Free convection effects on MHD Stokes problem for a vertical plate

An exact analysis is made of the effects of mass transfer and free convection currents on MHD Stokes' (Rayleigh's) problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started vertical plate, under the action of a transversely applied magnetic field. The heat due to viscous and Joule dissipation and the induced magnetic field is neglected. During the course of the discussion, the effects of heating (Gr < 0, Gr = Grashof number) or cooling (Gr > 0) of the plate by the free convection currents, Gr_m (modified Grashof number), Sc (Schmidt number) and M (Hartmann number) and the velocity and skin-friction are studied.     

Effects of mass transfer and free convection currents on MHD Stokes' problem for a vertical plate

An exact analysis is made of the effects of mass transfer and free convection currents on MHD Stokes' (Rayleigh's) problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started vertical plate, under the action of a transversely applied magnetic field. The heat due to viscous and Joule dissipation and the induced magnetic field is neglected. During the course of the discussion, the effects of heating (Gr < 0, Gr = Grashof number) or cooling (Gr > 0) of the plate by the free convection currents, Gr_m (modified Grashof number), Sc (Schmidt number) and M (Hartmann number) and the velocity and skin-friction are studied.     

安全壳内置换料水箱内自然对流现象试验研究

以第3代核电技术中广泛采用的安全壳内置换料水箱（IRWST）为对象,通过比例分析获得了自然对流现象的相似准则,设计了缩比试验装置,对事故条件下IRWST内的自然对流现象进行了试验研究,分析了IRWST内自然对流的演变规律及初始条件的影响。结果表明：相似格拉晓夫数、相似雷诺数和相似普朗特数是IRWST自然对流现象试验装置设计应遵循的相似准则;加热初期,IRWST内以轴向上升羽流为主,随冷热分层的形成,流体的轴向上升运动被抑制,转变为以IRWST中下部区域的径向横流为主;不同初始条件下IRWST内自然对流的演变规律基本一致,但流场演变过程的快慢、流体速度的大小不同。     

流体动压型核主泵机械密封腔内流动与传热研究

To study the distribution of the flow and temperature field in a type of hydrodynamic mechanical seal of a nuclear reactor coolant pump, a three-dimensional model of the mechanical seal and the seal chamber is established based on the software Pro/E. The N-S equations and energy equation coupling with the k-ε turbulence model are solved based on ANSYS Fluent. The heat generation between the mechanical seal rings and the heat transfer distribution in the sealing chamber is studied. The fluid flow and temperature field of the mechanical seals is analyzed. The results show that the pressure distribution of the mechanical seals is divided into the high-pressure zone and the low-pressure zone by the sealing end face. The liquid film pressure in the mechanical seal end faces gradually decreases from the outer radius to the inner radius. The highest temperature appears at the sealing face, and the temperature decreases gradually away from the sealing face. The viscous heat in the liquid film is transferred away through the seal rings and the heat convection of the fluid flow in the sealing chamber. The pumping ring of the mechanical seal strengths the heat convection of the end faces.     

流体动压型核主泵机械密封腔内流动与传热研究

为研究某型号流体动压型核主泵机械密封流场和温度场的分布规律,使用Pro/E软件建立了机械密封环及密封腔的三维实体模型。采用k-ε湍流模型,基于ANSYS Fluent软件求解了纳维-斯托克斯(N-S)方程和能量方程。研究了密封环生热与密封腔散热的规律。分析了流体流动与温度变化趋势。结果表明:该型核主泵机械密封的压力以密封端面为界,分为高压区和低压区。在密封端面液膜压力由外径到内径逐渐降低。最高温度出现在密封端面处,由密封端面向外温度逐渐降低。液膜粘性剪切热通过密封环的热传导及腔内流体的对流换热作用而带走。机械密封的泵送环强化了端面热量的散失。     

Natural convection heat transfer of water on a horizontal downward facing stainless steel disk in a gap under atmospheric pressure conditions

An experimental study on natural convection heat transfer on a horizontal downward facing heated surface in a water gap has been carried out under atmospheric pressure conditions. A total of 7204 experimental data points are correlated using Rayleigh versus Nusselt number correlations in various forms, based on different independent variables. The effects of different characteristic lengths and film temperatures are discussed. The buoyancy force acts as a resistance force for natural convection heat transfer on a downward facing horizontal heated surface in a confined space. For the estimation of the natural convection heat transfer under the present conditions, empirical correlations in which Nusselt number is expressed as a function of Rayleigh number, or Rayleigh and Prandtl numbers both, may be used. However, the best accuracy is provided by an empirical correlation which expresses the Nusselt number as a function of the Rayleigh and Prandtl numbers, as well as the gap width-to-heated surface diameter ratio; and uses the temperature difference between the heated surface and the ambient fluid in the definition of Rayleigh number. The characteristic length is the gap size and the film temperature is the average fluid temperature.     

