACTOne key task in computational aeroelasticity is to calculate frequency response functions of aerodynamic coefficients due to structural excitation or external disturbance. Computational fluid dynamics methods are applied for this task at edge-of-envelope flow conditions. Assuming a dynamically linear response around a non-linear steady state, two computationally efficient approaches in time and frequency domain are discussed. A non-periodic, time-domain function can be used, on the one hand, to excite a broad frequency range simultaneously giving the frequency response function in a single non-linear, time-marching simulation. The frequency-domain approach, on the other hand, solves a large but sparse linear system of equations, resulting from the linearisation about the non-linear steady state for each frequency of interest successively. Results are presented for a NACA 0010 aerofoil and a generic civil aircraft configuration in very challenging transonic flow conditions with strong shock-wave/boundary-layer interaction in the pre-buffet regime. Computational cost savings of up to 1 order of magnitude are observed in the time domain for the all-frequencies-at-once approach compared with single-frequency simulations, while an additional order of magnitude is obtained for the frequency-domain method. The paper demonstrates the readiness of computational aeroelasticity tools at edge-of-envelope flow conditions.</jats:p

Influence of gust modelling on free-flight aerofoils

Gust analysis is one key task during design and certification of new aircraft. In the industrial standard, the gust is modelled as a disturbance in velocity and is superposed with the general velocity field surrounding the aircraft. The shape, typically sinusoidal or 1-cos, is uniform in vertical direction and is not changing while travelling through the computational domain. These assumptions known as the field or disturbance velocity method facilitate an efficient way of simulating gust encounter within computational fluid dynamics methods. However, how this frozen gust model effects the accuracy of loads predictions compared to more-realistic models remains an open question. A novel approach to simulate a so-called resolved gust is presented herein. An initial perturbation of the x-velocity is prescribed using a 1-cos shape in two spatial directions. Disturbances in vertical velocity as well as density and pressure are developing after some simulated time. Results are compared to the field-velocity method using the CRANK aerofoil covering subsonic and transonic flow conditions. Lift and moment responses are analysed as well as time histories of velocities at different grid locations. Furthermore, a second aerofoil is added as a horizontal tail-plane to represent a large civil aircraft. This configuration is used to include the effects of flight dynamics while analysing the responses due to the two gust models

Rapid gust response simulation of large civil aircraft using computational fluid dynamics

ABSTRACTSeveral critical load cases during the aircraft design process result from atmospheric turbulence. Thus, rapidly performable and highly accurate dynamic response simulations are required to analyse a wide range of parameters. A method is proposed to predict dynamic loads on an elastically trimmed, large civil aircraft using computational fluid dynamics in conjunction with model reduction. A small-sized modal basis is computed by sampling the aerodynamic response at discrete frequencies and applying proper orthogonal decomposition. The linear operator of the Reynolds-averaged Navier-Stokes equations plus turbulence model is then projected onto the subspace spanned by this basis. The resulting reduced system is solved at an arbitrary number of frequencies to analyse responses to 1-cos gusts very efficiently. Lift coefficient and surface pressure distribution are compared with full-order, non-linear, unsteady time-marching simulations to verify the method. Overall, the reduced-order model predicts highly accurate global coefficients and surface loads at a fraction of the computational cost, which is an important step towards the aircraft loads process relying on computational fluid dynamics.</jats:p

Model reduction for gust load analysis of free-flying aircraft

The coupling of computational fluid dynamics and rigid body dynamics promises enhanced multidisciplinary simulation capability for aircraft design and certification. Industrial application of such coupled simulations is limited however by computational cost. In this context, model reduction can retain the fidelity of the underlying model while decreasing the computational effort. A model reduction technique is presented herein based on modal decomposition and projection of the non-linear residual function. Flight dynamics eigenmodes are obtained with an operator-based identification procedure which is capable of calculating these global modes of the coupled Jacobian matrix also for an industrial use case with nearly 50 million degrees-of-freedom. Additional modes based on proper orthogonal decomposition to describe the aerodynamic response due to gust encounter are combined with the eigenmode basis. Results are presented for initial disturbance analysis using flight dynamics modes only and for gust encounter simulations using the combined modal basis. Overall, the reduced model is capable of predicting the full order results accurately

