Transient flows in enclosures: A generalised approach for modelling the effects of geometry, heat gains and wind

Transient flows in a confined ventilated space induced by a buoyancy source of time-varying strength and an external wind are examined. The space considered has varying cross-sectional area with height. A generalised theoretical model is proposed to investigate the flow dynamics following the activation of an external wind and an internal source of buoyancy. To investigate the effect of geometry, we vary the angle of the wall inclination of a particular geometry in which a point source of constant buoyancy is activated in the absence of wind. Counter-intuitively the ventilation is worse and lower airflow rates are established for geometries of increasing cross-sectional areas with height. We investigate the effect of the source buoyancy strength by comparing two cases: (1) when the buoyancy input is constant and (2) when the buoyancy input gradually increases over time so that after a finite time the total buoyancy inputs for (1) and (2) are identical. The rate at which the source heat gains are introduced has a significant role on the flow behaviour as we find that, in case (2), a warmer layer and a more pronounced overshoot are obtained than in case (1). The effect of assisting and opposing wind on the transient ventilation of an enclosure of constant cross-sectional area with height and constant heat gains is examined. A Froude number Fr is used to define the relative strengths of the buoyancy-induced and wind-induced velocities and five different transient states and their associated critical Fr are identified. © 2010 Elsevier Ltd.

Large-eddy simulation of complex geometry jets

Computations are made for chevron and coflowing jet nozzles. The latter has a bypass ratio of 6:1. Also, unlike the chevron nozzle, the core flow is heated, making the inlet conditions reminiscent of those for a real engine. A large-eddy resolving approach is used with circa 12 × 10 6 cell meshes. Because the codes being used tend toward being dissipative the subgrid scale model is abandoned, giving what can be termed numerical large-eddy simulation. To overcome near-wall modeling problems a hybrid numerical large-eddy simulation-Reynolds-averaged Navier-Stokes related method is used. For y + ≤ 60 a Reynolds-averaged Navier-Stokes model is used. Blending between the two regions makes use of the differential Hamilton-Jabobi equation, an extension of the eikonal equation. For both nozzles, results show encouraging agreement with measurements of other workers. The eikonal equation is also used for ray tracing to explore the effect of the mean flow on acoustic ray trajectories, thus yielding a coherent solution strategy. © 2011 by Cambridge University.

Geometry of Miura-folded metamaterials.

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

Effects of Boundary Layer Ingestion on the Aero-Acoustics of Transonic Fan Rotors

The use of boundary-layer-ingesting, embedded propulsion systems can result in inlet flow distortions where the interaction of the boundary layer vorticity and the inlet lip causes horseshoe vortex formation and the ingestion of streamwise vortices into the inlet. A previously-developed body-force-based fan modeling approach was used to assess the change in fan rotor shock noise generation and propagation in a boundary-layer-ingesting, serpentine inlet. This approach is employed here in a parametric study to assess the effects of inlet geometry parameters (offset-to-diameter ratio and downstream-to-upstream area ratio) on flow distortion and rotor shock noise. Mechanisms related to the vortical inlet structures were found to govern changes in the rotor shock noise generation and propagation. The vortex whose circulation is in the opposite direction to the fan rotation (counter-swirling vortex) increases incidence angles on the fan blades near the tip, enhancing noise generation. The vortex with circulation in the direction of fan rotation (co-swirling vortex) creates a region of subsonic relative flow near the blade tip radius which decreases the sound power propagated to the far-field. The parametric study revealed that the overall sound power level at the fan leading edge is set by the ingested streamwise circulation, and that for inlet designs in which the streamwise vortices are displaced away from the duct wall, the sound power at the upstream inlet plane increased by as much as 9 dB. By comparing the far-field noise results obtained to those for a conventional inlet, it is deduced that the changes in rotor shock noise are predominantly due to the ingestion of streamwise vorticity.

Effects of Boundary Layer Ingestion on the Aero-Acoustics of Transonic Fan Rotors

The use of boundary-layer-ingesting, embedded propulsion systems can result in inlet flow distortions where the interaction of the boundary layer vorticity and the inlet lip causes horseshoe vortex formation and the ingestion of streamwise vortices into the inlet. A previously-developed body-force-based fan modeling approach was used to assess the change in fan rotor shock noise generation and propagation in a boundary-layer-ingesting, serpentine inlet. This approach is employed here in a parametric study to assess the effects of inlet geometry parameters (offset-to-diameter ratio and downstream-to-upstream area ratio) on flow distortion and rotor shock noise. Mechanisms related to the vortical inlet structures were found to govern changes in the rotor shock noise generation and propagation. The vortex whose circulation is in the opposite direction to the fan rotation (counter-swirling vortex) increases incidence angles on the fan blades near the tip, enhancing noise generation. The vortex with circulation in the direction of fan rotation (co-swirling vortex) creates a region of subsonic relative flow near the blade tip radius which decreases the sound power propagated to the far-field. The parametric study revealed that the overall sound power level at the fan leading edge is set by the ingested streamwise circulation, and that for inlet designs in which the streamwise vortices are displaced away from the duct wall, the sound power at the upstream inlet plane increased by as much as 9 dB. By comparing the far-field noise results obtained to those for a conventional inlet, it is deduced that the changes in rotor shock noise are predominantly due to the ingestion of streamwise vorticity.

