Identification of heat transfer dynamics for non-modal analysis of thermoacoustic stability

A systematic approach for non-modal stability analysis of thermoacoustic systems with a localized heat source is proposed. The response of the heat source to flow perturbations is obtained from unsteady computational fluid dynamics combined with correlation-based linear system identification. A model for the complete thermoacoustic system is formulated with a Galerkin expansion technique, where the heat source is included as an acoustically compact element. The eigenvalues of the resulting system are obtained from discretization of the solution operator, the maximum growth factor is estimated from the pseudospectra using Kreiss’ theorem.The approach is illustrated with a simple Rijke tube configuration. Results obtained with a simple “baseline” model for the heat source dynamics based on King’s law - widely used in hot wire anemometry - are compared against the more advanced treatment developed here. Analysis of pseudospectra diagrams shows that the choice of the heat source model does influence the sensitivity of eigenvalues to perturbations and hence the non-normal behavior. The maximum growth factor for the system with the heat source model based on King’s law is more sensitive to changes in the heat source location than the CFD-based heat source model.     

Mathematical Model of Ice Melting on Transmission Lines

During ice storms, ice forms on high voltage electrical lines. This ice formation often results in downed lines and has been responsible for considerable damage to life and property as was evidenced in the catastrophic ice storm of Quebec recently. There are two main aspects, viz., the formation of ice and its timely mitigation. In this paper, we mathematically model the melting of ice due to a higher current applied to the transmission wire. The two dimensional cross-section contains four layers consisting of the transmission wire, water due to melting of ice, ice, and the atmosphere. The model includes heat equations for the various regions with suitable boundary conditions. Heat propagation and ice melting are expressed as a Stefan-like problem for the moving boundary between the layers of ice and water. The model takes into account gravity which leads to downward motion of ice and to forced convection of heat in the water layer. In this paper, the results are applied to the case when the cross-sections are concentric circles to yield melting times for ice dependent on the increase in intensity of the electrical flow in the line. This research has been supported in part by Manitoba Hydro and NSERC.     

Correlation of design parameters with performance for electrostatic Precipitator. Part I. 3D model development and validation

As the first part of a two-paper series, this paper develops a three-dimensional model that describes corona discharge, turbulent flow, particle charging and tracking in electrostatic precipitators (ESP). To capture the shielding effects between discharge wires in a multi-wire ESP, the corona-discharge-induced space charge density at an arbitrary point between the discharge wire and grounded plates is specified as the sum of two components: (i) a uniform value on the wire surface which is resolved individually for each wire; and (ii) a space-dependent variation relative to the uniform part. The present model is solved with the finite element method and validated with experimental and numerical results from literature. Good agreement is obtained and illustrated in terms of distributions of electric potential, current density, electrohydrodynamic flow pattern, and particle trajectories, as well as corona current and particle collection efficiency. This validated model will be applied in Part II and integrated with the design-of-experiment approach to analyze both individual and interactive effects of design parameters on ESP performance.     

Travelling Waves with a Singularity in Magnetic Nanowires

We model the evolution of the magnetization in an infinite cylinder by harmonic map heat flow with an additional external field. Using variational methods, we prove the existence of corotationally symmetric travelling wave solutions with a moving vortex. We moreover show that for weak and strong fields the travelling waves connect the original state anti-parallel to the external magnetic field with the totally reversed state in direction of the external field. Our results match numeric simulations. For thicker wires several groups have found a reversal mode where a domain wall with a corotational symmetry and a vortex is propagating through the wire.     

Non-Smooth Optimization for Robust Control of Infinite-Dimensional Systems

We use a non-smooth trust-region method for H _∞-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it avoids the use of system reduction or identification. For illustration the method is applied to control a reaction-convection-diffusion system, a Van de Vusse reactor, and to a cavity flow control problem.     

