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.     

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.     

Integral boundary layer heat transfer modeling for Tehran Research Reactor

In the present work the validity of applying the Boussinesq approximation in the analysis of natural convection heat transfer along nuclear fuel plates with large coolant channel aspect ratios is evaluated. The Boussinesq approximation is introduced into the integral boundary layer equations governing the system to describe the velocity and temperature distributions of the coolant in the cooling channels. The fuel plate temperature is related to the adjacent coolant fluid temperature by a fundamental law in conduction heat transfer. Air and water are considered as fluids. The coolant flow is assumed to be fully developed which is a convenient assumption for coolant channels having large aspect ratios. Obtained results indicate that the Boussinesq approximation is merely applicable over a limited range of coolant channel outlet fluid temperatures. The use of this approximation produces conservative estimation of the critical plate power for air flow and non-conservative estimation of the critical plate power for water flow.     

Heat transfer effects on flow past an impulsively started semi-infinite vertical plate with uniform heat flux

An implicit finite-difference technique is employed to derive a solution to the flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with uniform heat flux. Transient and steady-state velocity and temperature profiles, the local and average skin-friction and the Nusselt number are shown graphically. The velocity profiles at small values of time t are shown to agree with theoretical solution of the flow past an impulsively started infinite vertical plate with uniform heat flux. The effect of different parameters Pr (the Prandtl number) and Gr (the Grashof number) are studied. It is found that the number of time steps to reach steady-state depends strongly on Grashof number.     

Thermodynamic’s Second Law Analysis for Laminar Non-Newtonian Fluid Flow

In this paper, the entropy generation of a non-Newtonian fluid such as Tho₂ inside a circular channel with constant surface temperature has been investigated. The pressure gradient along the pipe line, the difference between the dimensionless inlet wall temperature and fluid temperature and modified Stanton number are the key elements to calculate the entropy generation for three different non-Newtonian fluids. Also the variation of the dimensionless entropy generation and the pumping power to heat transfer rate ratio is calculated for two different cases, the first case involves fixed pipe length and variable inlet temperature and the second case considers fixed fluid inlet temperature and variable pipe length.     

Analysis and Optimization Laminar Viscous Flow Through a Channel

Optimizing of laminar viscous flow through a pipe by two dimensionless values is investigated analytically. Dimensionless entropy generation and pumping power to heat transfer rate ratio are used as basis for constant viscous and the temperature dependence on the viscosity. For this matter we calculate entropy generation and pumping power for a fully developed in a pipe subjected to constant wall temperature for either constant viscosity and the variable viscosity. The variation entropy generation increase along the pipe length for viscous fluid is drawn, either the variation summation dimensionless entropy generation and the pumping power to heat transfer rate ratio are varying the fluid inlet temperature for fixed pipe length and are varying pipe length for fixed fluid inlet temperature are drawn. For low heat transfer conditions the entropy generation due to viscosity friction becomes dominant and the dependence of viscosity with the temperature becomes essentially important to be considered.     

The attenuation of temperature oscillations by liquid metal boundary l layers

This paper is concerned with one aspect of the problem of predicting the endurance of components subject to thermal fatigue in liquid metal cooled reactors: the extent to which oscillations in fluid temperature are transmitted to metal surfaces, such as the above-core structure. A solid plate in contact with a layer of stagnant fluid, in which temperature oscillations are imposed at a given distance from the plate, is first considered, and then transmission through a laminar boundary layer developing over the plate surface.     

MHD flow past a steadily moving infinite vertical porous plate with constant heat flux

A study of the flow of an electrically conducting fluid past a steadily moving vertical infinite plate is presented. It is assumed that there is a constant heat flux and constant suction at the plate. Presence of induced magnetic field is also taken into account. The velocity profiles, the temperature profiles, the induced magnetic field, the skin-friction, the Nusselt number and the current density are shown on graphs. The results are discussed.     

压水堆下腔室流量分布数值分析

建立了压水堆下腔室流场的三维数值计算模型,计算了不同环腔厚度和环腔内冷却剂速度条件下,下腔室内冷却剂的流场,分析了环腔厚度和环腔内冷却剂速度对下腔室流向堆芯的流量分布的影响。入口速度不同或环腔厚度不同,在下腔内冷却剂流动形成漩涡的位置、大小和流动速度均会发生改变,导致通过流量孔板通孔的流量分布不同。入口速度较低时,流量孔板上所有通孔的流量分布比较均匀,在平均值附近波动,流量最高的通孔小组出现在边缘处;入口速度较高时,流量明显地呈现出中心高边缘低的特点。通孔小组的流量最大值随着环腔厚度增加由孔板的中心向边缘移动。     

Effect of Negative Ion Parameters on Sheath Formation Criterion in Electronegative Plasmas

Using a fluid model for three types of particles, the plasma-sheath formation criterion has been analyzed in collisional electronegative plasma, and the effects of the negative ion temperature and density are examined on the positive ion transition velocity. It is shown that in the collisional sheath, there will be an allowable interval for the positive ion velocity between two upper and lower limits as the plasma-sheath formation criterion; by increasing the mean temperature of the negative charge carriers, this velocity interval decreases. To confirm the correction of the allowable interval, the plasma sheath equations are numerically solved, and the negative ion temperature effect for example, is examined on the sheath formation.     

