Finite state induced flow models. I - Two-dimensional thin airfoil

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

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The Influence of Real Gas Radiation On the Stability and Development of Benard Convection in a Two-Dimensional Layer

Journal of Heat Transfer ◽

10.1115/1.4051499 ◽

2021 ◽

Author(s):

Brent W. Webb ◽

Vladimir Solovjov

Keyword(s):

Rayleigh Number ◽

Critical Rayleigh Number ◽

Radiative Heating ◽

Two Dimensional ◽

Gas Temperature ◽

Layer Depth ◽

Real Gas ◽

Gas Radiation ◽

Induced Flow ◽

Buoyancy Induced Flow

Abstract The influence of real gas radiation on the thermal and hydrodynamic stability is investigated in a two-dimensional layer of radiatively participating H2O and/or CO2 heated from below. The non-gray radiation effects of the two species are treated rigorously using a global spectral approach, the Spectral Line Weighted-sum-of-gray-gases model. The phenomena are explored by solving the full coupled laminar equations of motion, energy, and radiative transfer from the low-Rayleigh number, pure conduction-radiation regime through the onset of buoyancy-induced flow to the developed Bénard convection regime. The evolution of the thermal, velocity, and radiative heating fields is studied, and the critical Rayleigh number is characterized as a function of species mole fraction, average layer gas temperature, layer depth, wall emissivity, and the total gas pressure. It is found that participating radiation in the medium has the effect of stabilizing the layer, delaying transition to buoyancy-induced flow. The development of buoyancy-induced flow and temperature, along with the radiative heating are presented. It is found that the critical Rayleigh number in the radiatively participating gas layer can be more than an order of magnitude higher than the classical convection-only scenario. The onset of instability is found to depend on the species mole fractions, average gas temperature in the layer, wall emissivity, layer depth, and total pressure. Generally, all other variables being the same, H2O has a greater stabilizing influence on the layer than CO2.

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The Application of a Two-Dimensional Zone Model to the Design and Control of a Continuously Operated, Gas-Fired Furnace

Energy Conversion ◽

10.1115/imece2002-39297 ◽

2002 ◽

Cited By ~ 2

Author(s):

Sara A. C. Correia ◽

John Ward

Keyword(s):

Dynamics Simulation ◽

Relative Mass ◽

Zone Model ◽

Two Dimensional ◽

Furnace Design ◽

Simplified Approach ◽

Flow Models ◽

Discharge Temperature ◽

Wide Range ◽

And Control

This paper describes the development of a two-dimensional zone model to predict the throughput and thermal performance of a continuously operated gas-fired furnace heating steel bars to a nominal discharge temperature of 1250°C. Ultimately the model is intended to be a tool which can be used for the design and control of industrial furnaces. Consequently relatively short computing times are necessary and this was achieved by employing an isothermal computational fluid dynamics simulation to estimate the relative mass flows, and hence enthalpy flows to or from adjacent volume zones in the overall model. This simplified approach, which utilises a single “once off” isothermal computation of the flows, was considered to be adequate since isothermal flow models have been used successfully in the past to study the flow related behaviour of combustion systems. The coupling of a multi-zone model with a single “once off” isothermal computation of the flows enables a wide range of furnace design modifications to be studied quickly and easily. To illustrate the potential use of the model in a furnace design application, it was then used to investigate the effects of inclining the burners downwards towards the load as well as those associated with increasing the length of the furnace.

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Preface

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001497000676 ◽

1997 ◽

Vol 11 (07) ◽

pp. 1023-1024

Author(s):

Serge Miguet ◽

Annick Montanvert ◽

P. S. P. Wang

Keyword(s):

Finite State Machine ◽

Finite Automata ◽

Upper Bounds ◽

Two Dimensional ◽

Turing Machines ◽

Closure Properties ◽

Working Space ◽

Finite State ◽

The Individual ◽

Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

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A Review of Nonsteady Flow Models for Compressor Stability

Journal of Turbomachinery ◽

10.1115/1.2928354 ◽

1994 ◽

Vol 116 (2) ◽

pp. 202-215 ◽

Cited By ~ 59

Author(s):

J. P. Longley

Keyword(s):

Fluid Dynamics ◽

Flow Field ◽

Rotating Stall ◽

Time Development ◽

Mathematical Treatment ◽

Two Dimensional ◽

Nonsteady Flow ◽

Physical Processes ◽

Flow Models ◽

Modeling Techniques

This paper presents a review of the different approaches to modeling the nonsteady fluid dynamics associated with two-dimensional compressor flow fields. These models are used to predict the time development of flow field disturbances and have been found useful in both the study of rotating stall and the development of active control. The opportunity to digest the earlier investigations has now made it possible to express the modeling ideas using only a very simple mathematical treatment. Here, the emphasis is on the underlying physical processes that the models simulate and how the assumptions within the models affect predictions. The purpose of this work is to produce, in a single document, a description of compressor modeling techniques, so that prospective users can assess which model is the most suitable for their application.

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