Lifted flow cover inequalities for mixed 0-1 integer programs

We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lifting of flow cover inequalities is computationally very demanding. We present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and give computational results that show the effectiveness of our lifting procedures. Received May 15, 1996 / Revised version received August 7, 1998 Published online June 28, 1999     

Revisiting the single-phase flow model for liquid steel ladle stirred by gas

Ladle stirring is an important step of the steelmaking process to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions before casting. Gas is injected from the bottom of the bath to induce a turbulent flow of the liquid steel. Multiphase modeling of ladle stirring can become computationally expensive, especially when used within optimal flow control problems. This note focuses therefore on single-phase flow models. It aims at improving the existing models from the literature. Simulations in a 2d axial-symmetrical configuration, as well as in a real 3d laboratory-scale ladle, are performed. The results obtained with the present model are in a relative good agreement with experimental data and suggest that it can be used as an efficient model in optimal flow control problems.     

Cutting plane approach for the maximum flow interdiction problem

The maximum flow interdiction is a class of leader–follower optimization problems that seek to identify the set of edges in a network whose interruption minimizes the maximum flow across the network. Particularly, maximum flow interdiction is important in assessing the vulnerability of networks to disruptions. In this paper, the problem is formulated as a bi-level mixed-integer program and an iterative cutting plane algorithm is proposed as a solution methodology. The cutting planes are implemented in a branch-and-cut approach that is computationally effective. Extensive computational results are presented on 336 different instances with varying parameters and with networks of sizes up to 50 nodes, 1200 edge, and 800 commodities. The computational results show that the proposed cutting plane approach has significant computational advantage over the direct solution of the monolithic formulation of the maximum flow interdiction problem for the majority of the tested instances.     

Nonlinear Kelvin-Helmholtz instability of two miscible ferrofluids in porous media

The nonlinear theory of the Kelvin-Helmholtz instability is employed to analyze the instability phenomenon of two ferrofluids through porous media. The effect of both magnetic field and mass and heat transfer is taken into account. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and a Ginzburg–Landau equation, for the higher-order problem, describing the behavior of the system in a nonlinear approach. The stability criterion is expressed in terms of various competing parameters representing the mass and heat transfer, gravity, surface tension, fluid density, magnetic permeability, streaming, fluid thickness and Darcy coefficient. The stability of the system is discussed in both theoretically and computationally, and stability diagrams are drawn.     

Improved formulation,branch-and-cut and tabu search heuristic for single loop material flow system design

The single loop material flow system design is a combinatorial optimization problem, arising in material handling system design, which amounts to designing an unidirectional loop flow pattern as well as to locate pickup and delivery stations. The objective is to minimize the time required to carry out all material flow movements between cells. In this paper, we develop valid inequalities for a previously proposed formulation. The valid inequalities are then embedded into a branch-and-cut framework which is shown to solve much larger instances to optimality than those reported in the literature. A tailored tabu search heuristic is also illustrated and computationally assessed.     

Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials

The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g., in historic buildings, and the durability assessment of these therefore needs a reliable and probabilistic simulation of transport processes, which is related to the suitable identification of material parameters. In order to include expert knowledge as well as experimental results, one can employ an updating procedure such as Bayesian inference. The classical probabilistic setting of the identification process in Bayes’ form requires the solution of a stochastic forward problem via computationally expensive sampling techniques, which makes the method almost impractical.     

Estimation of terrestrial heat flow from temperature measurements in bottom sediments

Under study is the problem of estimation of the terrestrial heat flow from the temperature measurements in the bottom sediments. The problem is divided into the two subproblems: first, we solve the one-dimensional inverse problem of estimating the heat conductivity λ and, second, compute the heat flow value by solving the direct stationary problem using the just-found value of λ. We develop a sweep method for solving the direct problem which differs from the standard. An optimization approach is used for solving the inverse problem, and the explicit formulas are obtained for computing the gradient of the error functional. We analyze the factors that cause errors in estimating the heat flow. We show that the main contribution to the errors is given by the presence of harmonics with the periods exceeding the temperature monitoring time interval. We show that if the parameters of the harmonics are known then we can calculate some corrections for the obtained value of the heat flow. The results were applied to the data of temperature measurements carried out at the bottom of Lake Teletskoye from June of 2008 to September of 2010. For finding the long-period harmonics, we use the meteorological data about the bottom water temperature from 1968 to 2011. This allowed us to estimate the heat flow through the bottom of Lake Teletskoye as well as the thermal diffusivity in the upper layer of the sediments.     

