Numerical modelling of hydraulic jumps in a spiral channel with rectangular cross section

Abstract

We present two ÿnite di erence methods for numerical modelling of nonstationary compressible uid ows in a spiral channel with rectangular cross section. One of these methods is an explicit TVD scheme. Another scheme uses splitting in terms of physical processes and an implicit approximation of the friction term. The implemented numerical methods serve not only for computation of the damping of pressure jumps and evaluation of pressure compensators in percussion-rotary drilling devices but are also of great methodical and practical importance for the treatment of such ow problems.

Vorticity cumulation in a rectangular tank with a sloping bottom after a sharp deceleration in rotation

“…At the same time, the structure of the flow is determined by the source terms (3.4)-(3.6). Therefore, in order to stabilize the numerical algorithm [12], we must approximate the friction force (3.4) and the Coriolis force (3.5) implicitly. In view of this, as in [13], we construct the difference scheme by the physical process splitting method [14] on a spaced uniform difference grid.…”

“…In view of this, as in [13], we construct the difference scheme by the physical process splitting method [14] on a spaced uniform difference grid. For calculating complex wave flows determined by source terms, this scheme is much more solvable [12] than various monotonic TVD schemes [15,16].…”

Numerical modelling of three-dimensional fluid flow in a spiral compensator

“…The percussion-rotary drilling technique was implemented in the hydraulic drilling hammers of several types (Pixton, 1990;Zhao, 1998). Following Schacht et al (2002), we now describe in detail the design and the functioning of a typical hydraulic drilling hammer and the spiral compensator. The hydraulic drilling hammer (Fig.…”

“…The mathematical modelling of time-dependent hydrodynamic processes in spiral compensators is of great practical importance for an optimal design of such pressure compensators. The hydrodynamic processes in a spiral compensator were modelled by Schacht et al (2002) on the basis of the equations of the model of an inviscid compressible barotropic fluid in the one-dimensional approximation. These equations were approximated by two different finite difference schemes: the scheme of splitting in terms of physical processes and a TVD scheme.…”

“…The one-dimensional formulation, however, does not enable the consideration of the curvature effects of the spiral compensator walls as well as the centrifugal forces. In this connection we propose below an extension of the mathematical model of fluid flow applied by Schacht et al (2002) for the case of a three-dimensional time-dependent compressible fluid flow in a spiral compensator.…”