Boundary between elastic and inelastic models in hydraulic transients analysis with entrapped air pockets
In contrast with the beneficial effects of dispersed air, large pockets of entrapped air can be a source of severe transients. The importance of these unexpected large pressures, justifies from a practical point of view, the interest devoted to the subject by many researchers.
The standard situation investigated can be resumed as follow: a confined pocket of air is trapped in a pipe between a dead end and a source which provide sufficient energy to cause the acceleration of the liquid column and the compression of the air pocket.
If we can use rigid column theory instead of the elastic theory the saving in computational effort is very important; the difficulty, in our view, is how decide which one methodology must be used. The answer is not straightforward and, in general, the question of quantifying the boundary between the validity of rigid and elastic models will depend on each particular hydraulic system being the main goal of this paper to establish a criterium to know where this boundary is located.
As there is not analytic solutions to the general problem using rigid column theory (numerical methods are the only available technique) a simplified preliminary analysis of the rigid model is proposed for the frictionless case. This approach permits to obtain close expressions for maximum head and for the period and maximum velocity of small oscillations. The complete rigid model is later used to ‘generalize’ the previous equations and checking how sensitive the results are with the variation of some parameters - index of compression, valve opening time, friction factor -. It is also analyzed when the assumption of a fixed length of the liquid column has a more relevant influence on the results.
In order to compare rigid and elastic models for different cases, a brief review of this last methodology is described, taking into account the variation of the liquid length.
Finally from an adequate physical characterization of rigid column theory, and after comparing different results coming from both methodologies, a general boundary between both theories is proposed.