Magnetic shielding with YBCO coated conductors: Influence of the geometry on its performances

A superconducting magnetic shield can be built as a stack of several sections of milled 2G coated conductors. Each section consists of a closed loop where persistent currents can flow and provide a strong attenuation of external dc magnetic fields. The purpose of the present work is to study experimentally several geometries of such magnetic shields made out of YBa2Cu 3O7 (YBCO) coated conductors from SuperPower. Our aim is to investigate in detail the influence of the aspect ratio and the number of layers of the assembly on the magnetic shielding properties. In order to do so, the magnetic shield is subjected to an axial quasi-static ('dc') magnetic field ramped slowly at a fixed sweep rate. A Hall probe is used to measure the local magnetic induction inside the assembly as a function of the applied magnetic induction. Results show that the shielding factor, SF, (defined as the ratio between the applied magnetic induction and the magnetic induction measured inside the shield) is improved for increasing aspect ratios of the global coated conductor assembly and that the threshold magnetic induction (defined for SF = 10) increases with the number of layers. Using a double layer of 18 sections at T = 77K , dc magnetic fields up to 56 mT can be shielded by a factor larger than 10. Finally, the effect of an air gap of constant width between coated conductor sections is also characterized. © 2002-2011 IEEE.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Guidance of collective cell migration by substrate geometry.

Collective behavior refers to the emergence of complex migration patterns over scales larger than those of the individual elements constituting a system. It plays a pivotal role in biological systems in regulating various processes such as gastrulation, morphogenesis and tissue organization. Here, by combining experimental approaches and numerical modeling, we explore the role of cell density ('crowding'), strength of intercellular adhesion ('cohesion') and boundary conditions imposed by extracellular matrix (ECM) proteins ('constraints') in regulating the emergence of collective behavior within epithelial cell sheets. Our results show that the geometrical confinement of cells into well-defined circles induces a persistent, coordinated and synchronized rotation of cells that depends on cell density. The speed of such rotating large-scale movements slows down as the density increases. Furthermore, such collective rotation behavior depends on the size of the micropatterned circles: we observe a rotating motion of the overall cell population in the same direction for sizes of up to 200 μm. The rotating cells move as a solid body, with a uniform angular velocity. Interestingly, this upper limit leads to length scales that are similar to the natural correlation length observed for unconfined epithelial cell sheets. This behavior is strongly altered in cells that present a downregulation of adherens junctions and in cancerous cell types. We anticipate that our system provides a simple and easy approach to investigate collective cell behavior in a well-controlled and systematic manner.

Differential geometry and design coupling in MDO

The notion of coupling within a design, particularly within the context of Multidisciplinary Design Optimization (MDO), is much used but ill-defined. There are many different ways of measuring design coupling, but these measures vary in both their conceptions of what design coupling is and how such coupling may be calculated. Within the differential geometry framework which we have previously developed for MDO systems, we put forth our own design coupling metric for consideration. Our metric is not commensurate with similar types of coupling metrics, but we show that it both provides a helpful geo- metric interpretation of coupling (and uncoupledness in particular) and exhibits greater generality and potential for analysis than those similar metrics. Furthermore, we discuss how the metric might be profitably extended to time-varying problems and show how the metric's measure of coupling can be applied to multi-objective optimization problems (in unconstrained optimization and in MDO). © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The influence of room geometry on the overturning of smoke owing to a floor fire

The present paper explores the influence of room geometry on the overturning of smoke owing to a centrally located floor fire, and examines the implications on smoke filling times. The focus is on presenting practical design guidelines based on the theoretical predictions of the model of Kaye and Hunt. An engineering platform is developed for the prediction of smoke filling times, and a rational basis is provided by way of which smoke behaviour can be specified for simple room designs. The time taken for smoke to fill a room to a given height is critically affected by the room aspect ratio and the characteristic size of the buoyancy source. At large times, taller (small aspect ratio) rooms are shown to fill with smoke at a faster rate than wide (large aspect ratio) rooms owing to large-scale overturning and engulfing of ambient air during the initial transients. Larger area sources of buoyancy also decrease significantly the smoke filling times, with important implications for fire and smoke safety design. Simplified design curves incorporating the main findings have been developed for use as a tool by practising fire-safety engineers.