1,721,098 research outputs found
Numerische Untersuchungen zum Einfluß linearelastisch nachgiebiger Festkörper auf den Kollaps einer benachbarten Kavitationsblase
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Contribution to the development of an adaptive solver for numerical simulation of steady and unsteady flows
No full textThe work deals with enhancing the capabilities of the unstructured adaptive Finite Volume flow solver QUADFLOW for compressible fluid flow. The solver exists as an integrated tool with multiscale based grid adaptation and B-spline based quadrilateral/hexahedral multi-block grid generation modules. Due to hanging nodes introduced through grid adaptation, data structure is cell face based. Upwind methods are implemented for flux discretisation in combination with explicit time integration as well as implicit temporal discretisation using Newton linearisation and Krylov subspace method. In the thesis, a preconditioner based on the formulation of Weiss and Smith is implemented for simulating inviscid and viscous flows at low Mach number over airfoils in cruise as well as high lift configurations. The results demonstrate the achievement of Mach number independent lift and drag coefficients (D'Alembert's paradox) and have an excellent agreement with results available in the literature. The wall distance for the turbulence modelling in the presence of highly stretched, refined cells and hanging nodes close to the wall is correctly estimated using vector algebra. With this formulation, the wriggles in the skin friction distribution due to grid adaptation are avoided. Detached Eddy formulation based on the Spalart-Allmaras turbulence model is shown to be effective together with the grid adaptation and demonstrated to have excellent stall capturing characteristics for high lift configurations. A second order accurate, geometrically conservative implicit scheme, based on Backward Difference discretisation is formulated, implemented and validated to simulate the unsteady inviscid flow over the pitching NACA0012 profile. The method shows an advantage over the existing Mid-point scheme allowing relatively higher time steps and higher global CFL numbers during the simulation. The non-linear multigrid method based on the Full Approximation Storage scheme with V-cycle is implemented to improve the convergence behaviour of the explicit scheme in solving inviscid flow problems. The coarsening is based on the hierarchical agglomeration strategy to combine the fine cells belonging to the identical parent cell at the same level to generate a series of coarse grid levels. The restriction operator is based on the volume weightiness and the prolongation operation is carried out using the upwind scheme. The implementations in the solver are extensively validated using results from available experiments and numerical solutions existing in the literature. Fully turbulent flow computations at different free stream Mach numbers and Reynolds numbers are carried out and compared with data obtained from the KRG experiments conducted in Goettingen on behalf of SFB 401, including some tests where strong shock-boundary layer interaction with buffet was observed. These are studied at three different grid resolutions. It is concluded that the adequate resolution of the grid cells along the stream-wise direction is vital in accurately resolving the flow physics in shock buffet. Furthermore, code extensions are carried out to offer the capability to the adaptive solver for simulating three-dimensional flow and some first computations are performed with the available computational power
Aeroservoelastisches Modell zur Beschreibung der instationären Aerodynamik für nichtlineare beliebige Eingangsgrößen im Zeitbereich
No full textIn this thesis an aeroservoelastic model for an airfoil-rudder-system with three degrees of freedom is established in time domain. This leads to the design of control laws for active flutter suppression. The response of the unsteady aerodynamics and the system behav-iour with respect to a non-linear time dependent doublet deflection of the rudder and the angle of attack are calculated. An integrated areoservoelastic model in time domain is set up by means of the indicial concept. The unsteady aerodynamics in incompressible and compressible flow for arbi-trary movements is approximated by indicial functions using the following approach: 1. The aerodynamic forces and moments are derived in integral form from the lin-earized potential theory.2. The indicial functions are validated for compressible and incompressible flow in frequency and time domain.3. The lift system for arbitrary variations of angle of attack, pitching and rate of rud-der deflection is derived from DUHAMEL-superposition integral.4. The transfer function of the lift system is derived by LAPLACE transformation.5. The state space equation for the airfoil-rudder-system for unsteady aerodynamics in compressible and incompressible flow are set up.6. The differential equations of motion of the airfoil-rudder-system are expressed by the LAGRANGE equations of second kind and combined with the aerodynamic equations to the aeroelastic system.7. The validation of the aeroelastic is carried out by comparison of the flutter speed using the root locus method according U-g-method, p-k-method and g-method from literature. The three most important results of this work are three new formulas for the approxima-tion of the unsteady aerodynamics for incompressible and compressible flow: 1. A new and better constant for the approximation of the WAGNER function in in-compressible flow. The indicial function is validated by comparison with the THEODORSEN function in LAPLACE domain. Compared to other approximations this procedure yields better imaginary parts of the indicial lift. This results in a better prediction of the flutter speed.2. The two other formulas are related to the time constants KaM and KaM1/4, which are used for the approximation of the non-circulatory indicial moments relative to the elastic axis and the 1/4-chord in compressible flow. Therefore, the explicit start and end values of the indicial response according to LOMAX are used. In particular, the constants KaM, which are related to the elastic axis, are important for the aeroelastic modelling. The substantial effects for the unsteady aerodynamic due to non-harmonic motion or disturbances can be calculated in a very fast and efficient way in time domain. This al-lows the simultaneous consideration of the flexibility of the lift system within the aerody-namic system and the set-up of an integrated model including the control laws and the flight mechanic system
Numerical investigation of unsteady transonic shock boundary layer interaction for aeronautical applications : 7 Tabellen, 92 Literaturstellen
No full textAdaptive Schrittweitensteuerung zur robusten numerischen Simulation aeroelastischer Anwendungen