Heat transfer in liquid metals

This article is a survey of basic work on heat transfer between solid surfaces and flowing liquefied metal that has been reported by both Soviet and foreign authors. The results of experiments on heat transfer to liquid metals are analyzed for cases where flow took place in both long and short tubes, flat channels, over bundles of rods and over a plate along their longitudinal directions, across cylinders, with free convection and condensation of liquid metal vapors. The effect of additives on the rate of heat transfer is examined. Questions that arise in connection with boiling of liquid metals are discussed, as are problems of wetting effects on fluid friction and on heat transfer rate. Equations for calculation of heat transfer rates are given.     

On LBE natural convection and its water experimental simulation

This paper deals with stability and distribution of coolant flow in a pool type of lead-bismuth eutectic (LBE) cooled accelerator driven system (ADS) under natural convection conditions. Two approaches are proposed for solving the problems, namely, (i) theoretical model for stability analyses; (ii) water experimental simulation for the flow distribution in the natural convection state.The stability analysis is carried out based on a simplified integral flow model, where hot and cold free surface oscillations are taken into account. There is a transition from an absolutely stable state under the forced convection condition to a damped oscillation state under the natural convection condition.Reynolds, Richardson (Grashof) and thermal power similitude laws are revealed for the water experimental simulation. The water model scale, power and other factors can be determined by the similitude laws. By choosing the inlet and outlet temperatures even the local Reynolds number law can be approximately satisfied. By the variation of the inlet temperature in the water experiment several similitude solutions are presented. In particular, they are shown in detail for the model scale one to one. It is concluded that the water experiment can be applied for the simulation of LBE natural convection flow in a pool type of reactor.     

Hydromagnetic free convection effects on the oscillatory flow of an electrically conducting rarefied gas past an infinite vertical porous plate

Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible rarefied gas, past an infinite vertical porous plate in the presence of a transverse magnetic field is studied. The freestream velocity oscillates in time about a constant mean, while the suction velocity, normal to the porous plate, is constant. The magnetic Reynolds number of the flow is not taken to be small enough, so that the induced magnetic field is not negligible. The plate temperature is constant and the difference between the temperature of the plate and the freestream is moderately large causing the free convection currents. The flow field is described by a nonlinear coupled system of equations subjected to the first-order velocity slip and temperature jump boundary conditions. With viscous dissipative heat and Joule heating taken into account, approximate solutions of the problem are obtained for the velocity, temperature and induced magnetic field, as well as, for the related to them quantities of the skin friction, rate of the heat transfer and electric current density.     

Laminar combined convection heat transfer of liquid sodium flowing through a single horizontal row of cooling tubes in the direction of gravity

The laminar combined convection heat transfer of the liquid sodium which flows through a single horizontal row of cooling tubes in the direction of gravity are studied using numerical analysis. The heat transfer characteristics at large Reynolds numbers are improved when Richardson numbers (= GR/Re²) are increased and the improvement rate is enlarged with an increase in value. The temperature field at small Reynolds numbers does not exhibit much change even when the Richardson number reaches a high value. Consequently the Nusselt numbers do not differ from those of forced convection. In other words, in a decay heat removal system at a low velocity, there is a possibility that an improvement in the heat transfer characteristics by combined convection cannot be expected even in a system with a large Richardson number.     

自然循环换热器壳侧传热及流动的数值模拟

为分析换热器的求解模型和内部结构的不同对传热和流动特性的影响,用等效自然循环换热器的模型进行多种变换。用Fluent软件对等效模型进行非稳态数值模拟,研究其传热和流动特性。通过比较分析不同模型的温度场和流场的变化,对该换热器的传热过程和自然对流情况有较深刻的认识。结果表明：自然循环换热器的传热管内外温差较大,且流动较复杂,选用湍流模型计算更为合理;传热管位置的不对称性,引起左右两侧传热和流动的不对称性,使得流体相互影响,增强了自然对流作用;传热管的形状由直管变为C型弯管,结构的复杂性在一定程度上增强了流体温度分布和流动的不规则性,使得湍流强度增加,致使换热效果得到改善。     

规则球床堆熔盐流动压降与对流换热CFD模拟

球床堆复杂的几何结构导致直接建模进行热工水力模拟非常困难,一般使用多孔介质模型简化处理,但多孔介质已有的压降和对流换热公式在熔盐冷却球床中的有效性仍待验证。本文基于固态燃料熔盐堆建立了6 cm直径小球的规则球床模型,给定球床进口熔盐流量和球壳发热功率,模拟了球床内的稳态流动与换热,计算了对应的压降和对流换热系数,并分别得到了球床压降、对流换热Nu随球床内流动Re变化的曲线。对比发现:模拟压降结果与已有公式差异较大,而模拟对流换热Nu结果与已有公式的差异相对较小。结合模拟结果和已有的公式,拟合得到了修正的压降和对流换热Nu公式。将修正公式应用于3 cm直径规则球床中,结果表明多孔介质修正模型与直接模拟结果一致。     

A study of non-Boussinesq integral boundary layer analysis for an MTR research reactor

