scholarly journals An efficient steady-state analysis of the eddy current problem using a parallel-in-time algorithm

2019 ◽  
Author(s):  
I. Kulchytska-Ruchka ◽  
H. De Gersem ◽  
S. Schöps
Keyword(s):  
Steady State ◽  
Eddy Current ◽  
Current Problem ◽  
Time Algorithm ◽  
Steady State Analysis ◽  
Eddy Current Problem ◽  
State Analysis

scholarly journals Simulating induction heating processes using harmonic balance FEM

2019 ◽  
Vol 38 (5) ◽  
pp. 1562-1574
Author(s):  
Klaus Roppert ◽  
Florian Toth ◽  
Manfred Kaltenbacher
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Induction Heating ◽  
Eddy Current ◽  
Current Problem ◽  
Heating Process ◽  
Solution Strategy ◽  
Content Type ◽  
Good Convergence ◽  
Eddy Current Problem

Purpose The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role. Design/methodology/approach To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity. Findings The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics. Originality/value Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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