Modeling of the dynamics of tornado structures in a pipe with turbulators of square, semicircular and triangular profiles

Objectives. To carry out mathematical simulations of changes in time of tornado compositions in channels with projections of semicircular, triangular, square profiles for average Reynolds criteria based on multiblock computing technology with the solution of finite- volume factorized methods of the Reynolds equation and energy equations.Method. The calculations were carried out on the basis of theoretical approaches based on the solution of Reynolds equations by finite-volume factorized methods, which were closed using the simulation of Menter stresses, and the energy of a structured grid.Result. The calculations of time-dependent flow and heat transfer parameters carried out in the article showed that the excess dissipation of turbulence generation for projections of sharp profiles - square profile, triangular profile - and rounded profiles - semicircular profile, segment profile - is provided with radically different hydraulic losses: channels with protrusions of rounded profiles, for example, semicircular, have much lower hydraulic resistance coefficients than channels with protrusions with sharp profiles, for example, triangular or square, rectangular.Conclusion. In the article, mathematical simulations of time-dependent tornado compositions were performed in channels with transversal profiles in the form of a square, triangle and semicircle, which is as informative as possible in terms of studying turbulent flows and heat transfer arising under average Reynolds criteria based on computer multiblock technology when using solutions of finite-volume factorized methods (FCOM-am) Reynolds equations and energy equations. The following protrusions were considered in the article: square transversal profiles, in which tornadoes are most pronounced, and side tornadoes affect the flow in the maximum way; triangular transversal profiles, where tornadoes are not so strong, and side tornadoes affect the main flow weaker than with square protrusions; semicircular transversal profiles, in which the incoming main tornado moves along the stream with the generation of limited side tornadoes. The calculated information obtained in the article correlates to a high degree with the available experimental data, which indicates the verification of the mathematical modeling involved in the article.

The influence of landscape and urban development on modeling of transport of pollutants in Krasnoyarsk city

The paper presents the numerical simulation of the distribution of pollutants in winter in the atmosphere of Krasnoyarsk city. The source of the pollution is the suburban areas of the city of Krasnoyarsk, in which coal stove heating prevails. A micro-scale mathematical model based on the solution of the system of non-stationary Reynolds equations is used for modeling. The influence of various factors, such as elements of terrain and urban development, on the distribution of pollutants is studied in the paper.

Determining the influence of structural and operational parameters of a double bearing on the thickness of its disc

This paper describes the main advantages of hydrostatic dynamic bearings of the double type, which have several lubricant films. It is indicated that they have an increased carrying capacity, by 1.8 times, and an extended range of stable operation, by 1.5 times, compared to conventional sleeve bearings with one lubricating film. The importance of determining the thickness of the bearing disk has been demonstrated, as it affects its durability. The goal was to investigate the impact of changes in the operational and structural parameters of a double bearing on the thickness of its disk. A sequence for determining the disk thickness has been proposed, including a joint solution to Reynolds equations, the balance of work fluid flow rate, as well as determining the loads acting on a bearing disk, which makes it possible to rationally assign the thickness of the bearing disk. The most common and effective methods of successive approximations have been used in the numerical implementation of Reynolds equations and flow rate balances. The action of centrifugal forces caused by the rotation of the disk has been taken into consideration in determining the total load acting on the bearing disk. The bending strength of the bearing disk was considered under its exposure to the total load. It was noted that due to the high flow rate of the working liquid pumped through the bearing, and the small change in the temperature of the liquid inside the bearing, the temperature deformations of the disk were not taken into consideration. The magnitude of change in the thickness of the double bearing disk has been determined, caused by the action of centrifugal forces in the examined range of angular speeds of the disk's rotation with the shaft. The reported results could be especially useful in the design of rotor supports for nuclear power plants where bearings have large dimensions, as well as for other units in power plants.

Theory of Heat Transfer in Straight Round Pipes with Square and Triangular Turbulators Under High Reynolds Criteria

Objectives: To carry out mathematical modeling of the structure of vortex zones between periodic flow turbulators with a surface arrangement of triangular and square transverse profiles on the basis of multi-block computing technologies based on solutions of the Reynolds equations (closed by means of the Menter shear stress transfer model) and energy equations (on multi-scale intersecting structured grids) with high Reynolds criteria Re = 106 with an exhaustive analysis of the corresponding current lines. Method: The calculations were carried out on the basis of a theoretical method based on the solution of the Reynolds equations by the factorized finite-volume method, which are closed using the low-Reynolds model of the Menter shear stress transfer, and the energy equation on multi -scale intersecting structured grids (FCOM). Result: Mathematical simulations of the heat exchange process in straight and round pipes with turbulators with d / D = 0.95 ... 0.90 and t / D = 0.25 ... 1.00 square and triangular cross-sections at large Reynolds numbers (Re = 106) on a foundation with multi-block computing technologies, which are based on solutions of the Reynolds equations and energy equations in a finite-volume and factorized way. It is found that the relative intensification of heat transfer [(Nu / Nusm) | Re = 106] / [(Nu / Nusm) | Re = 105] in round pipes with square air turbulators for large Reynolds numbers (Re = 106), which may well be relevant in the channels used in heat exchangers, may be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re = 105), for relatively high flow turbulators d / D = 0. 90 for the entire range under consideration for the parameter of the relative step between them t / D = 0.25 ... 1.00 a little more than 3%; for turbulators of triangular cross-section, similar indicators are approximately the same. For lower square turbulators with d / D = 0.95, this increase in relative heat transfer for large Reynolds numbers (Re = 106) compared to smaller numbers (Re = 105) does not exceed 6%; for triangular cross-section turbulators, similar indicators are slightly more than 4%. Conclusion: According to the results of calculations based on the developed model, it is possible to optimize the intensification of double turbulators, as well as to control the process of heat transfer intensification. It is shown that for higher square turbulators and at higher Reynolds numbers, a slight increase in the relative Nusselt number Nu / Nusm is accompanied by a significant increase in the relative hydraulic resistance due to the very significant influence of return currents, which can flow directly on the turbulator itself to the greater extent, the higher the Reynolds number; for triangular turbulators, the above trend persists and even deepens.

