MODELING OF THE VISCOPLASTIC FLOW OF A BINGAM FLUID WITH TRANSVERSE CIRCULATION IN A RECTANGULAR CHANNEL OF A WORM MACHINE
DOI:
https://doi.org/10.15421/081921Keywords:
Bingham fluid, flow, circulation, model, channel, worm machine.Abstract
Introduction. We proposed a mathematical description of the flow of a Bingham fluid with transverse circulation in a rectangular channel of a worm machine. Materials and methods. As a material, we chose Bingham fluids with two constant parameters - viscosity and fluidity thresholds. We overviewed the influence of the transverse circulation on such characteristics of the visco-plastic flow as the size of the solid core, velocity of the core and flow rate. The flow in a rectangular channel is formed as a result of superposition of flows in two plane channels which are crossed at right angles. Results. During the simulation of the three-dimensional flow of Bingham fluid in the channel of a rectangular cross-section with transverse circulation, two basic elements are applied. The first one consists of dividing the rectangle into a solid core and four rectangular sections of the viscous flow. The second element is that the viscous flow in each of the plots is two-dimensional, that is, longitudinal and transverse, but depends on one coordinate. This means that such flows are equivalent to flows with transverse circulation in a flat channel, the core of the flow of the Bingham fluid has a rectangle at the intersection. This approach allows to calculate all the basic characteristics of a complex three-dimensional flow in the explicit analytical form and analyze its dependence on the boundary conditions, taking into account the influence of all eight longitudinal and transverse conditions, with any possible distribution on the boundaries of the channel. We proposed the calculation formulas for determining the velocity of the core of the current, flow rates, and the values of dissipation energy in a symmetric form with respect to the coordinates. Conclusion. The mathematical description of the longitudinal flow of a Bingham fluid with transverse circulation in a rectangular channel of a worm machine allows for the simulation of various flows of visco-plastic liquids and to determine the macro-kinetic characteristics at each point of the channel.References
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