Techniques of analysis for nonlinear transient flow in a pipe

Analytical solutions to the time-dependent, nonlinear equation governing incompressible, one dimensional flow in a pipe are presented. The flow is pressure-driven, and a valve on the pipe controls the flow rate. Power-law losses and an exponential closing action of a valve are assumed. Four differen...

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Bibliographic Details
Published in:International journal of mechanical sciences 2012, Vol.54 (1), p.182-189
Main Authors: Cai, Weihua, Sen, Mihir, Yang, K.T.
Format: Article
Language:English
Subjects:
Approximation
Exact sciences and technology
Flows in ducts, channels, nozzles, and conduits
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Homotopy analysis method
Incompressible flow
Mathematical analysis
One dimensional flow
Perturbation
Perturbation methods
Physics
Pipe
Pipe flow
Tuning
Valves
WKB method
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Summary:Analytical solutions to the time-dependent, nonlinear equation governing incompressible, one dimensional flow in a pipe are presented. The flow is pressure-driven, and a valve on the pipe controls the flow rate. Power-law losses and an exponential closing action of a valve are assumed. Four different approximation methods are used. Of these, perturbation and Adomian's decomposition are seen to be valid only for small time. The WKB approximation works only for a quadratic loss term. Homotopy analysis is broadly applicable but needs parameter tuning, optimal values of which have been determined. ► Analytical solutions time-dependent, nonlinear equation governing incompressible, one dimensional flow in pipe are presented. ► Four different approximation methods are used. ► Homotopy analysis is broadly applicable but needs parameter tuning.
ISSN:0020-7403
1879-2162
DOI:10.1016/j.ijmecsci.2011.10.008