Basic Equations Of Fluid Mechanics Research Articles

Novel Calculation Method for Windage Power Loss of Double-Helical Gear Transmission

Abstract This paper presents a novel fast calculation method for windage power loss (WPL) of the meshing double-helical gear pair. Firstly, based on the basic equations of fluid mechanics and computational fluid dynamics simulation method, the calculation method for single-tooth windage torque at the zone of meshing/nonmeshing is established; Secondly, the WPL of meshing gear pair with different gear parameters and operating conditions are obtained according to the single-tooth windage torque during a rotation period and the windage torque at the end faces, and the accuracy of the proposed WPL method is verified through the WPL test measurement and simulation; Finally, the effect of gear parameters and operating conditions on the WPL is studied.

Обоснование параметров и создание высокоэкономичных вентиляторных установок аппаратов воздушного охлаждения

Introduction. Sustainable development of regions with high subsoil use demands performance improvement in gas cooling at compressor stations of main gas pipelines and environmental safety. Low energy prices specified the design parameters of gas transmission units throughout the boost of the gas industry. Therefore, the crucial task is to enhance the economic efficiency of main gas pipelines. One of the most energy-intensive units here is the cooling system of transported gas, which enables the reduction in operating costs. Gas air-cooling units used for cooling transported gas flow have spread significantly being notable for their increased energy output. Simulation methods of fan system parameters in gas air cooling units are assuming great importance in a rapidly globalizing world depending on their specific speed. Research objective. This study aims to develop a simulation model and guidelines on the construction of fans with high specific speed comparable cost-effectively to industrial fans. To support business objectives it is essential to specify the principles of cost-efficiency variation from that of specific speed, the influence of geometric and kinematic parameters, to conduct an experimental investigation to verify the results. Materials and methods. The research was based on a hypothesis for the consistency of the ratio between the pressure loss in a fan and the specific energy of transferrable air. Aerodynamic efficiency was accepted as a criterion for a fan local efficiency in order to determine the dependency of fan cost-effectiveness against its specific speed. Basic equations of fluid mechanics and theory of optimization were used as research mathematical tools. Results and discussion. In this study, we have established the influence pattern of the structural elements of a fan air duct and its geometrical parameters on the efficiency over a wide range of alterations of specific speed. We have obtained a mathematical model of correlation between geometrical and kinematic parameters of fans and their cost-effectiveness in a function of specific speed and residual flow swirl. The study has proved that it is essential to improve the aerodynamic quality of impeller airfoils and reduce the aerodynamic drag of air duct elements with the increase in specific speed of fans to extend their cost-effectiveness. Conclusion. The research described in this paper confirms the commercial importance of utilizing fans in air-cooling units according to aerodynamic configurations with a single wheel “K” and high specific speed ny ≥400, as far as they provide the highest possible aerodynamic efficiency at minimum weight dimension characteristics. The paper shows the capability of designing aerodynamic configurations of fan units of high specific speed ny ≥ 400 with the efficiency ≥ 0,85 where ԑy ≤ 0,2 achieves aerodynamic efficiency of impeller sections К ≥ 25. It has been established that the optimal region of theoretical pressure coefficient of fan units with a specific speed 380≤ny≤450 is located in the range 0,02<ΨТ <0,08. We have determined that when the aerodynamic drag coefficient of an air duct of a fan unit is equal to ԑy ≥ 1,2, its efficiency declines by more than 25 percent relative to ԑy ≤ 0,1. The authors have designed an aerodynamic scheme and produced an industrial prototype of a fan unit OGM VU 2.7-1.2 K3 with OV- 121TOH airfoils.

