Abstract
Aim: The purpose of this research is to examine overhead movements of inclined hydraulic streams of foam and with the aid of a mathematical model illustrate the mutual interaction of mechanical foam streams with variations of expanded foam.
Methodology: Calculations are based on differential equations for material movement points with due regard to environmental resistance. With this in mind, the movement of inclined foam streams was described by means of dynamic equations for two or more propelled material bodies which are linked by forces. Wherein the overhead location of bodies, in the time interval t, is described by two co-ordinates: x = x(t) and y = y(t). Based on an analysis of literature, it was established that an adequate mathematical description is provided by a quadratic function of the resistance force generated by the stream to its friction with air. It was also accepted that dependence of interacting forces between streams and their velocity difference will be described by a quadratic function.
Results: Initially a model was identified, which revealed the delivery process of a medium-expansion foam jet with the use of two streams of low-expansion foam. Additionally, a model with an optimal configuration of the stream system was identified and a description provided, dealing with the influence of wind on the trajectory of a combined jet. The most effective model turned out to be the one where the low-expansion foam stream is located in the lower position. However, with four such streams there is an overall decrease of expanded foam in the resulting jet and an increase in the consumption of foaming agent. For this reason the authors performed comparative calculations for variations with the location of a lesser number of foam streams. This included the use of three and two streams of low-expansion foam. It was found that a link of three streams of low-expansion foam, instead of four, leads to a reduction in the jet range by only 3% (0.7m), but overall, significantly improves the quality of foaming in the combined jet. A further reduction of streams (to two) results in a noticeable decrease to the range of effectiveness (5.3%, 1.1m) and does not improve the quality of foaming in the combined jet. In this way, taking account of the influence of low-expansion foam streams on the overall foaming quality, the most logical approach is to use of the third variant of the combination - three streams of low-expansion foam, supporting at the base,an encircled jet generating middle-expansion foam.
Conclusions: During research, tests were performed on the mutual influence of mechanical foam streams with variations of expanded foam. On the basis of experiments, an optimal location of foam streams was specified, which allows the attainment of maximum results (range) in the distribution of foam with minimal losses. Results from tests may be utilised in the future for the development of an experimental foam generating model.
Keywords: inclined hydraulic stream, mathematical model, mechanical foam, equation, optimal construction scheme, multiple foaming, foam delivery range
Type of article: short scientific report