Nonlinear Kelvin-Helmholtz instability of two miscible ferrofluids in porous media

The nonlinear theory of the Kelvin-Helmholtz instability is employed to analyze the instability phenomenon of two ferrofluids through porous media. The effect of both magnetic field and mass and heat transfer is taken into account. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and a Ginzburg–Landau equation, for the higher-order problem, describing the behavior of the system in a nonlinear approach. The stability criterion is expressed in terms of various competing parameters representing the mass and heat transfer, gravity, surface tension, fluid density, magnetic permeability, streaming, fluid thickness and Darcy coefficient. The stability of the system is discussed in both theoretically and computationally, and stability diagrams are drawn. Received: July 25, 2002; revised: April 16, 2003     

Morse homology for the heat flow

We use the heat flow on the loop space of a closed Riemannian manifold—viewed as a parabolic boundary value problem for infinite cylinders—to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined by counting, modulo time shift, heat flow trajectories between geodesics of Morse index difference one. By Salamon and Weber (GAFA 16:1050–138, 2006) this heat flow homology is naturally isomorphic to Floer homology of the cotangent bundle for Hamiltonians given by kinetic plus potential energy.     

Optimal wire ordering and spacing in low power semiconductor design

A key issue for high integration circuit design in the semiconductor industry are power constraints that stem from the need for heat removal and reliability or battery lifetime limitations. As the power consumption depends heavily on the capacitances between adjacent wires, determining the optimal ordering and spacing of parallel wires is an important issue in the design of low power chips. As it turns out, optimal wire spacing is a convex optimization problem, whereas the optimal wire ordering is combinatorial in nature, containing (a special class of) the Minimum Hamilton Path problem. While the latter is ${\mathcal{NP}}A key issue for high integration circuit design in the semiconductor industry are power constraints that stem from the need for heat removal and reliability or battery lifetime limitations. As the power consumption depends heavily on the capacitances between adjacent wires, determining the optimal ordering and spacing of parallel wires is an important issue in the design of low power chips. As it turns out, optimal wire spacing is a convex optimization problem, whereas the optimal wire ordering is combinatorial in nature, containing (a special class of) the Minimum Hamilton Path problem. While the latter is -hard in general, the present paper provides an algorithm that solves the coupled ordering and spacing problem for N parallel wires to optimality. Dedicated to Prof. Martin Gr?tschel on the occasion of his 60th birthday.     

Solving the Segregated Storage Problem with Benders' Partitioning

We investigate the application of Benders' partitioning to a mixed integer programming formulation of the segregated storage problem. The dual subproblem reduces to an efficiently-solvable network flow problem. This approach is compared empirically to Neebe's multiplier adjustment procedure. Benders' procedure is shown to be computationally effective for an important class of practical applications having high demand-to-capacity ratios and fewer products than compartments.     

Flow,heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer

In this paper, we investigate the flow, heat and mass transfer of a viscous fluid flow over a stretching sheet by including the blowing effects of mass transfer under high flux conditions. Mass transfer in this work means species transfer and is different from mass transpiration for permeable walls. The new contribution from this work is, for the first time, to consider the coupled blowing effects from massive species transfer on flow, heat, and species transfer for a stretching plate. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy and mass transfer equations are solved exactly and the effects of the blowing parameter, the Schmidt number, and the Prandtl number on the flow, heat and mass transfer are presented and discussed. The solution is given in terms of an incomplete Gamma function. It is found the coupled blowing effects due to mass transfer can have significant influences on velocity profiles, drag, heat flux, as well as temperature and concentration profiles. These solutions provide rare results with closed form analytical expressions and can be used as benchmark problem for numerical code validation.