Unsteady conjugate thermogravitational convection in a cylindrical region with local energy source

The mathematical modelling of unsteady regimes of natural convection in a closed cylindrical region with a heat-conducting shell of finite thickness was carried out in the presence of a local heat source under the conditions of convective heat exchange with the ambient medium. The mathematical model was constructed in dimensionless variables “stream function — vorticity vector — temperature” in the cylindrical coordinate system. The influence of the Rayleigh number, 10⁴ ≤ Ra ≤ 10⁶, of the unsteadiness factor 0 < τ < 300, of the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 4.3·10⁻², and the energy source sizes on both local characteristics (streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) was analysed in detail. Thermohydrodynamic peculiarities due to the geometry of the object of research were established.     

Reversals of large-scale circulation in turbulent convection in rectangular cavities

The behavior of large-scale circulation appearing against the background of Rayleigh-Bénard turbulent convection in rectangular cavities of various geometries (from a thin layer to a cubic cell) has been experimentally investigated. It has been shown that the regimes of large-scale circulation with spontaneous reversals separated by long periods of quasistationary circulation appear both in a limited range of the Rayleigh number and in a limited range of the aspect ratio, which determines the ratio of the thickness of a cell to the side in the circulation plane. A regime without reversals is established in a thick layer, whereas a regime characterized by numerous changes in the direction of circulation, which are not separated by intervals with the stable direction of the large-scale flow, arises in a thin layer. The spectra of oscillations of the amplitude of large-scale circulation have been analyzed. It has been shown that a dominant frequency appears in the spectrum of oscillations of the cubic cell.     

Numerical investigation of air free convection in a room with heat source

Mathematical modelling of three-dimensional steady free convective incompressible viscous gas flows in the rooms with a heat source is carried out within the framework of the Navier — Stokes equations with the effective viscosity determined on the basis of the κ-ɛ turbulence model. The investigation is carried out for the case of model rooms and heat sources having the form of rectangular parallelepipeds with square bases. The influence of the heat source power and the sizes of the room base on local and averaged values of the air velocity and temperature in the rooms is analysed. The flow pattern in the room is shown to have a torus-like shape. It is found that the variation of sizes of the room base rather than the capacity variation of the heat source is of determining importance for the gas motion character in a closed volume.     

Surface radiation influence on the regimes of conjugate natural convection in an enclosure with local energy source

A numerical analysis of the unsteady regimes of the natural convection and thermal radiation in a square enclosure with heat-conducting walls has been carried out in the presence of a heat source of finite sizes located in the base zone under the conditions of convective exchange with the ambient medium. The mathematical model formulated in the dimensionless variables “stream function — vorticity — temperature” has been implemented numerically by a finite difference method. The influence of the reduced emissivity of internal surfaces of bounding walls on the local characteristics (the streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) has been analyzed in detail for 0 ≤ ? < 1, the location of the heat source 0.1 ≤ l/L ≤ 0.4, and its length 0.2 ≤ l _hs /L ≤ 0.6 for Ra = 10⁶, Pr = 0.7. The approximation relations have been derived for the mean convective and radiation Nusselt numbers depending on the reduced emissivity of the internal surfaces of bounding walls and the energy source location relative to vertical walls.     

Mathematical modelling of heat and mass transfer under conditions of mixed convection in rectangular region with heat source and heat-conducting walls

Numerical modelling of a conjugate convective-conduction heat transfer in a rectangular region with a heat-release source was carried out in the presence of forced flow and mass exchange. The distributions of thermal and hydrodynamic characteristics, which describe the specific peculiarities of flow regimes under study, were obtained. The mutual influence of forced and free-convective flow was analysed. The scales of the effect of determining dimensionless complexes (Gr, Br, Re) on flow regimes were established. The evolution of analysed process was shown.     