具有水平流动的对流斑图成长和动力学特性

The growth and dynamic characteristics of convection patterns with horizontal flow for Prandtl number Pr=0.72 were numerically simulated with 2D basic equations of fluid mechanics. The results show that, for given relative Rayleigh number Ra_r=5(Rayleigh number Ra=8 540) and Reynolds number Re=22.5, the growth of the traveling wave convection pattern can be divided into 3 stages: the convection development stage, the exponential growth stage and the periodic variation stage (including the transition adaptation region and the stable periodic variation region). The average wave number in the traveling wave convection decreases with time or with the growth of the convection pattern. The exponential growth stage length in traveling wave convection becomes shorter and the growth rate of the maximum vertical velocity of convection increases with relative Rayleigh number Ra_r.For Reynolds number Re=5,the growth rate of the maximum vertical velocity of convection relates with the variation of relative Rayleigh number Ra_r in the form of γ_m=0.004 8Ra^{6.065 3}_r.In the periodic variation stage, after the transition adaptation region of the convection pattern and parameters in traveling wave convection, the convection enters the stable periodic variation region of the convection pattern and parameters. For given relative Rayleigh number Ra_r=5,dimensionless period T_t of traveling wave convection varying with Re can be expressed as T_t=0.001 4Re^{2.363 5}.

Diagnostic one-stop-shop in suspected coronary artery disease gets closer. Coronary computed tomography angiography based fractional flow reserve.

Diagnostic one-stop-shop in suspected coronary artery disease gets closer. Coronary computed tomography angiography based fractional flow reserve.

Theory of ice-skating

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).

Theoretical derivation of the conservation equations for single phase flow in porous media: a continuum approach

This paper deals with the theoretical derivation of the conservation equations for single phase flow in a porous medium. The derivation is obtained within the framework of the continuum mechanics and classical thermodynamics. The adopted procedure provides the conservation equations of mass, momentum, mechanical energy, total energy, internal energy, entropy, temperature, enthalpy, Gibbs free energy and Helmholtz free energy. The obtained results highlight the connection between the basic equations of fluid mechanics and of fluid flow in porous media, as well as the restrictions and the limitations of Darcy’s law and Richards’ equation.

Distinctive flow properties of liquid jet generated by EHD pump and conical nozzle

AbstractThe electrohydrodynamic liquid jets induced by the mechanism which is referred to as pure conduction pumping were investigated in isothermal weakly conducting liquids, HFC43‐10 and HCFC123. The properties of the liquid jets (flow velocity, pumping pressure, and flow pattern) were examined by using grounded electrodes of four different types opposite a pseudo‐doughnut electrode under an applied DC voltage. These electrode systems gave rise to a powerful liquid jet, but in the working liquids used here, there was an effect of the voltage polarity on the flow direction. In order to create a more effective liquid jet with high directivity, a special nozzle (referred to as a conical nozzle in this paper) was used together with the electrode system. This nozzle can produce a distinctive pattern (spiral structure) of jets emerging from the outlet of the nozzle. In this paper, the spiral structure of the liquid jets has been analyzed using the basic equations of fluid mechanics. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 154(1): 9–19, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20133

Numerical calculation of shapes and detachment times of bubbles generated from a sieve plate

A mathematical model describing the formation, breakage and rising of a gas bubble generated in a submerged orifice is proposed. The model considers an axisymmetric bubble based on a finite-difference formulation. The model can predict detachment of the bubble from the plate as a result of the predictive equations. Bubble shapes and detachment times obtained theoretically are compared with images of experimental bubbles obtained using high-speed video technology, finding good agreement between both. A theoretical description of the different stages of bubble formation and rising supported on the basic equations of fluid mechanics is the first step in the development of an accurate mass transfer correlation for devices where bubbles are generated in sieve plates.

EHDポンプと円錐ノズルによる液体ジェットの特徴的な流動特性

The electrohydrodynamic liquid jets induced by the mechanism which is referred to as pure conduction pumping were investigated in isothermal weakly conducting liquids, HFC43-10 and HCFC123. The properties of the liquid jets (flow velocity, pumping pressure, and flow pattern) were examined by using grounded electrodes of four different types opposite a pseudo-doughnut electrode under an applied DC voltage. These electrode systems gave rise to a powerful liquid jet, but in the working liquids used here, there was an effect of the voltage polarity on the flow direction. In order to create a more effective liquid jet with high directivity, a special nozzle (referred to as a conical nozzle in this paper) was used together with the electrode system. This nozzle can produce a distinctive pattern (spiral structure) of jets emerging from the outlet of the nozzle. In this paper, the spiral structure of the liquid jets has been analyzed using the basic equations of fluid mechanics. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 154(1): 9–19, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20133

