Two-Layer Thin Plate Temperature Control

In this paper, we develop a non‐iterative way to solve biharmonic boundary value problems by using a radial basis meshless method. This is an original application of meshless method to solving inverse problems without any iteration, since traditional numerical methods for inverse boundary value problems mainly are iterative and hence very time‐consuming. Numerical examples are presented for inverse biharmonic boundary value problems and corresponding direct problems, since solving direct problems is a preliminary step for inverse problems. All our examples of direct and inverse problems are solved within seconds in CPU time on a standard PC, which makes our proposed technique a great potential candidate for wide‐spread applications to other inverse problems. Copyright © 2004 John Wiley & Sons, Ltd.

This paper concerns the source scattering problems for acoustic wave propagation, which is governed by the two- or three-dimensional stochastic Helmholtz equation. As a source, the electric current density is assumed to be a random function driven by an additive colored noise. Given the random source, the direct problem is to determine the radiated random wave field. The inverse problem is to reconstruct statistical properties of the source from the boundary measurement of the radiated random wave field. In this work, we consider both the direct and inverse problems. We show that the direct problem has a unique mild solution via a constructive proof. Using the mild solution, we derive effective Fredholm integral equations for the inverse problem. A regularized Kaczmarz method is developed by adopting multifrequency scattering data to overcome the challenges of solving the ill-posed and large scale integral equations. Numerical experiments are presented to demonstrate the efficiency of the proposed method....

Modeling ore generation in a magmatic context

An on-line transient stability emergency control approach is proposed, which couples an open-loop and a closed-loop emergency control technique. The open-loop technique uses on-line transient stability assessment in order to adapt the settings of automatic system protection schemes to the current operating conditions. On the other hand, the closed-loop technique uses measurements in order to design and trigger countermeasures, after the contingency has actually happened, then to continue monitoring in a closed-loop fashion. The approach aims at combining advantages of event-based and measurement-based system protection schemes, namely, speed of action and robustness with respect to uncertainties in system modeling. It can also comply with economic criteria.

The paper presents a new approximate method of solving non-Fourier heat conduction problems. The approach described here is suitable for solving both direct and inverse problems. The way of generating Trefftz functions for non-Fourier heat conduction equation has been shown. Obtained functions have been used for solving direct and boundary inverse problems (identification of boundary condition). As a rule, inverse problems are ill-posed. Therefore, each method of solving these problems has to be checked according to disturbance of the input data. Presented examples confirm high usability of the presented approach for solving direct and inverse non-Fourier heat conduction problems.

The solution of direct and inverse transient heat conduction problems with layered materials using exponential basis functions

All known analytical solutions of the integral equation of the turbulent thermal boundary layer for a rotating disk have been obtained for the case of direct problem. This means finding the Nusselt number at a given distribution of the wall temperature. This distribution is described by power law and is monotone (derivative of wall temperature with respect to the radial coordinate does not change its sign). Outlined in this paper is an analytical form of non-monotone distribution of the wall temperature, which provided a new analytical solution for the turbulent Nusselt number including earlier known equations as a specific particular case. The solution is based on the integral method, which proved to be more precise than known Dorfman’s approach. Chosen for validation of the proposed method were turbulent heat transfer experiments of Northrop and Owen (1988). Predictions presented include analytical studies using inverse and direct problem solutions as well as numerical simulations using polynomial approximations of the experimental wall temperature distributions.

A model-based method has been developed for the performance simulation and conceptual design of rocket-type pulse detonation engines (PDEs). A reduced-order model (ROM) has been generated based on the high order singular value decomposition of a data tensor obtained from CFD computations. This ROM could be used to solve the direct (performance) and inverse (design) problems in the context of the early phases of pulse detonation engine design. Output performance parameters are predicted from prescribed input operation/geometry parameters in the direct problem, and vice versa in the inverse problem. The focus of this method is industrial application in situations where large parametric searches are to be performed with a reasonable level of fidelity at a low computational cost. It was found that the performance and conceptual design tool thus developed provides results that deviate, on average, by less than 10% from the CFD results. Regarding practical implementation, the method allows for shifting the heavier computational load off-line. In this way, when working on-line, the user can obtain results in less than a second for every single case. The main contribution of this study is showing that a model-based approach that combines CFD and tensor decomposition has the potential to extract a maximum of information from a given computational effort. This characteristic makes the method of interest for early design phases in the aerospace industry.

