Simulation of three-dimensional viscous flow in turbomachinery geometries using a solution-adaptive unstructured mesh methodology

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier-Stokes equations with k-ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis

This paper demonstrates how a finite element model which exploits domain decomposition is applied to the analysis of three-phase induction motors. It is shown that a significant gain in cpu time results when compared with standard finite element analysis. Aspects of the application of the method which are particular to induction motors are considered: the means of improving the convergence of the nonlinear finite element equations; the choice of symmetrical sub-domains; the modelling of relative movement; and the inclusion of periodic boundary conditions. © 1999 IEEE.

A discrete dislocation analysis of fatigue crack growth

Cyclic loading of a plane strain mode I crack under small scale yielding is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic solid. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a non-singular complementary solution that enforces the boundary conditions, which is obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. An irreversible relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, which permits crack growth to emerge naturally. It is found that crack growth can occur under cyclic loading conditions even when the peak stress intensity factor is smaller than the stress intensity required for crack growth under monotonic loading conditions; however below a certain threshold value of ΔKI no crack growth was seen.

Three-dimensional SBLI control for transonic airfoils

The application of shock control to transonic airfoils and wings has been demonstrated widely to have the potential to reduce wave drag. Most of the suggested control devices are two-dimensional, that is they are of uniform geometry in spanwise direction. Examples of such techniques include contour bumps and passive control. Recently it has been observed that a spanwise array of discrete three-dimensional controls can have similar benefits but also offer advantages in terms of installation complexity and drag. This paper describes research carried out in Cambridge into various three-dimensional devices, such as slots, grooves and bumps. In all cases the control device is applied to the interaction of a normal shock wave (M=1.3) with a turbulent boundary layer. Theoretical considerations are proposed to determine how such fundamental experiments can provide estimates of control performance on a transonic wing. The potential of each class of three-dimensional device for wave drag reduction on airfoils is discussed and surface bumps in particular are identified as offering potential drag savings for typical transonic wing applications under cruise conditions.

Duty cycle and modelling considerations in three-phase induction motor drives for washing machines

Three-phase induction motors offer significant advantages over commutator motors in some domestic appliances. Models for wide speed range three-phase induction motors for use in a horizontal axis washing machine have been developed using the MEGA finite element package with an external formulation for calculating iron losses. Motor loss predictions have been verified using a novel high accuracy calorimeter. Good agreement has been observed over a wide speed range at different loadings. The model is used to predict motor temperature rise under typical washing machine loading conditions to ensure its limiting temperature is not exceeded and enables alternative designs to be investigated without recourse to physical prototypes. © 2005 IEEE.

Shock / boundary-layer interaction control using three-dimensional bumps for transonic wings

Three-dimensional bumps have been developed and investigated, aiming at the two major objectives of shock-wave / boundary-layer interaction control, i.e. drag reduction and suppression of separation, simultaneously. An experimental investigation has been conducted for a default rounded bump in channel now at University of Cambridge and a computational study has been performed for a spanwise series of rounded bumps mounted on a transonic aerofoil at University of Stuttgart. Observed in both cases are wave drag reduction owing to A-shock structures produced by three-dimensional surface bumps and mild control effects on the boundary layer. The effects of rough surface and tall extension have been investigated as well as several geometric variations and multiple bump configurations. A double configuration of narrow rounded bumps has been found to best perform amongst the tested, considerably reducing wave drag through a well-established A-shock structure with little viscous penalty and thus achieving substantial overall drag reduction. Counter-rotating streamwise vortex pairs have been produced by some configurations as a result of local flow separation, but they have been observed to be confined in relatively narrow wake regions, expected to be beneficial in suppressing large-scale separation under off-design condition despite increase of viscous drag. On the whole a large potential of three-dimensional control with discrete rounded bumps has been demonstrated both experimentally and numerically, and experimental investigation of bumps fitted on a transonic aerofoil or wing is suggested toward practical application.

Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine

A multi-dimensional combustion code implementing the Conditional Moment Closure turbulent combustion model interfaced with a well-established RANS two- phase flow field solver has been employed to study a broad range of operating conditions for a heavy duty direct-injection common-rail Diesel engine. These conditions include different loads (25%, 50%, 75% and full load) and engine speeds (1250 and 1830 RPM) and, with respect to the fuel path, different injection timings and rail pressures. A total of nine cases have been simulated. Excellent agreement with experimental data has been found for the pressure traces and the heat release rates, without adjusting any model constants. The chemical mechanism used contains a detailed NOx sub-mechanism. The predicted emissions agree reasonably well with the experimental data considering the range of operating points and given no adjustments of any rate constants have been employed. In an effort to identify CPU cost reduction potential, various dimensionality reduction strategies have been assessed. Furthermore, the sensitivity of the predictions with respect to resolution in particular relating to the CMC grid has been investigated. Overall, the results suggest that the presented modelling strategy has considerable predictive capability concerning Diesel engine combustion without requiring model constant calibration based on experimental data. This is true particularly for the heat release rates predictions and, to a lesser extent, for NOx emissions where further progress is still necessary. © 2009 SAE International.

Behaviour of unsteady transonic shock / boundary layer interactions with three-dimensional effects

An experimental investigation into the response of transonic SBLIs to periodic down-stream pressure perturbations in a parallel walled duct has been conducted. Tests have been carried out with a shock strength of M ∞ = 1.5 for pressure perturbation frequencies in the range 16-90 Hz. Analysis of the steady interaction at M∞ = 1.5 has also been made. The principle measurement techniques were high speed schlieren photography and laser Doppler anemometry. The structure of the steady SBLI was found to be highly three-dimensional, with large corner flows and sidewall SBLIs. These aspects are thought to influence the upstream transmission of pressure information through the interaction by affecting the post-shock flow field, including the extent of regions of secondary supersonic flow. At low frequency, the dynamics of shock motion can be predicted using an inviscid analytical model. At increased frequencies, viscous effects become significant and the shock exhibits unexpected dynamic behaviour, due to a phase lag between the upstream transmission of pressure information in the core flow and in the viscous boundary layers. Flow control in the form of micro-vane vortex generators was found to have a small impact on shock dynamics, due to the effect it had on the post-shock flow field outside the viscous boundary layer region. The relationship between inviscid and viscous effects is developed and potential destabilising mechanisms for SBLIs in practical applications are suggested. Copyright © 2009 by Paul Bruce and Holger Babinsky.

Finite volume distance field solution applied to medial axis transform

Accurate and efficient computation of the nearest wall distance d (or level set) is important for many areas of computational science/engineering. Differential equation-based distance/ level set algorithms, such as the hyperbolic-natured Eikonal equation, have demonstrated valuable computational efficiency. Here, in the context, as an 'auxiliary' equation to the main flow equations, the Eikonal equation is solved efficiently with two different finite volume approaches (the cell vertex and cell-centered). Application of the distance solution is studied for various geometries. Moreover, a procedure using the differential field to obtain the medial axis transform (MAT) for different geometries is presented. The latter provides a skeleton representation of geometric models that has many useful analysis properties. As an alternative approach to the pure geometric methods (e.g. the Voronoi approach), the current d-MAT procedure bypasses many difficulties that are usually encountered by pure geometric methods, especially in three dimensional space. It is also shown that the d-MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.

Experimentally validated three dimensional GCT wafer level simulations

In this paper we present a wafer level three-dimensional simulation model of the Gate Commutated Thyristor (GCT) under inductive switching conditions. The simulations are validated by extensive experimental measurements. To the authors' knowledge such a complex simulation domain has not been used so far. This method allows the in depth study of large area devices such as GCTs, Gate Turn Off Thyristors (GTOs) and Phase Control Thyristors (PCTs). The model captures complex phenomena, such as current filamentation including subsequent failure, which allow us to predict the Maximum Controllable turn-off Current (MCC) and the Safe Operating Area (SOA) previously impossible using 2D distributed models. © 2012 IEEE.

Fluid-structure interaction of three-dimensional magnetic artificial cilia

A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width. © 2012 Cambridge University Press.

A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

3D modeling of high-T c superconductors by finite element software

A three-dimensional (3D) numerical model is proposed to solve the electromagnetic problems involving transport current and background field of a high-T c superconducting (HTS) system. The model is characterized by the E-J power law and H-formulation, and is successfully implemented using finite element software. We first discuss the model in detail, including the mesh methods, boundary conditions and computing time. To validate the 3D model, we calculate the ac loss and trapped field solution for a bulk material and compare the results with the previously verified 2D solutions and an analytical solution. We then apply our model to test some typical problems such as superconducting bulk array and twisted conductors, which cannot be tackled by the 2D models. The new 3D model could be a powerful tool for researchers and engineers to investigate problems with a greater level of complicity.