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.     

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.     

Turbulent free convection between vertical isothermal plates with asymmetrical heating

Results of numerical investigation of the flow and heat transfer at turbulent free convection between the vertical parallel isothermal plates with different temperatures are presented. The temperature factor R _T varied within ?2 ÷ 1. The Rayleigh number changed within Ra = 10⁷ ÷ 10⁹, and the ratio of geometrical sizes of plates and distances between them was constant A = L/w = 10. Numerical studies were performed via the solution to the two-dimensional Navier—Stokes equations and energy equation in Boussinesq approximation. The considered boundary-value problem has the unknown conditions at the inlet and outlet between the plates. To describe turbulence, the modified low-Reynolds k-? model was used. The effect of the temperature factor on the flow structure at the channel inlet and outlet was analyzed. Data on distributions of velocities and temperatures between the plates, local and integral heat transfer allow deeper understanding of the mechanism of transfer processes between the parallel plates with asymmetrical heating.     

A methodology for multivariate simulation with massively parallel computing systems for NPP safety assessment: VARIA code

The paper is focused on the practical application of parallel computing techniques in uncertainty assessment in simulation of heat transfer, mechanical and some other problems related to deterministic analysis of NPP safety. A methodology is developed and implemented in VARIA computer code that performs simultaneous run of multiple simulations on a parallel computing system with further statistical analysis of the array of their results. The current version of the code allows automated preparation and execution of multivariate simulations of thermal and mechanical behavior of pressurized water reactor structures by best-estimate (BE) codes in the scope of NPP safety assessment under severe accident conditions. The number of simultaneously launched tasks is limited only by the computer cluster capacity. The VARIA code is verified on multivariate simulation with HEFEST code of thermal behavior of a core melt in the VVER-440 reactor vessel during a severe accident. The influence of the variation of input parameters (decay heat value and coefficients of the applied convective heat transfer model) on the simulation results is studied. It is concluded that the potential field of applying the program is beyond the scope of analyzing severe accidents at NPP and includes also software product quality assurance and analysis of uncertainties of obtained simulation results.     

The ultimate state of thermal convection in Rayleigh-Taylor turbulence

This paper discusses the so-called ultimate state of thermal convection, first proposed by Kraichnan almost 50 years ago and recently observed in numerical simulations of turbulent convection in the absence of boundaries. We focus on numerical simulations of turbulence generated by the Rayleigh-Taylor instability in a wide range of Rayleigh and Prandtl numbers. Our results point out to the conclusion that RT turbulence provides a natural realization of the ultimate state of thermal convection thus highlighting the relationship between the absence of boundaries and the emergence of the ultimate state scaling for global statistical quantities.     

自然对流换热的高精度非结构网格有限体积法

用非结构网格有限体积法求解自然对流换热时,传统的对流项离散格式难以兼顾数值精度与计算效率,我们发展了一种耦合高精度格式的延迟修正方法,用于对流项的离散.高Re数下方腔驱动流数值计算验证了该方法具有较高的计算精度和较好的稳定性.Boussinesq流体的自然对流换热数值模拟,表明该方法能有效克服高Ra数时数值计算发散,可准确捕捉自然对流换热问题中不同偏心率下的等温线和流线分布特征.     

轿车热环境模拟及风口面积对乘客舒适性的影响

通过数值计算的方法模拟了车内的速度场和温度场。计算采用SIMPLE算法,紊流采用k-ε模型,考虑了自然对流换热的影响,应用整体求解法计算气固耦合传热问题。用射线追踪法计算太阳热辐射,S2S模型计算固体壁面间的辐射。利用PMV和EHT指标从总体和局部两个方面分析车内舒适程度,并研究了喷口面积对热环境的影响。研究表明,改变喷口面积可以在一定范围内调节车内热舒适性,空调设计时可以利用这一点来提高冷负荷的利用率。     

Numerical investigation of using micropolar fluid model for EHD flow through a smooth channel