湍流热对流Prandtl数效应的数值研究

本文采用直接数值模拟的并行直接求解方法,计算了Ra=10~(10),0.05≤Pr≤20的系列Prandtl(Pr)数二维湍流热对流.通过流动显示技术,讨论了Pr数对羽流形态和大尺度环流结构的影响.在Ra=10~(10)时,随着Pr数减小,羽流的运动和分布表现出更强的湍流性质,较高Pr数的羽流则表现出较强的规律性,当Pr4.3时,流场中存在明显的大尺度环流和角涡结构.不同Pr数的温度边界层厚度差异不大,并随Pr数存在标度率变化关系.当Pr数较低时,系统的传热Nusselt(Nu)数随着Pr数增加而增加,当Pr数较高时,Nu数随Pr数的变化不敏感.靠近底板处速度脉动随Pr数有显著的变化,Pr数越低速度波动越剧烈.通过底板中心位置水平脉动速度和平均场水平速度最大值给出的雷诺数Re_((u))和Re_(U_(max)),两种Re数随Pr数的变化满足同一标度律,为Re～Pr~(-0.81).     

Mathematical simulation of conjugate turbulent natural convection in an enclosure with local heat source

A numerical analysis of turbulent regimes of the natural convection in a closed rectangular region with heat-conducting walls of finite thickness was carried out in the presence of a locally concentrated heat source under the conditions of the radiative-convective heat exchange with the ambient medium on one of the external boundaries. The mathematical model was constructed on the basis of the Reynolds equations in dimensionless variables stream function — vorticity vector — temperature. Special attention was paid to the investigation of the influence of the Grashof number er 10⁸≤Gr<10¹⁰, of the unsteadiness factor 0< τ <1000, and the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 6.8·10⁻⁵ on both the local and integral characteristics of the problem.     

On combustion in a closed rectangular channel with initial vorticity

This article examines the detailed combustion process in a theoretical model with applicability to combustion in a wave rotor or wave disc engine. The model comprises a single channel into which an initial loading of methane and air is admitted and ignited after all inlet and exit ports have been closed. Combustion takes place at constant volume. However, the initial gaseous mixture in the channel is not at rest. The initial opening and closing of the ports generates significant vorticity which influences the evolution of the combustion process. Numerical evaluations are provided for the detailed flame shape for simplified (one-step) chemistry and a simulation using the detailed 235-step San Diego scheme. Quantities examined are the evolution of vorticity, pressure fluctuations, mass consumption rate, flame surface area and the influences on combustion of adiabatic and non-adiabatic channel walls. Combustion regimes are identified and compared with simpler model studies (no initial flow). Pointwise quantities are examined to describe the various stages of burning in the channel. The focus of the study is directed towards quantities that influence overall burning rate and completeness of combustion.     

Measurement, analysis and correction of the closed orbit distortion in Indus-2 synchrotron radiation source

The paper presents the measurement, analysis and correction of closed orbit distortion (COD) in Indus-2 at 550 MeV injection energy and 2 GeV synchrotron radiation user run energy. The measured COD was analysed and fitted to understand major sources of errors in terms of the effective quadrupole misalignments. The rms COD was corrected down to less than 0.6 mm in both horizontal and vertical planes. A golden orbit was set for the operating synchrotron radiation beamlines. With COD correction, the injection efficiency at 550 MeV was improved by ~50% and the beam lifetime at 2 GeV was increased by ~8 h. In this paper, the method of global COD correction based on singular value decomposition (SVD) of the orbit response matrix is described. Results for the COD correction in both horizontal and vertical planes at 550 MeV injection energy and at 2 GeV synchrotron radiation user run energy are discussed.     

Numerical simulation of the ignition of liquid fuel with a limited-energy source under turbulent flow conditions

The ignition of a typical liquid fuel with a limited-energy source, a small metal particle heated to high temperature is numerically simulated with consideration given to the possible turbulization of the fuel vapor flow. The dependences of the integral ignition characteristics on the key parameters of the local heat source are established. The integral ignition characteristics, as well as the fields of fuel vapor concentrations and velocities predicted by models accounting for the laminar and turbulent modes of the vapor-oxidizer mixture flow are compared.     

Bifurcations analysis of turbulent energy cascade

This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.     

Numerical simulation of turbulent natural convection of oxide heat generating melt in a core catcher at NPP with VVER-1000

The problem statement and simulation results are presented concerning turbulent natural convection in a vertical cylindrical molten pool with internal heat generation and other parameters (inner Rayleigh number Ra _i ∼ 10¹⁶–10¹⁷) corresponding to oxide core melt in a core catcher for NPP with VVER-1000. Commercial code FLUENT 6.3 was used for CFD calculations. The results on heat transfer are approximated by power law correlations for mean Nusselt numbers vs. Rayleigh number and pool height, describing the heat transfer at upper, lateral, and total boundaries of the cylinder. The influence of volumetric heat generation and material properties is studied. Spatial distribution of wall heat transfer is analyzed for different pool heights possible in the real core catcher. Along with serial calculations with isothermal boundary conditions, the cases with heat radiation conditions are considered. The results may be used for estimations of heat transfer and melt overheating in a VVER core catcher and for coefficient identification of simplified models of integrated system severe-accident codes.     

