Wave speed calculation for water hammer analysis
DOI:
https://doi.org/10.4067/S0718-28132016000200007Keywords:
wave speed, water hammer, Courant numberAbstract
In order to accurately solve the water hammer problem using the Method of the Characteristics MOC is necessary to fulfil with the so-called Courant condition which establishes mandatorily that Cn = f(a) = 1 in each pipeline of the system, where a is the wave speed. The value of Cn is dependant of a whose value depends in turn on the fluid properties (density, bulk modulus) and physical characteristics of each pipeline (elasticity modulus, diameter, wall thickness, supporting condition). Because water distribution systems usually has many different pipes, and therefore, many different wave speeds, it can be said that fulfil with Cn = 1 in each pipeline is a very difficult task, more when the solution by MOC needs a common time step At for all pipe sections of the system. A way of solution to this problem is applying the method of the wave-speed adjustment that involves modifying the value of a in each pipe section in a certain percentage up to obtain Cn = 1. With this procedure optimum results are guaranteed in numerical terms, but it is possible to say the same in physical terms? The question which arises is: what parameters within the formula of a must (or can) be changed without exceeding the characteristic values of the component material of the pipes?. This work shows that in some cases the wave speed modification can significantly alter the value of the parameters that define a, leading to values that can be physically inconsistent, fictitious or without practical application.
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