A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielke's (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.

A characteristics model of transient friction in pipes

The sections in this article are:


1
Modeling the Respiratory System as a Linear System
1.1
Models

1.2
Elemental Equations

1.3
Sinusoidal Forcing and Complex Impedance

1.4
Continuity and Compatibility Conditions

1.5
General Formulation of System Models

1.6
System Functions

1.7
Equivalent Circuits

1.8
Distributed-Parameter Models




2
History

3
Experimental Methods
3.1
Equipment

3.2
Inputs and Data Processing

3.3
Upper Airway Variability and Shunt




4
Frequency Responses Below 100 HZ
4.1
Total Respiratory System

4.2
Input Impedance Forcing at the Airway Opening

4.3
Transfer Impedance Forcing at the Chest

4.4
Transfer Impedance Forcing at the Mouth

4.5
Pressure and Flow Transfer Functions

4.6
Lung Impedance

4.7
Chest Wall Impedance

4.8
Airway Impedance




5
Frequency Responses Above 100 HZ
5.1
Wave Propagation in the Airways

5.2
Input Impedance Forcing at the Airway Opening

5.3
Pressure Transfer Functions

5.4
Airway Area by Acoustic Reflections




6
Clinical Applications
6.1
Pulmonary Function in Children

6.2
Obstructive Lung Diseases

6.3
Restrictive Lung Diseases

6.4
Miscellaneous Lung Diseases

Oscillation Mechanics of the Respiratory System

A critical review on pulsatile pipe flow studies directing towards future research topics

In this paper, basic unsteady flow types and transient event types are categorized, and then unsteady friction models are tested for each type of transient event. One important feature of any unsteady friction model is its ability to correctly model frictional dissipation in unsteady flow conditions under a wide a range of possible transient event types. This is of importance to the simulation of transients in pipe networks or pipelines with various devices in which a complex series of unsteady flow types are common. Two common one-dimensional unsteady friction models are considered, namely, the constant coefficient instantaneous acceleration-based model and the convolution-based model. The modified instantaneous acceleration-based model, although an improvement, is shown to fail for certain transient event types. Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model. The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.

/pdf/systematic-evaluation-of-one-dimensional-unsteady-friction-4hr9bu7wus.pdf

Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines

This paper presents a hierarchical classification of linear, distributed parameter models which have been used in the study of rigid, uniform fluid transmission lines. The development of the models from the fundamental equations of fluid dynamics is discussed, and the assumptions necessary in obtaining each model are shown. The solutions to the models are presented in general Laplace forms, and the terms that appear in the solutions are discussed with reference to the initial and subsequent assumptions. The existence of seven distinct forms of models was identified and verified by comparison with a vast number of apparently different models quoted in over three hundred research papers covering various engineering, medical, and biological applications. Significant contributions by various researchers over the last eighty years to the development of distributed parameter models of fluid transmission lines are reviewed. The application of the various models based upon comparisons made in the literature is de...

R. P. Shah

Papers

Small-Amplitude Frequency Behavior of Fluid Lines With Turbulent Flow