Comparative Study on Dynamic Characteristics of Double-Pad Inwardly and Outwardly Pumping Water-Lubricated Spiral-Groove Thrust Bearings

The dynamic characteristics of the double-pad inwardly pumping water-lubricated spiral-groove thrust bearing (SGTB) is different from that of the outwardly pumping version, especially under a high-speed condition. However, no literature on this topic can be found up to now. In this study, a comparative study on the dynamic characteristics of the two types of SGTBs is conducted. First, a turbulent lubrication model considering centrifugal and cavitating effects for the double-pad SGTB is developed based on gas–liquid two-phase flow. The steady-state and perturbed Reynolds equations of liquid phase are derived using linear perturbation method. Subsequently, the boundary fitted coordinate system and control volume method are applied to solve the Reynolds equations. Then, the axial stiffness coefficients of high-speed water-lubricated bearings are verified by an experimental study. Finally, the influence of operating conditions and configuration parameters on the dynamic behaviors for the two types of SGTBs is investigated. The results show that the double-pad outwardly pumping bearing is superior to the inwardly pumping version in all the dynamic coefficients when the radius ratio exceeds 0.65. When the tilt angle exceeds 1.2 × 10−4 as well as when the eccentricity ratio exceeds 0.7, the dynamic damping, angular and cross-coupled stiffness coefficients of the outwardly pumping bearing may be larger than those of the inwardly pumping one.

Estimated Fluid Force and Damping Characteristics of a Thin Film Damper Comparison Between Closed-Form Solutions and Numerical Analysis

Analytical solutions of thin film dampers are useful for determining critical speeds and stability of rotor systems. Most thin film dampers in use are of short axial length, and closed-form solutions to the Reynolds equations exist for estimating pressure, forces, and damping for these types of dampers. This article compares the fluid film forces and damping estimated by the short film bearing model form of the Reynolds equations to the calculated forces and damping of a transient computational fluid dynamic simulation. For this comparison, the fluid was assumed to be incompressible, laminar, and isoviscous. The fluid film forces and damping are calculated from integrating the pressure distribution over the surface of the damper due to small amplitude motions about a steady state static off-center circular orbit. In this case, no cavitation is assumed, and the journal has no angular velocity, so direct stiffness cannot be calculated from the closed-form solution. Radial clearance, journal length, and journal eccentricity have a significant effect on fluid force and damping within a thin film damper. Fluid density does not affect fluid force or damping substantially, while fluid viscosity does. Both the closed-form solutions and computational fluid dynamics simulation compare well with each other and reflect these trends.

Investigation of Turbulence Effects on the Nonlinear Vibration of a Rigid Rotor Supported by Finite Length 2-Lobe and Circular Bearings

This study investigated the effect of turbulence on the nonlinear vibration of a symmetrical rigid rotor supported by two identical journal bearings. The bearings consisted of various length to diameter (L/D) ratio circular and 2-lobe bearings with differing pad preloads. Two turbulent (Ng–Pan–Elrod and Constantinescu model) and one laminar Reynolds equations were selected for comparison, and they were solved using a finite difference method to obtain nonlinear bearing forces. The nonlinear equations of motion for the rotor-bearing system were solved using a shooting method and arclength continuation to obtain limit cycles for each bearing configuration. Floquet multiplier analysis was then utilized to identify the stability of the obtained limit cycles. For the cases of the circular and 2-lobe bearing without pad preload, the turbulent Reynolds equations yielded a lower onset speed of instability and L/D ratio at which the bifurcation type changed from supercritical to subcritical than the laminar Reynolds equation. However, at higher pad preloads (preloads of 0.25 or 0.5), the turbulence effects increased the onset speed of instability, especially for L/D ratios > 0.7, and only supercritical bifurcation was observed. For all bearing configurations, the ratio of the limit cycle whirl frequency to shaft rotational speed for both turbulence bearing models was higher than that of the laminar bearing model, and the Ng–Pan–Elrod turbulence model always generated lower onset speed of instability than the Constantinescu model.

Numerical Modeling of the Process of Thermal Impact of Wildfires on Buildings Located near Forests

The mathematical modeling of wildland fires impact on buildings have been carried out to study the effects of fires at different conditions of buildings ignition. The forest is modeling as a porous reactive medium. The formulation of this problem was developed using standard nonstationary three-dimensional Reynolds equations for flow in a multiphase reactive medium. These equations are solved numerically using finite volume method. The influence of meteorological conditions, properties of the forest and its state on the possibility of ignition of buildings located near forests is studied.