In this paper, a numerical method is presented to investigate the Electrohydrodynamic effect using micropolar fluid model. The EHD flow for the forced convection heat transfer in a smooth channel is simulated. The computed results were compared with the fully turbulent flow approach. It is found that the micropolar model can be used to simulate the hydraulically laminar flow. In addition, the heat transfer enhancement has the same efficiency for both the micropolar and the k-ε models. The change of the applied voltage and the Reynolds number caused various deviations of the results obtained from the two approaches up to a maximum of 20.79%, and a minimum of 0.03%.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

水平板自然对流换热的非线性特性

采用SIMPLE算法,QUICK差分方案,对封闭方腔内水平板自然对流换热进行了数值模拟.数值结果显示,低Ra数时流动和换热处于稳态,当Rayleigh数超过某一临界值时,流动和换热就会发生非稳态振荡,此时流动和换热表现出非对称性.对不同Rayleigh数,流动和换热通过单周期分岔从稳态过渡到非稳态,并通过倍周期分岔过渡到混沌.在混沌区,仍然会出现周期性窗口,并且数值结果与初始条件有关.     

Adaptation of mesoscale turbulence parameterisation schemes as RANS closures for ABL simulations

The present study presents different k-ε turbulence closures for atmospheric boundary layer flows using computational fluid dynamics (CFD) simulations that are consistent with inflow conditions from numerical weather prediction (NWP) simulations. Eight different mesoscale turbulence parameterisation schemes of the Weather Research and Forecasting (WRF) model are covered. To ensure consistency between the NWP and CFD simulations, different closure coefficients of the k ? ε turbulence model for each NWP scheme are proposed. This is achieved by combining production–dissipation closure coefficient relationships based on the Monin–Obukhov similarity theory and the formulation based on the Coriolis parameter proposed by Detering and Etling. The proposed methodology has been implemented in the open source CFD toolbox OpenFOAM and is demonstrated at near-neutral stability conditions for the classical Askervein Hill case.     

含不同形状内热源的圆管内纳米流体自然对流及换热数值研究

采用格子玻尔兹曼方法对有三种恒温热源(圆形、三角形、方形)参与的圆管内纳米流体(铜-水)自然对流进行数值研究.主要研究瑞利(Ra)数,纳米颗粒体积分数以及热源几何形状等控制参数对纳米流体的流动与传热的影响.结果发现纳米颗粒体积分数的增加有利于强化传热,且在Ra数较小时,平均努塞尔(Nu)数增加的幅度要优于Ra数较大的情...     

对流作用下枝晶形貌演化的数值模拟和实验研究

合金凝固过程中存在于枝晶尖端液相区的强制对流和自然对流均能改变溶质扩散层厚度,从而会对枝晶形貌产生较大影响.在元胞自动机模型基础上,耦合液体流动方程、热传导方程和溶质对流扩散方程,建立了新的计算微观组织演化的数值模型,并利用该模型研究了强制对流和自然对流对枝晶生长的影响.三维数值模拟结果再现了强制对流作用下等轴枝晶的生长过程,揭示了强制对流对枝晶生长速率和尖端半径的影响特点.同时利用该模型模拟了NH₄Cl-H₂O溶液定向凝固过程中自然对流对柱状晶生长的影响,并采用相应的实验进行验证.模拟结果与实验结果符合良好,从而证明该模型是可靠的,可推广到实际合金系中. 关键词： 元胞自动机 对流 4Cl-H₂O溶液')" href="#">NH₄Cl-H₂O溶液 定向凝固     

Thermal calculation for a furnace with three-tiered near-wall burners

The paper considers using a differential method for thermal calculation of a furnace with finding the thermal and aerodynamic parameters within the radiation chamber of a tube furnace. The furnace is equipped with acoustictype burners allocated in three tiers on the lateral walls. The method implies joint numerical solution of 2D radiation transfer equations using the S ₂-approximation of the discrete ordinate method, of energy equations, flow equations, k-ε turbulence model, and single-stage modeling of gas fuel combustion. Typical results of simulation are presented.     