No full textIn this work the concept of a new time step control is developed for an adaptive flow solver to solve (a)synchronously (pseudo)transient problems of the fluid-structure interaction numerically robust while coupling the flow solver with a structure solver algebraically (partitioned coupling). By the analytically determined APRIORI time steps it facilitates the convergence of the applied Newton method and it is emperically observable, that the numerical method generates only physically correct iteration states. The APRIORI time steps are not chosen maximum possible. Thus it seems rational to increase the local time steps gradually until some certain upper limit is exceeded, above which divergence or a physical illegitimate iteration state appears. In this case the time integration step has to be repeated a posteriori with adequately decreased time step size. This principle of trial and error is improved by the Kalman filter and other smoothing methods to estimate the limiting factor more accurately and therefore to smooth the (erratic) convergence history. Furthermore the optimal updating Newton step is iteratively determined, which reduces the number of time step repetitions and consequently the simulation time. As a special case of asynchronous time integration the synchronous integration uses the smallest APRIORI time step and increases it, as long as the convergence criterium is fulfilled and only physically admissible iteration states are generated. Otherwise the actual time integration step is repeated with adequately decreased time step size. The upper limit for this time step control is prescribed by the user in form of a physically relevant maximum time step. Within the scope of aeroelastic applications the flows around a 2D panel and 2D profiles with NLR-7301 and BAC-3-11 shapes are investigated. Stability regions are determined by numerical simulation of these aeroelastic problems varying fluid and structure relevant parameters. The correct and stable numerical simulation of fluid-structure problems requires conservative transfers of load, torsional moment and energy in space and time. The spatially conservative interpolation of loads for section by section linear or curved grid elements is derived and combined with a (fast) octree based neighborhood search. It is used for the simulation of the transonic panel problem. These interpolation methods make a transfer of discrete or linear load distributions between fluid and structure boundary mesh feasible. The partitioned fluid-structure coupling in this work consists of staggered calls of the fluid and structure solvers. Three different coupling schemes have been investigated: the loose, the extrapolation and the fixed-point iteration coupling scheme. Only the fixed-point scheme can diminish the accumulating time lag of the other two coupling schemes completely. Banachs fixed-point theorem implies the existence of an upper limit in the choice of time steps for a convergent fixedpoint iteration coupling. The surveillance of a prescribed convergence criterium forces the fixed-point scheme to converge successfully. Although the fixed-point coupling scheme is numerically the most expensive of all considered coupling schemes, it is the most accurate one and also indispensable for an exact energy transfer between fluid and structure in time. Several other improvements have been implemented in the flow solver QUADFLOW, for example the Kalman filter and some smoothing and damping methods. Also new differentiable limiters with iterative monotony correction have been introduced, which can not be described in detail here due to space restrictions
Ein modulares Verfahren für die numerische aeroelastische Analyse von Luftfahrzeugen
No full textIn order to assure economic efficiency and operational safety of new aircrafts, it is necessary to accurately consider the interaction of the elastic aircraft structure and the airflow in early stages of design. For a reliable prediction of effects arising from the interaction of the fluid and the structure the simultaneous solution of the governing equations for both domains is essential. Since flight speeds close to the speed of sound lead to significant flow-induced non-linear effects it is necessary to apply the Navier-Stokes equations in order to model the compressible, viscous fluid flow. The computational method SOFIA (Solid-Fluid-Interaction) solves the system of aeroelastic equations in the time-domain under consideration of flow induced non-linearities and facilitates the analysis of static and dynamic aeroelastic effects especially in the transonic flow regime. The core of SOFIA is the Aeroelastic Coupling Module (ACM), which has been developed and applied in the framework of the present dissertation. The ACM allows for a modularized assembly of SOFIA from different Euler- or Navier-Stokes-based flow solvers and FE-based structural solvers. Generalized program interfaces ensure the exchangeability of the codes for the different fields. The coupling module ACM coordinates the sequence of solver calls for static and dynamic aeroelastic computations in the sense of a partitioned procedure. Different improved “loose” strategies with prediction-/correction-steps and strong coupling strategies are provided. These strategies are aiming for a minimization of numerical errors resulting from inadequate energy transfer which is often inherent in basic loose coupling strategies. The improved staggered strategies allow for a good compromise between numerical effort and accuracy and stability of the partitioned procedure and thus facilitate the application of SOFIA to realistic problems. The ACM provides a local node-based method to exchange loads and displacements between the discretized sub-domains even with non-matching interface meshes. This method fulfils the requirement to conserve mechanical energy as well as global forces and moments. The applied load/displacement transfer algorithm is capable of exchanging coupling information between the discretized fluid domain and a structural model, which optionally consists of beam, shell, or volume elements. The validation of SOFIA for steady and unsteady aeroelastic applications has been performed by comparison of numerical results with experimental data for a swept wing model in subsonic flow. A good agreement for all test cases in terms of global aerodynamic forces and moments, pressure distributions and model deformations was found. SOFIA has been applied in the framework of the project HiReTT (High Reynolds Number Tools and Techniques) to investigate the influence of wing deformations on the aerodynamic characteristics of wind tunnel models in high Reynolds number experiments. The investigations revealed, that occurring wing deformations can significantly alter the flowfield and that experimental data can not be interpreted correctly without knowledge about the underlying model deformation. After extensive validation for subsonic and transonic aeroelastic problems, SOFIA has been used for the design and analysis of a wind tunnel model for transonic aero-structural dynamics experiments at realistic flight Reynolds numbers in a cryogenic wind tunnel. The main focus of SOFIA’s application was the assessment of the steady and unsteady aeroelastic behaviour under systematic variation of angle of attack, Reynolds number, Mach number and wind tunnel pressure. The extensive set of data collected during the numerical investigations was used to optimize the test programme for the planned, cost-intensive wind tunnel experiments
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