In this article, we study a class of direct and inverse coefficient problems defined for a nonlinear parabolic equation. An existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. Direct problem is solved numerically by using semi-implicit finite difference scheme and then some examples are presented related to steady-state solution of the nonlinear direct problem and ill-posedness of the inverse problem.

Consider the scattering of a time-harmonic electromagnetic plane wave by an arbitrarily shaped and filled cavity embedded in a perfect electrically conducting infinite ground plane. A method of symmetric coupling of finite element and boundary integral equations is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases. Given the incident field, the direct problem is to determine the field distribution from the known shape of the cavity; while the inverse problem is to determine the shape of the cavity from the measurement of the field on an artificial boundary enclosing the cavity. In this paper, both the direct and inverse scattering problems are discussed based on a symmetric coupling method. Variational formulations for the direct scattering problem are presented, existence and uniqueness of weak solutions are studied, and the domain derivatives of the field with respect to the cavity shape are derived. Uniqueness and local stability results are established in terms of the inverse problem.

The measurement, control, and validation of critical parameters in an electron beam sterilization facility

Determination of temperature wall functions for high Rayleigh number flows using asymptotics: A systematic approach

The closed-loop control of a turbulent round air jet is experimentally investigated based on two unsteady minijets, with a view to enhancing jet mixing. The two minijets are placed at diametrically opposite locations upstream of the nozzle exit. The open-loop control experiments are first performed. Given the mass flow rate ratio C m of the minijets to that of the main jet, the decay rate $$\overline{K}$$ of jet centerline mean velocity exhibits a maximum at the frequency ratio f e/f 0 ≈ 1.0, where f e and f 0 are the excitation frequency of minijets and the preferred mode frequency of the natural main jet, respectively. An extremum-seeking feedback control has been developed to achieve autonomously the optimal control performance. It has been found that, given C m, this closed-loop control technique may obtain automatically and rapidly the optimal value of f e and the desired or maximum $$\overline{K}$$ , as achieved in the open-loop control. This control technique is robust and adaptable when the Reynolds number and initial excitation frequency are changed separately. A flow-physics-based feedback control strategy has also been investigated, which could achieve the optimal control performance automatically with a shorter convergence time than the extremum-seeking control, not robust though.

One of the main merits offered by multiphase machines is their high fault-tolerant capability. Literature has demonstrated that the performance of multiphase induction machines under fault conditions is affected by the employed stator winding connection. In open-loop controlled five-phase machines, the star connection is favorable under healthy conditions while the pentagon connection is favorable and yields a lower derating factor under the open phase condition. In this paper, a new combined star/pentagon single layer winding layout that combines the advantages of both star and pentagon connections is proposed for a five-phase induction machine. Although the proposed winding is intrinsically an asymmetrical ten-phase machine, the proposed connection allows for only five-phase terminals. Moreover, the proposed winding not only yields better flux distribution compared to a conventional single layer winding, but also provides a complete cancellation of the third-order harmonic flux component caused by the induced third sequence currents due to the saturation effect and/or under unbalanced operation. Hence, the machine losses are decreased, which improves the overall machine efficiency. For the healthy case, the machine is similar to a conventional star connected five-phase machine. However, with one phase open, the proposed connection results in a lower derating factor compared to conventional connections for both open-loop and optimal current control techniques. A 1-kW prototype machine is used for experimental verification.

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing a transparent boundary condition. Given the incident field, the direct problem is to determine the displacement of the wave field from the known obstacle; the inverse problem is to determine the obstacle's surface from the measurement of the displacement on an artificial boundary enclosing the obstacle. In this paper, we consider both the direct and inverse problems. The direct problem is shown to have a unique weak solution by examining its variational formulation. The domain derivative is studied and a frequency continuation method is developed for the inverse problem. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.