The Mathematical Description of the Pseudoplastic Fluid Motion and Its Application
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The paper presents the derivation of a mathematical model of the movement of the working environment; the application of the compiled system of equations of motion of the working medium in a cylindrical coordinate system is shown. The validity and possibility of using a rotary rheometer to determine the rheological characteristics of liquids are mathematically proved. An equation is obtained for the moment of resistance during the movement of Newtonian and non-Newtonian fluids in a coaxially cylindrical developed measuring system, taking into account the rheological parameters of the fluid: “k” is measures of fluid consistency and «n» is characteristics of the degree of non-Newtonian behavior of the material. Verification of the obtained results on the example of two liquids is given, and the corresponding conclusions are drawn. The issues of phase transition in gas-liquid mixtures of adjustable chokes are considered. The criteria for the occurrence of cavitation and hydrate formation in liquid and gaseous media are presented. Equations are described that make it possible to determine the condition for a phase transition from a liquid to a gas-liquid state. The paper presents a modern method of protecting the design of an adjustable throttle from the cavitation phenomenon, which consists in the use of throttle cells or throttling stages. The result of using throttle cells is given. An example of the formation of hydrates in a gas-liquid mixture during its flow through an adjustable throttle is considered. The criterion and method for determining the conditions of hydrate formation in the flow channel of an adjustable throttle are given, which consists in constructing an operating curve of an adjustable throttle, an envelope curve and their intersection with the curve of hydrate formation of a gas-liquid mixture to determine the conditions and areas of hydrate formation. The paper gives an example of the use of a hydraulic communication channel for information transfer. The main mathematical dependences of the mathematical model of the hydraulic communication channel, boundary and initial conditions are given. The form of the pressure pulse is obtained, and one of the main methods of encoding information for a hydraulic communication channel is considered. The condition for ensuring the required purity class of the working fluid for hydraulic systems is determined. The scientific novelty of the work includes the relations obtained, which make it possible to study the hydrodynamics of a fluid with variable viscosity, predict and evaluate the values of the shear stress in the fluid during its movement, the shear strain rate, the moment of friction forces, etc., with known rheological characteristics of the fluid. In addition, the scientific novelty of the work is the formulated criteria for the conditions of the phase transition, as well as the provision of practical recommendations to specialists involved in the design and operation of adjustable chokes. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 “Hydraulic machines and hydropneumatic drives”.
The paper presents the derivation of a mathematical model of the movement of the working environment; the application of the compiled system of equations of motion of the working medium in a cylindrical coordinate system is shown. The validity and possibility of using a rotary rheometer to determine the rheological characteristics of liquids are mathematically proved. An equation is obtained for the moment of resistance during the movement of Newtonian and non-Newtonian fluids in a coaxially cylindrical developed measuring system, taking into account the rheological parameters of the fluid: “k” is measures of fluid consistency and «n» is characteristics of the degree of non-Newtonian behavior of the material. Verification of the obtained results on the example of two liquids is given, and the corresponding conclusions are drawn. The issues of phase transition in gas-liquid mixtures of adjustable chokes are considered. The criteria for the occurrence of cavitation and hydrate formation in liquid and gaseous media are presented. Equations are described that make it possible to determine the condition for a phase transition from a liquid to a gas-liquid state. The paper presents a modern method of protecting the design of an adjustable throttle from the cavitation phenomenon, which consists in the use of throttle cells or throttling stages. The result of using throttle cells is given. An example of the formation of hydrates in a gas-liquid mixture during its flow through an adjustable throttle is considered. The criterion and method for determining the conditions of hydrate formation in the flow channel of an adjustable throttle are given, which consists in constructing an operating curve of an adjustable throttle, an envelope curve and their intersection with the curve of hydrate formation of a gas-liquid mixture to determine the conditions and areas of hydrate formation. The paper gives an example of the use of a hydraulic communication channel for information transfer. The main mathematical dependences of the mathematical model of the hydraulic communication channel, boundary and initial conditions are given. The form of the pressure pulse is obtained, and one of the main methods of encoding information for a hydraulic communication channel is considered. The condition for ensuring the required purity class of the working fluid for hydraulic systems is determined. The scientific novelty of the work includes the relations obtained, which make it possible to study the hydrodynamics of a fluid with variable viscosity, predict and evaluate the values of the shear stress in the fluid during its movement, the shear strain rate, the moment of friction forces, etc., with known rheological characteristics of the fluid. In addition, the scientific novelty of the work is the formulated criteria for the conditions of the phase transition, as well as the provision of practical recommendations to specialists involved in the design and operation of adjustable chokes. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 “Hydraulic machines and hydropneumatic drives”.
The paper presents the derivation of a mathematical model of the movement of the working environment; the application of the compiled system of equations of motion of the working medium in a cylindrical coordinate system is shown. The validity and possibility of using a rotary rheometer to determine the rheological characteristics of liquids are mathematically proved. An equation is obtained for the moment of resistance during the movement of Newtonian and non-Newtonian fluids in a coaxially cylindrical developed measuring system, taking into account the rheological parameters of the fluid: “k” is measures of fluid consistency and «n» is characteristics of the degree of non-Newtonian behavior of the material. Verification of the obtained results on the example of two liquids is given, and the corresponding conclusions are drawn. The issues of phase transition in gas-liquid mixtures of adjustable chokes are considered. The criteria for the occurrence of cavitation and hydrate formation in liquid and gaseous media are presented. Equations are described that make it possible to determine the condition for a phase transition from a liquid to a gas-liquid state. The paper presents a modern method of protecting the design of an adjustable throttle from the cavitation phenomenon, which consists in the use of throttle cells or throttling stages. The result of using throttle cells is given. An example of the formation of hydrates in a gas-liquid mixture during its flow through an adjustable throttle is considered. The criterion and method for determining the conditions of hydrate formation in the flow channel of an adjustable throttle are given, which consists in constructing an operating curve of an adjustable throttle, an envelope curve and their intersection with the curve of hydrate formation of a gas-liquid mixture to determine the conditions and areas of hydrate formation. The paper gives an example of the use of a hydraulic communication channel for information transfer. The main mathematical dependences of the mathematical model of the hydraulic communication channel, boundary and initial conditions are given. The form of the pressure pulse is obtained, and one of the main methods of encoding information for a hydraulic communication channel is considered. The condition for ensuring the required purity class of the working fluid for hydraulic systems is determined. The scientific novelty of the work includes the relations obtained, which make it possible to study the hydrodynamics of a fluid with variable viscosity, predict and evaluate the values of the shear stress in the fluid during its movement, the shear strain rate, the moment of friction forces, etc., with known rheological characteristics of the fluid. In addition, the scientific novelty of the work is the formulated criteria for the conditions of the phase transition, as well as the provision of practical recommendations to specialists involved in the design and operation of adjustable chokes. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 “Hydraulic machines and hydropneumatic drives”.
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