Mathematical Models of Throttle Elements of Gas-hydrodynamic Measuring Transducers

Abstract

This is a review article and it presents the flowrate characteristics of throttle elements used for measuring diagrams of transducers of fluids parameters. The review includes a wide range of research on the characteristics of incompressible and compressible fluids, Newtonian and Non-Newtonian fluids at the conditions of laminar, transient and turbulent flow through the channels of different cross-sections. The article considers equations for macroscopic flows. The theoretical equations for calculating the pressure drop for fluid flow in microchannels are presented. The conditions and the range of their application are presented for these equations. The results of experimental research of friction factor for compressible and incompressible fluids in microchannels of various sizes and shapes with smooth and rough surfaces are considered. The obtained results can be used for computer research of static and metrological characteristics of gas-hydrodynamic measuring transducers of specific physical and mechanical parameters of fluids.

Modeling throttle bridge measuring transducers of physical-mechanical parameters of Newtonian fluids

“…The mathematical model of each throttle is determined by its type, design, and working conditions in the diagram. Such a model is a flowrate characteristic of the throttle: the dependence between flowrate and pressure drop on the throttle element while the fluid is flowing [13]. Usually, laminar and turbulent throttle elements are used in hydrodynamic transducers.…”

Resources for structural optimization of gas-hydrodynamic measuring transducers

“…It follows from expressions (4), (5), and (6) that there are two variants of second order diagrams, five different variants of third order diagrams, and fifteen different variants of fourth order diagrams (each subset included in the sets D 2 , D 3 and D 4 describes a specific diagram structure). Substituting a given set of primary elements D 1 into the equations ( 4), (5), or (6) and performing the corresponding operations of direct and indirect products of subsets, we find structures for all possible diagrams of the second, the third, or the fourth order, respectively.…”

“…It follows from expressions (4), (5), and (6) that there are two variants of second order diagrams, five different variants of third order diagrams, and fifteen different variants of fourth order diagrams (each subset included in the sets D 2 , D 3 and D 4 describes a specific diagram structure). Substituting a given set of primary elements D 1 into the equations ( 4), (5), or (6) and performing the corresponding operations of direct and indirect products of subsets, we find structures for all possible diagrams of the second, the third, or the fourth order, respectively. For example, for the simplest case, when D 1 =d (we use a throttle d as a primary element) we obtain the following diagram structures: Similar to the expressions ( 7)-( 9), one can describe sets of diagrams of higher orders using a set of primary elements and obtain the descriptions of structures of all possible diagrams.…”

“…In turbulent throttles, the fluid flow is characterized by the layers mixing, speed, and pressure pulsation. Local resistances cause pressure losses at the inlet and the outlet of the throttle [5].…”

“…where Q is the mass flow rate of the fluid through the throttle; P in and P out are the absolute pressures of the fluid at the inlet and the outlet of the throttle, respectively; B c , B p and B e are the constructive, parametric and empirical complexes, respectively, which depend on the throttle design, the parameters of the fluid, and empirical coefficients that take into account the reality of the fluid and thermodynamic processes in the throttle element. Flow rate characteristics of different types of throttles are discussed in detail in [5].…”