Validity of Viscous Core Correction Models for Self-Induced Velocity Calculations

Viscous core correction models are used in free wake simulations to remove the infinite velocities at the vortex centreline. It will be shown that the assumption that these corrections converge to the Biot-Savart law in the far field is not correct for points near the tangent line of a vortex segment. Furthermore, the self-induced velocity of a vortex ring with a viscous core is shown to converge to the wrong value. The source of these errors in the model is identified and an improved model is presented that rectifies the errors. It results in correct values for the self-induced velocity of a viscous vortex ring and induced velocities that converge to the values predicted by the Biot-Savart law for all points in the far field.Comment: 8 pages, 5 figure

A KBE Application for Automatic Aircraft Wire Harness Routing

Wire harness design is an increasingly complex task. Knowledge Based Engineering (KBE) and optimization techniques can be used to support designers in handling this complexity. The wire harness design process can be divided in three main parts, namely electrical design, configuration design and geometrical routing. This paper describes the latest progress in the development of a KBE application aiming at the automation of the routing phase. Discrete optimization techniques are used to design shortest path harnesses, while complying with different type of constraints. Some preliminary results have been presented in a previous paper, where only geometrical constraints were addressed. However, wire harness design is affected also by other types of rules and constraints, which need to be accounted to obtain more realistic design results from the optimization process. This paper describes some new developments in the routing application to account for the presence of critical zones inside the aircraft. As study case, the presence of heat sources inside the airframe is considered, which either force the harness to be routed elsewhere, or require the use of wire protections, with obvious consequences on weight and manufacturing. First, some mathematic transformation techniques are used to model the presence of heat sources inside the routing environment. Then the A* algorithm is used for compute the 3D routing, aiming at minimum wire harness weight. The main architecture of the routing application is presented and its functionality is demonstrated with samples of wire harness routing inside a wing. The results show that the proposed KBE application can automate the routing of wire harness while taking into account different rules and constraints. The modeling approach for a heat source can be generalized and extended to address other criticality such as abrasion, electromagnetic interference, corrosion, etc. The achieved level of automation relieves designers from the repetitive work associated with the frequent changes affecting the design environment

Development of the Discrete Adjoint for a Three-Dimensional Unstructured Euler Solver

The discrete adjoint of a reconstruction-based unstructured finite volume formulation for the Euler equations is derived and implemented. The matrix-vector products required to solve the adjoint equations are computed on-the-fly by means of an efficient two-pass assembly. The adjoint equations are solved with the same solution scheme adopted for the flow equations. The scheme is modified to efficiently account for the simultaneous solution of several adjoint equations. The implementation is demonstrated on wing and wing–body configurations

Adjoint-based aerodynamic shape optimization on unstructured meshes

In this paper, the exact discrete adjoint of an unstructured finite-volume formulation of the Euler equations in two dimensions is derived and implemented. The adjoint equations are solved with the same implicit scheme as used for the flow equations. The scheme is modified to efficiently account for multiple functionals simultaneously. An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to algorithms for constrained optimization, is tested on airfoil design cases involving transonic as well as supersonic flows. The effect of some approximations in the discrete adjoint, which aim at reducing the complexity of the implementation, is shown in terms of optimization results rather than only in terms of gradient accuracy. The shape-optimization method appears to be very efficient and robust

Aerodynamic shape optimization by means of sequential linear programming techniques

A Sequential Linear Programming technique, known as the method of centers, is the driver of an aerodynamic shape optimization framework on unstructured meshes. The first order information required by this technique, functional values and their gradients, are computed by a median-dual flow/adjoint solver which is coupled to an analytical shape parameterization. Functional and geometric constraints are easily handled by the algorithm which appears to be very effective in obtaining efficiently near-optimal designs. Shape optimization results are presented for transonic as well as supersonic flows involving appreciable shape deformations