Numerical weather prediction

This overview describes a brief history of the numerical weather prediction proposed by L.F. Richardson in 1922. He had a dream of forecasting weather based on time integration of basic equations of fluid mechanics that express the atmospheric circulation. However, his idea was not successful at that time, because he had neither enough meteorological data for initial condition nor a high-speed computer for numerical calculation. It was after World War II that his dream has come true owing to incredible development of electronic computers and increase of upper-air sounding data. Today, most meteorological offices in the world predict weather based on numerical simulations of the global atmospheric circulation. The numerical model used in Japan consists of three models: a meso-scale model which covers the region of East Asia with horizontal resolution of 10 km is nested in a regional model with 20 km resolution which is nested in a global model with 50 km resolution. The short-term forecast is based on a single calculation with the best initial condition, but 1 month forecast is based on statistics of 26 different simulations with slightly different initial conditions (ensemble forecast).

Thermodynamic aspects of thermoacoustic theory

The study of thermoacoustic phenomena has a long history, and a fluid mechanics description of them has been developed in this century. Thermodynamic aspects of the thermoacoustic theory are discussed in this paper. Work flux, heat flux and energy conversion are introduced. Two thermodynamic media (a solid and an oscillating fluid) are regarded as catalysts for the heat flow and energy conversion. Three basic equations of fluid mechanics in Lagrange's frame are linearized in terms of three oscillating variables, namely pressure, entropy and displacement or velocity of the fluid element. The energy conversion is shown to consist of viscous dissipation of kinetic energy and the trajectory area in the temperature-entropy space. The entropy oscillation is discussed using the general equation of heat transport and the second law of thermodynamics. Finally the heat flux and energy conversion are expressed in terms of oscillating pressure and displacement or velocity. Transverse inhomogeneity of oscillating entropy or temperature, including phase lag, results in standing components of energy conversion W stand and heat flux Q stand, in addition to the pressure induced dissipation W P and displacement enhanced heat conduction Q D .

Hierarchial structure theory for basic equations of fluid mechanics (BEFM) and the simplified Navier-Stokes equations (SNSE)

A hierarchial structure for the basic equations of fluid mechanics (BEFM) is found through the analysis of scales of length and time that proves a measure of the rate of change of the quantities describing the motion of the fluid as well as an estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure theory shows that if (1) the characteristic Reynolds numbersRe is larger than unity and (2) the length scale in one coordinate direction is larger than that in other coordinate directions. BEFM can be classified into some levels according to the estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure of BEFM has two branches: one is from BLE- to BEFM inner hierarchy, the other is from EE- to BEFM outer hierarchy, where BLE and EE are abbreviations of the boundary-layer equations and of Euler equations, respectively. The relationship between the two branches of the hierarchial structure, the characteristics, subcharacteristics and mathematical properties of the hierarchial equations are studied. A comparison between the present hierarchial equations and the Simplified Navier-Stokes equations (SNSE) appeared in literatures is also made. BLE-, EE-and Inner-outer-matched (IOM) equations hierarchies are the most important and useful three levels for solving viscous flow-fields approximately.

Vectors, Tensors, and the Basic Equations of Fluid Mechanics.

Vectors, tensors, and the basic equations of fluid mechanics , Vectors, tensors, and the basic equations of fluid mechanics , کتابخانه دیجیتال جندی شاپور اهواز

The Fluid Dynamic Theory of Gas-Lubricated Bearings

Abstract A differential equation for the pressure distribution in gas-lubricated slider bearings is derived from the basic equations of fluid mechanics. The equation is an extension of Harrison’s gas-bearing equation in that the infinite width and isothermal restrictions have been removed. A perturbation solution is proposed and is carried out for the special case of an infinitely wide, self-lubricating journal bearing. Comparisons with numerical solutions to Harrison’s equation indicate that the first three terms in the series solution are sufficient to determine the pressure distribution and bearing load with reasonable accuracy.