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Abstract Forthcoming

Investigation into gust load alleviation using computational fluid dynamics

Gust load alleviation has become an integral part of aircraft design to significantly decrease the impact of atmospheric turbulence on aircraft loads, handling qualities and also passenger comfort. During the design of an active control system, the aerodynamic response of the aircraft subjected to gust encounter and control surface deflection effects needs to be modelled. Current industrial practice is based on low-fidelity linear-potential panel methods which are repeatedly evaluated in frequency domain to obtain so-called frequency response functions. Even though rapid turnaround times are possible, important aerodynamic effects such as shock waves and resulting boundary layer separation which define transonic flow conditions are neglected. Typically, robust and adaptive control laws have been designed to account for the shortcomings of the underlying aerodynamic modelling fidelity. In contrast to this, we present initial results of a basic gust controller while using an enhanced aerodynamic modelling by solving the linearised Reynolds-averaged Navier–Stokes equations in frequency domain. Results are presented both for an aerofoil and a large aircraft configuration near transonic cruise conditions. Control laws derived from different levels of the aerodynamic hierarchy are scrutinised during unsteady simulations of realistic gust-encounter scenarios

Frequency-Domain Gust Response Simulation using Computational Fluid Dynamics

The numerical investigation of dynamic responses to atmospheric turbulence is an important task during the aircraft design and certification process. Efficient methods are desirable because large parameter spaces spanned by, for example, Mach number, flight altitude, load case, and gust shape need to be covered. Aerodynamic nonlinearities such as shocks and boundary-layer separation should be included to account for transonic flight conditions. A linearized frequency-domain method is outlined to efficiently obtain gust responses using computational fluid dynamics. The Reynolds-averaged Navier–Stokes equations are linearized around a steady-state solution and solved for discrete frequencies. The resulting large but sparse system of linear equations can then be evaluated significantly faster than its time-domain counterpart. The method is verified analyzing sinusoidal gust responses for an airfoil and a large civil aircraft considering a broad range of reduced frequencies. Derivatives of aerodynamic coefficients and complex-valued surface pressures are compared for time- and frequency-domain approaches. Next, 1-cos gusts are investigated using an incomplete inverse Fourier transform in conjunction with a complex-valued weighting function to discuss time histories of lift coefficients as well as surface pressures. Finally, introduced techniques are applied to conditions arising from certification requirements to demonstrate the technical readiness. The methods discussed present an important step to establish computational fluid dynamics in the routine aircraft loads process

Podoplanin immunopositive lymphatic vessels at the implant interface in a rat model of osteoporotic fractures

Insertion of bone substitution materials accelerates healing of osteoporotic fractures. Biodegradable materials are preferred for application in osteoporotic patients to avoid a second surgery for implant replacement. Degraded implant fragments are often absorbed by macrophages that are removed from the fracture side via passage through veins or lymphatic vessels. We investigated if lymphatic vessels occur in osteoporotic bone defects and whether they are regulated by the use of different materials. To address this issue osteoporosis was induced in rats using the classical method of bilateral ovariectomy and additional calcium and vitamin deficient diet. In addition, wedge-shaped defects of 3, 4, or 5 mm were generated in the distal metaphyseal area of femur via osteotomy. The 4 mm defects were subsequently used for implantation studies where bone substitution materials of calcium phosphate cement, composites of collagen and silica, and iron foams with interconnecting pores were inserted. Different materials were partly additionally functionalized by strontium or bisphosphonate whose positive effects in osteoporosis treatment are well known. The lymphatic vessels were identified by immunohistochemistry using an antibody against podoplanin. Podoplanin immunopositive lymphatic vessels were detected in the granulation tissue filling the fracture gap, surrounding the implant and growing into the iron foam through its interconnected pores. Significant more lymphatic capillaries were counted at the implant interface of composite, strontium and bisphosphonate functionalized iron foam. A significant increase was also observed in the number of lymphatics situated in the pores of strontium coated iron foam. In conclusion, our results indicate the occurrence of lymphatic vessels in osteoporotic bone. Our results show that lymphatic vessels are localized at the implant interface and in the fracture gap where they might be involved in the removal of lymphocytes, macrophages, debris and the implants degradation products. Therefore the lymphatic vessels are involved in implant integration and fracture healing