Search

Introduction. The three-dimensional mathematical model of non-Newtonian fluid flow was introduced, with viscosity that depends of shear velocity in rectangular channels of food equipment. Materials and methods. Applying the method of superposition allows to build a field of longitudinal flow of non-Newtonian fluid in rectangular channel of technological equipment with moving borders and thus to define values of velocity and pressure at any point inside the channel. Results and discussion. We developed a model of longitudinal flow of non-Newtonian fluid in rectangular channels on borders of which different longitudinal velocities are set. The model is based on the solution of one-dimensional problem of the Couette flow in the channel. The composition of flows in the slit channels with mutually perpendicular pair of borders allows to receive a flow rate formula which satisfies the principle of limit correspondence between the currents in a rectangular and slit channels. We suggest a method of construction of the velocity field which is a subdivision of the final section of the channel into sections with a different dependence on the coordinates so that in some areas the velocity depends only on a single coordinate, while in others -- only on the other coordinate. We obtain the equations of lines delimiting these areas, and how to determine the shape of boundaries. Conclusion. The analytical formulas allow defining macrokinetic characteristics of each channel at the boundary with arbitrary distribution of velocities of the flow of non-Newtonian fluid the viscosity of which depends on the shear speed. [ABSTRACT FROM AUTHOR]

Introduction. Current paper introduces the method for defining hydraulic losses during coolants flow in conduits and channels of heat exchangers of food production equipment. The viscosity of these coolants has a power dependency on shifting velocity. Materials and methods. The power-law fluid were taken into consideration as a special case of silicone fluids. The method for determining hydraulic developed is obtained based on the method of analogies which consists of: analyzing how local resistances and friction resistances depend on Reynolds number of Newtonian fluid; changing the real Reynolds number for Newtonian fluid to Reynolds number for power-law fluid; and thus obtaining analytical formulas. These formulas allow to define hydraulic resistances during contraction and expansion of the channel and to define local resistances during flow of power-law fluids. Results and discussion. In order to construct expressions for defining local resistances during power-law fluids flow in stepped channel and in a turn (which are the most prevalent in technological equipment) the origins of Newtonian fluid flow in channels with the same hydraulic resistance were analyzed. Using the known expressions with the aid of method of analogy, the formulas for describing the hydraulic resistance during contraction and expansion of the channel were constructed. These formulas are represented as a sum of values, which are associated with acceleration or deceleration, contraction or expansion and turning of the flow. Using the principle of analogy for different cases of Reynolds formula, the formulas for defining the local resistances of power-law fluids were obtained. Conclusion. Obtained expressions can be used to determine coefficients of local resistances during power-law fluids flow. They are equally applicable in a wide range of Reynolds number, which allows to carry out an entirely new design of technological equipment for food industry in the direction of reducing energy consumption and material cost. [ABSTRACT FROM AUTHOR]

Introduction. The problems of simulating viscoplastic longitudinal and cross-sectional flow of non-Newtonian fluids are overviewed. Materials and methods. For the first time the superposition method by expressing the components of the stress tensor for building flow fields with higher dimension from flow fields with lower dimension with various boundary conditions when rheological parameters change depending on pressure was used. The flows in the channel are categorized by velocity and pressure values in each point of the section. Results. The theoretical methods for simulating flows of non-Newtonian fluids in channels of different geometry with moving bounds and pressure drop on channel edges with respect to functional connections between main process parameters are described using the superposition method. It is shown that longitudinal and cross-sectional are reduced to the collection of one-dimensional longitudinal flows of the same type which allow to describe three-dimensional isothermal in rectangular channel and two-dimensional flows in flat channels with different channel aspect ratio. The received theoretical two- and three-dimensional model of viscous flows in channels with basic geometry allow to research main regularities of the process and to establish optimal macro-kinetic and macro-dynamic flow characteristics of non-Newtonian materials which are aimed at reducing energy costs and material consumption of food processing equipment. Conclusion. The developed and theoretically reasonable three-dimensional models flows of non-Newtonian fluids in channels allow to perform qualitatively new design of food processing equipment which allows to reduce energy costs and material consumption. [ABSTRACT FROM AUTHOR]