Milan Vrdoljak

Composed Fluid–Structure Interaction Interface for Horizontal Axis Wind Turbine Rotor

In this paper we propose a technique for high-fidelity Fluid-Structure Interaction (FSI) spatial interface reconstruction, of a Horizontal Axis Wind Turbine (HAWT) rotor model composed of an elastic blade mounted on a rigid hub. The technique is aimed at enabling re-usage of existing blade Finite Element Method (FEM) models, now with high-fidelity fluid sub-domain methods relying on boundary-fitted mesh. The technique is based on the Partition of Unity method and it enables fluid sub-domain FSI interface mesh of different components to be smoothly connected. In the paper we use it to connect a beam FEM model to a rigid body, but the proposed technique is by no means restricted to any specific choice of numerical models for the structure components, or methods of their surface recoveries. To stress-test robustness of the connection technique we recover elastic blade surface from collinear mesh, and remark on repercussions of such a choice. For the HAWT blade recovery method itself we use Generalised Hermite Radial Basis Function Interpolation which utilises the interpolation of small rotations in addition to displacement data. Finally, for the composed structure we discuss consistent and conservative approaches to FSI spatial interface formulations.

Helicopter Pilot Model for Pitch Attitude Tracking Task

A helicopter pilot model as a part of the pilot-vehicle system is analyzed for the task of pitch attitude tracking in forward flight. Analytical helicopter pilot model, following the Efremov’s modification of the structural model, is defined through the optimization algorithm based on the minimum of the error variance. A set of the pilot-in-the-loop experiments were conducted at the research helicopter flight simulator with a fixed base and high fidelity visual system. In these experiments pilots were given different pitch commands visually at the primary flight display and the helicopter’s resulting pitch attitude was recorded. These results from the flight simulator experiments were used for the comparison with the results of the pilot-vehicle system with the defined analytical pilot model.

Lie Group Forward Dynamics of Fixed-Wing Aircraft With Singularity-Free Attitude Reconstruction on SO(3)

This paper proposes an approach to formulation and integration of the governing equations for aircraft flight simulation that is based on a Lie group setting, and leads to a nonsingular coordinate-free numerical integration. Dynamical model of an aircraft is formulated in Lie group state space form and integrated by ordinary-differential-equation (ODE)-on-Lie groups Munthe-Kaas (MK) type of integrator. By following such an approach, it is assured that kinematic singularities, which are unavoidable if a three-angles-based rotation parameterization is applied for the whole 3D rotation domain, do not occur in the proposed noncoordinate formulation form. Moreover, in contrast to the quaternion rotation parameterization that imposes additional algebraic constraint and leads to integration of differential-algebraic equations (DAEs) (with necessary algebraic-equation-violation stabilization step), the proposed formulation leads to a nonredundant ODE integration in minimal form. To this end, this approach combines benefits of both traditional approaches to aircraft simulation (i.e., three angles parameterization and quaternions), while at the same time it avoids related drawbacks of the classical models. Besides solving kinematic singularity problem without introducing DAEs, the proposed formulation also exhibits numerical advantages in terms of better accuracy when longer integration steps are applied during simulation and when aircraft motion pattern comprises steady rotational component of its 3D motion. This is due to the fact that a Lie group setting and applied MK integrator determine vehicle orientation on the basis of integration of local (tangent, nonlinear) kinematical differential equations (KDEs) that model process of 3D rotations (i.e., vehicle attitude reconstruction on nonlinear manifold SO(3)) more accurately than “global” KDEs of the classical formulations (that are linear in differential equations part in the case of standard quaternion models).

Numerical flight vehicle forward dynamics with state-space lie-group integration scheme

Dynamic simulation procedures of flight vehicle maneuvers need robust and efficient integration methods in order to allow for reliable simulation missions. Derivation of such integration schemes in Lie-group settings is especially efficient since the coordinate-free Lie-group dynamical models operate directly on SO(3) rotational matrices and angular velocities, avoiding local rotation parameters and artificial algebraic constraints as well as kinematical differential equations. In the adopted modeling approach, a state-space of the flight vehicle (modeled as a multi-body system comprising rigid bodies) is modeled as a Lie-group. The numerical algorithm is demonstrated and tested within the framework of the characteristic case study of the aircraft 3D maneuver.Copyright

Geometric Mathematical Framework for Multibody System Dynamics

The paper surveys geometric mathematical framework for computational modeling of multibody system dynamics. Starting with the configuration space of rigid body motion and analysis of it’s Lie group structure, the elements of respective Lie algebra are addressed and basic relations pertinent to geometrical formulations of multibody system dynamics are surveyed. Dynamical model of multibody system on manifold introduced, along with the outline of geometric characteristics of holonomic and non‐holonomic kinematical constraints.

Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems

Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint submanifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.Copyright