Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Improving discharge characteristics of indirect integral collector storage systems with multi-element storage

Desired performance of unpressurized integral collector storage systems hinges on the appropriate selection of storage volume and the immersed heat exchanger. This paper presents analytical results expressing the relation between storage volume, number of heat exchanger transfer units and temperature limited performance. For a system composed of a single storage element, the limiting behavior of a perfectly stratified storage element is shown to be superior to a fully-mixed storage element, consistent with more general analysis of thermal storage. Since, however, only the fully-mixed limit is readily obtainable in a physical system, the present paper also examines a division of the storage volume into separate compartments. This multi-element storage system shows significantly improved discharge characteristics as a result of improved elemental area utilization and temperature variation between elements, comparable in many cases to a single perfectly-stratified storage element. In addition, the multi-element system shows increased robustness with respect to variations in heat exchanger effectiveness and initial storage temperature.

Fast and compact simulation models for a variety of FET nano devices by the CMOS EKV equations

In this paper we explore the possibility of using the equations of a well known compact model for CMOS transistors as a parameterized compact model for a variety of FET based nano-technology devices. This can turn out to be a practical preliminary solution for system level architectural researchers, who could simulate behaviourally large scale systems, while more physically based models become available for each new device. We have used a four parameter version of the EKV model equations and verified that fitting errors are similar to those when using them for standard CMOS FET transistors. The model has been used for fitting measured data from three types of FET nano-technology devices obeying different physics, for different fabrication steps, and under different programming conditions. © 2009 IEEE NANO Organizers.

On separating propagating and non-propagating dynamics in fluid-flow equations

The ability to separate acoustically radiating and non-radiating components in fluid flow is desirable to identify the true sources of aerodynamic sound, which can be expressed in terms of the non-radiating flow dynamics. These non-radiating components are obtained by filtering the flow field. Two linear filtering strategies are investigated: one is based on a differential operator, the other employs convolution operations. Convolution filters are found to be superior at separating radiating and non-radiating components. Their ability to decompose the flow into non-radiating and radiating components is demonstrated on two different flows: one satisfying the linearized Euler and the other the Navier-Stokes equations. In the latter case, the corresponding sound sources are computed. These sources provide good insight into the sound generation process. For source localization, they are found to be superior to the commonly used sound sources computed using the steady part of the flow. Copyright © 2009 by S. Sinayoko, A. Agarwal, Z. Hu.

Model-based thermoacoustic oscillation control via ℋ ∞ loop-shaping and integral quadratic constraints

Lean premixed prevaporized (LPP) technology has been widely used in the new generation of gas turbines in which reduced emissions are a priority. However, such combustion systems are susceptible to the damage of self-excited oscillations. Feedback control provide a way of preventing such dynamic stabilities. A flame dynamics assumption is proposed for a recently developed unsteady heat release model, the robust design technique, ℋ ∞ loop-shaping, is applied for the controller design and the performance of the controller is confirmed by simulations of the closed-loop system. The Integral Quadratic Constraints(IQC) method is employed to prove the stability of the closed-loop system. ©2010 IEEE.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model. © 2011 Elsevier Ltd.

Geometrical properties and turbulent flame speed measurements in stationary premixed V-flames using direct numerical simulation

Three dimensional, fully compressible direct numerical simulations (DNS) of premixed turbulent flames are carried out in a V-flame configuration. The governing equations and the numerical implementation are described in detail, including modifications made to the Navier-Stokes Characteristic Boundary Conditions (NSCBC) to accommodate the steep transverse velocity and composition gradients generated when the flame crosses the boundary. Three cases, at turbulence intensities, u′/sL, of 1, 2, and 6 are considered. The influence of the flame holder on downstream flame properties is assessed through the distributions of the surface-conditioned displacement speed, curvature and tangential strain rates, and compared to data from similarly processed planar flames. The distributions are found to be indistinguishable from planar flames for distances greater than about 17δth downstream of the flame holder, where δth is the laminar flame thermal thickness. Favre mean fields are constructed, and the growth of the mean flame brush is found to be well described by simple Taylor type diffusion. The turbulent flame speed, sT is evaluated from an expression describing the propagation speed of an isosurface of the mean reaction progress variable c̃ in terms of the imbalance between the mean reactive, diffusive, and turbulent fluxes within the flame brush. The results are compared to the consumption speed, sC, calculated from the integral of the mean reaction rate, and to the predictions of a recently developed flame speed model (Kolla et al., Combust Sci Technol 181(3):518-535, 2009). The model predictions are improved in all cases by including the effects of mean molecular diffusion, and the overall agreement is good for the higher turbulence intensity cases once the tangential convective flux of c̃ is taken into account. © 2010 Springer Science+Business Media B.V.

Immersed Boundary Method for generalised finite volume and finite difference Navier-Stokes solvers

In Immersed Boundary Methods (IBM) the effect of complex geometries is introduced through the forces added in the Navier-Stokes solver at the grid points in the vicinity of the immersed boundaries. Most of the methods in the literature have been used with Cartesian grids. Moreover many of the methods developed in the literature do not satisfy some basic conservation properties (the conservation of torque, for instance) on non-uniform meshes. In this paper we will follow the RKPM method originated by Liu et al. [1] to build locally regularized functions that verify a number of integral conditions. These local approximants will be used both for interpolating the velocity field and for spreading the singular force field in the framework of a pressure correction scheme for the incompressible Navier-Stokes equations. We will also demonstrate the robustness and effectiveness of the scheme through various examples. Copyright © 2010 by ASME.