高重复频率水冷Nd:YAG激活镜放大器的温度特性

为解决高重复频率大能量激光放大器的热管理问题,采用数值模拟与实验分析的方法,对背面水冷Nd:YAG激活镜放大器的流体散热进行了研究.基于低雷诺数k-ε湍流模型,建立了流-固共轭传热多物理场藕合分析模型,对比分析了近壁面处理方法对流体流动、对流扩散和热传导过程及温度分布的影响,分析研究了不同冷却液流量和泵浦参数对流场特性、激光介质温度和波前分布的影响.数值模拟表明:激光介质的温度分布与固液边界层内的黏性作用密切相关,且冷却液的热扩散主要发生在100μm范围内;激光介质的热沉积分布中心对称,而温度分布沿水流方向不对称,最大温升位于出水口端且基本保持不变;增益介质前表面的温度分布与介质的波前分布随冷却液流量非线性变化,而随泵浦参数线性变化;实验结果与数值模拟符合较好.     

Buoyancy induced flow in a nanofluid filled enclosure partially exposed to forced convection

A numerical study was performed on natural convection for water–CuO nanofluid filled enclosure where the top surface was partially exposed to convection. The cavity has a square cross-section and differentially heated. Except exposed convection part on the top, all sides are adiabatic on horizontal walls. Effects of Rayleigh number (10³ ? Ra ? 10⁵), Biot number (0 ? Bi ? ∞), length of partial convection (0.0 ? L ? 1.0) and volume fraction of nanoparticles (0.0 ? φ ? 0.1) on heat and fluid flow were investigated. The results showed that for the case of high Biot number that heat transfer along the heated was enhanced by increasing the Rayleigh number mainly at the upper portion of the heated wall. When the top wall was totally exposed to convection, the results prevail that the heat transfer was more effective at high Biot number especially at the upper portion of the heated wall. For the case of high Biot number, the results prevailed that the heat transfer at the upper portion of the heated wall increases considerably at high exposed length to convection (L); however, for L ? 0.75 the effect of L was less pronounced. Contour maps for percentage of heat transfer enhancement were presented and it was shown that the location of maximum enhancement in heat transfer was sensitive to Ra, φ and L.     

基于LBM的部分热活跃边界下多孔腔体内自然对流换热

采用Boltzmann方法模拟部分热活跃边界下的多孔腔体内自然对流,探讨不同热边界布置方案、孔隙度、Da数及Ra数对其流动传热的影响.数值计算表明：Da=10^-4时,腔体内中央出现一个循环流模式,只在Ra数很大时孔隙度才对传热有影响; Da=10^-2时,腔体内出现两个循环流,在Ra数很小时孔隙度对传热产生强烈的的影响.热活跃边界位置影响腔体内流体对流传热的强度,加热边界布置在底部、而冷却边界布置在顶部（Bottom-Top布置方式）,对多孔腔体内对流传热最有利,优于全热边界布置方式的传热效果.     

Experimental and Numerical Study of Free Convection on an Isothermal Downward Cone

Abstract

The laminar free-convection heat transfer from an isothermal downward cone in air is investigated experimentally and numerically. The experimental investigation is carried out by Mach-Zehnder interferometery technique and the numerical simulation was done by Fluent. The cone tip angle has been kept constant to 45° and it was suspended from its base throughout the experiment. This article focuses on the effect of Rayleigh number variation on the local and average free-convection heat transfer coefficient over the conical surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 4.9×10⁵ to 1.1×10⁶. Also, the experiment and the numerical simulation were carried out on a vertical isothermal cylinder of circular cross section in order to compare results with other researchers for the verification of our experimental and numerical results. The significant influence of the upper end surface of the cone, both in the experimental and numerical studies, indicated a recirculation region above the upper end surface which affects the local convection heat transfer at the slant trailing edge and causes it to increase. Also, a correlation for the calculation of the local Nusselt number over the cone is proposed.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

具有蜂窝状结构夹板的空气层复合传热的研究

本研究在考虑了辐射换热的条件下对带六角形蜂窝状结构的竖直空气层的复合传热进行了数值解析蜂窝状芯材的温度是通过对流和辐射之间的热平衡来决定的，因此，在芯材极其薄的情况下，辐射换热将对自然对流产生影响。本文通过对辐射率ε＝０．０３～１．０，Ｐｒ＝０．７，Ｒａ＝１０３～１０５的各种组合条件下的计算，解明了辐射换热对对流换热所产生的影响。