In the present work, a non-Boussinesq (variable physical properties) integral boundary layer analysis is accomplished. The model analyzes laminar free convection between nuclear fuel plates having large fuel plate length to gap between plate ratio. The coolant channels are undergoing to a uniform, symmetric, heat flux and varying fluid properties. In the present study the flow is assumed to be fully developed. This is a good assumption for channels with large fuel plate length to gap between plate ratios. To describe the velocity and temperature distributions of the coolant the non-Boussinesq approximation is introduced into the integral boundary layer equations of flow between parallel plates. The fuel plate temperature is related to the adjacent coolant fluid temperature by a principle in conduction heat transfer. Fluids considered here are air and water. The obtained results show that the present heat transfer problem encountered in nuclear research reactor such Tehran nuclear research reactor (TRR) is characterized by high temperature ratios and thereby rendering the commonly applied Boussinesq approximation invalid. As a result, the use of the Boussinesq approximation (constant fluid properties) for high temperature ratios is not suggested.     

Numerical Analysis of Laminar Free Convection in Square Cavity Containing Heat Generating Kr-85 Gas

A laminar free convection of heat generating fluid in a horizontal square container with 10 cm × 10 cm cross section and infinite length was analyzed through the Newton iterative numerical solution of the equations of change without the Boussinesq approximation. Computations were performed for Kr gas in the case of charging pressure of 0.216, 0.540 and 1.081 MPa at 295 K. As the Newton iterating procedure requires initial values not far away from the true solution, the solution of slightly lower percentage of ⁸⁵Kr was used for the initial values. The percentage of ⁸⁵Kr (and, hence heat generating rate) was thus increased gradually untill the concentration of ⁸⁵Kr was so high (–13% at 0.216 MPa) that convergent solution could not be obtained. With increasing the concentration of ⁸⁵Kr, flow pattern is changed from “ordinary” free convection like one generated when heated from below to a complexed pattern with several vortices in the upper part of the container. Similarity of flow fields was shown among various sets of charging pressure and concentration of ⁸⁵Kr. Reason of an onset of the vortical flows was also discussed based on the temperature distribution within the cavity.     

超临界二氧化碳在印刷电路板式换热器内的流动换热特性研究

印刷电路板式换热器（PCHE）是一种微通道换热器，具有换热效率高、耐高温、耐高压等优势，可广泛应用于海洋工程、核能、光热发电等领域。本文采用数值模拟的方法，计算了跨拟临界点超临界二氧化碳（SCO₂）在印刷电路板式换热器内的流动换热特性。结果表明：SCO₂流体温度达到拟临界温度时，流通截面内流体温度分布最均匀，因为此时流体的有效导热系数最大；SCO₂侧对流换热热阻在总热阻中占比最大，其次为导热热阻，水侧对流换热热阻最小；采用等效厚度法计算得到的导热热阻偏大；雷诺数越大，在拟临界温度附近换热强化的程度越大。     

Temperature distributions in liquid metals for turbulent flow in a horizontal pipe with free convection

A general method is developed for utilizing limited experimental data to obtain velocity or temperature distributions over the cross-section of a heated horizontal pipe, under conditions where distortion occurs due to superimposed free convection effects. The method is applied to available temperature data for five cases of constant-flux heating of liquid metals in turbulent flow, and the resulting isotherms and wall temperature distributions are presented. Substantial asymmetry is demonstrated for Reynolds numbers as high as 10⁵, with a corresponding distortion of the wall temperature distribution, and it is found that local heat transfer coefficients may be as low as 30% of predicted values.     

Heat Transfer in a Fluid with Internal Heat Generation Flowing through a Vertical Tube

This paper deals with heat transfer in a fluid, with uniformly distributed internal heat source, flowing upwards through a vertical tube. Measurements were made of the temperature distribution in both laminar and turbulent flow, and both with and without heat transfer at wall. Heat generation within the fluid was brought about by passing an electrical current through the working fluid, which was an aqueous solution of sodium chloride. The experimental results were compared with analytical calculations.

Free convection, which occurs and is superimposed on the movement by forced convection, flattens the fluid temperature distribution in laminar flow through thermally insulated vertical tube. In turbulent flow with heat transfer to wall, the temperature distribution near the wall is affected considerably by the outgoing heat flux.     

Comparison of natural convection flows under VHTR type conditions modeled by both the conservation and incompressible forms of the Navier-Stokes equations

This paper illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated specific force quantities and velocity and temperature distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present.     

10 mm垂直单管通道内超临界水传热弱化现象的实验与数值分析

超临界压力下的流体因拟临界点附近物性的剧烈变化,形成了非常奇特的传热现象。因流体密度突变,在低流量下会引起强烈的浮升力作用,对超临界流体的流动和传热均有极大影响。本工作通过实验获得10 mm单管内传热弱化现象的实验数据,并采用改进的低雷诺数湍流模型,使用数值方法模拟该传热弱化现象。计算结果表明,不同于以往传统的模型会高估壁面温度,改进的低雷诺数湍流模型能较好预测实验结果。数值模拟结果还揭示了浮升力对湍流剪切应力和速度分布的影响,进而引起传热弱化和传热恢复。