Problem of hydrocannon nozzle form optimization for maximizing the force pulse of the ultrajet

Pulsed high-pressure liquid jets can destroy the rock of any hardness. The use of ultrajets can accelerate the dissociation of rocks and hasten the construction of buildings. However, due to the low reliability of hydraulic pulse equipment, the commercial use of pulsed jets is currently limited. It is possible to increase the reliability and efficiency of the hydrocannon by optimizing the design. Therefore, the article examines a direct extreme approach aimed at the piston hydrocannon nozzle form optimization in order to achieve the maximum average force of the jet on the barrier. The form of the nozzle (cross-sectional area) is present in the equations as a spatial derivative. The function of the derivative is chosen as a control, which makes it possible to exclude errors in numerical differentiation. Direct extreme approach involves iterative maximization of the functional by extremal methods based on the gradient. An analytical expression for the gradient as a function of the nozzle length and a necessary nozzle form optimality condition are obtained. The gradient is a function of spatial variables, which makes the optimization problem infinite-dimensional. The value of the gradient is determined by the solution of the conjugate problem. The gradient indicates the direction of maximizing the target functional, which can be used in infinite-dimensional extreme optimization algorithms. The criterion for achieving the optimal nozzle form is the fulfilment of the required condition with the best possible accuracy.

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