No parts of this publication may be reproduced by any means, transmitted, or translated into machine language without the written permission of the author. Requests for permisson to reproduce parts of the book should be adressed directly to Professor Olav Egeland, Preface Modeling and simulation of dynamic processes are very important subjects in control systems design. Most processes that are encountered in practical controller design are very well described in the engineering literature, and it is important that the control engineer is able to take advantage of this information. It is a problem that several books must be used to get the relevant modeling information of a particular process, and it may take a long time to go through all the necessary material. The idea of this book is to supply the control engineer with a sufficient modeling background to design controllers for a wide range of processes. In addition, the book provides a good starting point for going into the specialist literature of different engineering disciplines. In this connection the references indicate where to start. The book also contains more material than what will normally be covered in the lectures of a typical course, so that students may return to the book at a later stage and find additional information about a particular subject. This will be more efficient than to extract the required information from a series of other books. In this sense the book will be of great value for practising control engineers. The development of new products and systems is often done in a team of experts with different backgrounds. It is hoped that this book will help control engineers to communicate with other experts in this type of team. To achieve this we have been careful to use standard terminology and notation from the different engineering disciplines in question. Here we deliberately break the tradition evident in many books in the control literature where the emphasis is on having a unified formulation specific to automatic control. The selection of the material is based on the experience of the authors in teaching and research at the Norwegian University of Science and Technology. In addition to this, material has been selected on the basis of extensive industrial activity through research programs between university and industry, and product development in industry. In this activity there has been close cooperation with experts from other disciplines, and this has given …

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Modeling and simulation for automatic control

https://www.ece.uvic.ca/~bctill/papers/numacoust/Tijdeman_1975.pdf

On the propagation of sound waves in cylindrical tubes

This paper reviews a number of unsteady friction models for transient pipe flow. Two distinct unsteady friction models, the Zielke and the Brunone models, are investigated in detail. The Zielke model, originally developed for transient laminar flow, has been selected to verify its effectiveness for "low Reynolds number" transient turbulent flow. The Brunone model combines local inertia and wall friction unsteadiness. This model is verified using the Vardy's analytically deduced shear decay coefficient C ∗ to predict the Brunone's friction coefficient k rather than use the traditional trial and error method for estimating k. The two unsteady friction models have been incorporated into the method of characteristics water hammer algorithm. Numerical results from the quasi-steady friction model and the Zielke and the Brunone unsteady friction models are compared with results of laboratory measurements for water hammer cases with laminar and low Reynolds number turbulent flows. Conclusions about the range of v...

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Developments in unsteady pipe flow friction modelling

It is shown that the two main parameters governing the propagation of sound waves in gases contained in rigid cylindrical tubes, are the shear wave number, s = R ρ s ω / μ , and the reduced frequency, k = ωR/a 0 . It appears possible to rewrite the most significant analytical solutions for the propagation constant, Γ, as given in the literature, as simple expressions in terms of these two parameters. With the aid of these expressions the various solutions are put in perspective and their ranges of applicability are indicated. It is demonstrated that most of the analytical solutions are dependent only on the shear wave number, s , and that they are covered completely by the solution obtained for the first time by Zwikker and Kosten (1949) . The full solution of the problem has been obtained by Kirchhoff (1868) in the form of a complicated, complex transcendental equation. In the present paper this equation is rewritten in terms of the mentioned basic parameters and brought in the attractive form F =0, which is solved numerically by using the Newton-Raphson procedure. As first estimate in this procedure the value ofaccording to the solution of Zwikker and Kosten is taken. Results are presented for a wide range of s and k values.

Transient turbulent friction in smooth pipe flows

The Effect of Viscous Shear on Transients in Liquid Lines

An analysis is made of the performance of narrow porous metal bearings (e.g., sintered bronze powder) which operate with a full film of lubricant. The configuration considered is that in which the bearings are pressed tightly into housings with their ends remaining open to the atmosphere. A solution for the lubricant pressure is obtained which satisfies Reynolds’ equation in the film and Laplace’s equation in the porous metal. Expressions are developed which give the Sommerfeld and Ocvirk numbers, attitude angle, and coefficient of friction as functions of eccentricity ratio, permeability parameter, and thickness-to-length ratio. The results are shown graphically for situations of practical importance.

Hydrodynamic Lubrication of Narrow Press-Fitted Porous Metal Bearings

The inlet region for laminar flow in porous pipes with small injection or suction is analyzed numerically. Finite difference methods are developed and solutions obtained for the equations of fluid motion with two different wall boundary conditions: constant injection or suction velocity through the wall, and velocity through the wall proportional to local pressure. Solutions are found for both uniform and parabolic axial velocity profiles at the pipe inlet. The results are found to be in good agreement with the solution of Weissberg for the conditions of constant suction velocity and a parabolic inlet velocity profile. Hydrodynamic entrance lengths are found and are compared for uniform and parabolic inlet profiles in the presence of constant injection or suction.

Laminar Entry Problem in Porous Tubes

Partial porous metal bearings performance during steady state operation with full film of lubricant, determining pressure distribution

W. T. Rouleau

Papers

The Effect of Viscous Shear on Transients in Liquid Lines

Hydrodynamic Lubrication of Narrow Press-Fitted Porous Metal Bearings

Laminar Entry Problem in Porous Tubes

Hydrodynamic Lubrication of Partial Porous Metal Bearings

A Note on the Lubrication of Porous Metal Bearings