Power fluctuations in a closed turbulent shear flow

We study experimentally the power consumption P of a confined turbulent flow at constant Reynolds number Re. We analyze in details its temporal dynamics and statistical properties, in a setup that covers two decades in Reynolds numbers. We show that nontrivial power fluctuations occur over a wide range of amplitudes and that they involve coherent fluid motions over the entire system size. As a result, the power fluctuations do not result from averaging of independent subsystems and its probability density function Pi(P) is strongly non-Gaussian. The shape of Pi(P) is Reynolds number independant and we show that the relative intensity of fluctuations decreases very slowly as Re increases. These results are discussed in terms of an analogy with critical phenomena.     

Clustering of plumes in turbulent convection

Turbulent Rayleigh-Bénard convection produces fields of intense updrafts and downdrafts that are responsible for much of the vertical heat transport. These structures, called plumes or thermals, have horizontal scales comparable to the thicknesses of the boundary layers in which they arise. In the three-dimensional numerical simulations reported here, we have observed that convective plumes organize themselves into clusters with horizontal scales that grow with time and reach the width of the computational domain. In this two-scale process, kinetic energy is transferred mainly to low horizontal wave numbers while the sizes of individual plumes remain on the scale of the boundary layer thickness.     

源于边界层转捩区的单极子声辐射

基于 Lighthill方程和 Green理论,本文对边界层转捩区声辐射机理进行了分析和讨论,并对转捩区内各声源的基本类型作了分类.分析结果表明;边界层转捩区的声辐射由转捩区内处于完全湍流状态的流体流动引起的向边界展外辐射的声场以及另两个附加声场组成;边界层转捩区声源的主要类型为单极子、偶极子和四极子声源;本文的分析为Lauchle模型提供了理论依据,证明了利用Lauchle模型估算转捩区远场声辐射基本准确可靠.     

Numerical analysis of convective heat transfer in a closed two-phase thermosyphon

Mathematical modeling of the processes of heat transfer and hydrodynamics in a closed two-phase thermosyphon is carried out in a wide range of key parameters. The mathematical model is based on the laws of conservation of mass, momentum, and energy in dimensionless variables of stream function-vorticity vector-temperature. The influence of the Rayleigh number and the dimensionless time on the local and integral thermal hydrodynamic characteristics is estimated.     

Different localized states of travelling-wave convection in a rectangular container

We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendicular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and supercritical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable. The weak structures in the conducting region are demonstrated too.     

Galloping of rectangular prisms in a smooth and in a turbulent flow

Galloping of rectangular prisms ranging from 0·2 to 1·0, approximately, in thickness ratio has been investigated experimentally in a smooth and in a turbulent flow. Attention was focused on galloping instability which builds up spontaneously from rest and is referred to as soft galloping. A close relationship between the onset of soft galloping and the peak characteristic of the steady drag coefficient was observed. Some other experiments to shed light on the mechanism of the onset of soft galloping of a rectangular prism are also reported.     

Numerical simulation of experiments on turbulent natural convection of heat generating liquid in cylindrical pool

Available experimental data on heat transfer of a melt with volumetric heat generation are analyzed in order to use them for validating the computer codes that describe a core catcher. The problem for CFD simulation of the experiments on heat transfer by laminar and turbulent natural convection is described. Information that can be obtained from experiments for verifying the models of convective heat transfer in a melt is analyzed. The effect of variable viscosity on the integral heat flux is discussed. Calculation results are represented and compared with experimental data on temperature distribution and integral heat transfer. The calculations are in good agreement with the experiment. The results are numerically extrapolated to the range of Rayleigh numbers up to 7 · 10¹⁶. It is concluded that the CFD calculations with the κ-ɛ turbulence model can be used in problems concerned with analysis of melt convection in a core catcher.