Entropy generation minimization (EGM) to optimize mass flow rate in dual channel cable-in-conduit conductors (CICCs) used for fusion grade magnets

Dual channel cable-in-conduit conductors (CICCs) used in tokamaks such as International Thermonuclear Experimental Reactor (ITER) consist of annular channel packed with superconducting strands and a clear central channel separated by a spiral from the annular channel. Supercritical helium (SHe) operating at 4.5 K and 0.5 MPa is used for forced convective cooling of CICC. Pressure drop is inevitable in the process of forced convective cooling, leading to the development of velocity gradients and temperature gradients. These velocity gradients and thermal gradients result in entropy generation in CICCs.The present work aims at estimating volumetric rate of entropy generation (EG) in dual channel CICC. Subsequently, entropy generation minimization (EGM) technique is used to find optimum mass flow rate at which volumetric rate of EG is minimum. Pumping power and heat transfer corresponding to minimum rate of EG are also calculated. Computational fluid dynamics (CFD) is used as a tool to estimate EG as the analytical solution for turbulent forced convective flows requires inaccurate simplifications. A three dimensional model of dual channel CICC is developed in GAMBIT-2.1 and solved using a compatible solver FLUENT-6.3.26. The annular region of CICC is assumed to be porous and the central channel is assumed as clear region for EG analysis using CFD. The pressure gradients and heat transfer coefficient estimated from the simulations are validated against relevant experimental results available in the literature. The effect of mass flow rate on volumetric rate of EG in turbulent forced convective flow is studied using CFD.     

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.     

An exact solution for the moving boiling boundary problem

An exact transient solution of the fluid velocity and temperature fields in a one-dimensional incompressible flow within a non-uniformly heated channel is presented. The first order partial differential equations for mass and energy conservation governing this problem are solved using Laplace transform technique. An analytical expression for the boiling boundary (BB) location as a function of time is derived from the temperature field solution when the saturation temperature is inserted. Results obtained reveal the interesting behavior of the temperature field and BB in space and time due to a step change in the fluid inlet mass flow rate.     

基于Non-Boussinesq模型的多流体域高温差乏燃料容器的自然对流传热特性研究

基于Boussinesq模型和全浮力模型原理,建立了高温差环境下Non-Boussinesq多流体域自然对流模型,通过对比高温差封闭空腔自然对流实验结果和预测结果,研究了Boussinesq模型、全浮力模型和Non-Boussinesq模型在单流体域和多流体域高温差环境下对流速和温度的预测能力。结果表明,单流体域下Non-Boussinesq模型和全浮力模型预测的流速和温度符合实验结果,平均预测误差小于9%;Boussinesq模型在高温差环境下对流速的预测精度较低;全浮力模型不能同时保证多流体域获得合理的流场分布;Non-Boussinesq模型能有效克服Boussinesq、全浮力模型的缺点;自然对流模型选取主要会影响内外部气体流速的预测,对容器内外部温度的预测影响较小。本研究建立的数值预测方法能够用于高温差环境下其他多流体域的自然对流的预测。      

入口速度比对同轴喷射流三维温度振荡影响的实验研究

实验测量同轴喷射流模型三维温度场和二维速度矢量场,分析不同入口速度比对三维温度振荡的影响。实验结果表明：R<1时,冷热流在底部完成了混合行为,平均温度不呈轴对称分布,而R≥1时,呈轴对称分布,但流体瞬态温度不呈轴对称分布。随着R的增加,冷流随高度增加温度上升的梯度减小,而热流温度下降的梯度则增大;R>1时,流场温度振荡强度小于R≤1的,其强温度振荡发生在冷热流之间和热流与环境流之间的区域。不同R下,温度振荡主要频率均分布在7Hz以内。     

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H₀ at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {−θ′(0)} are entered in tables. We observe that both ƒ′(0) and {−θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).     

双钩波形板汽水分离器疏水钩优化研究

为提高双钩波形板汽水分离器的分离性能，采用计算流体力学方法建立波形板内的两相流动模型，并对不同结构疏水钩的波形板汽水分离器进行研究。通过数值计算得到了波形板内的速度云图和液滴运动轨迹，并分析了不同进口速度下疏水钩结构对压降和分离效率的影响。结果表明：大部分液滴在前两级通道被分离，进口速度为0.922 m/s时其质量份额可超过50%；疏水钩通过影响流场的局部流速和湍流强度进而影响压降和分离效率，疏水钩对液滴的直接拦截作用有利于提高分离效率。综合考虑分离效率和压力损失获得了综合性能良好的双钩波形板汽水分离器结构型式。     

Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable flat plate with thermal convective surface boundary condition,temperature dependent viscosity and thermal conductivity

We study a steady laminar 2-D MHD viscous incompressible flow over a permeable flat plate with thermal convective boundary condition and radiation effects. The viscosity and thermal conductivity of fluid are assumed to vary linearly with temperature. Similarity representation of the governing partial differential equations is obtained via group method. Similarity equations are then solved numerically by implicit finite difference technique. Effects of convective heat transfer parameter (b), radiation parameter (R,) magnetic field parameter (M), the thermal conductivity parameter (S), suction parameter (fw), Prandtl number (Pr) and Schmidt number (Sc) on the dimensionless axial velocity, temperature, concentration, wall temperature, the rate of heat transfer and the rate of mass transfer are investigated. Good agreement is found between the numerical results of the present paper with published result for special case.     

非稳态条件下平板通道内层流速度分布研究

针对平板通道内非稳定条件下层流的速度分布特点及阻力特性进行了理论和实验研究。基于非稳态条件下平板通道内的数学模型,分析了初始速度分布、压力梯度变化率、加（减）速时间对瞬时速度分布的影响。结果表明：非稳态层流的速度分布特点与通道尺寸、流体性质、压力梯度变化率和加速时间有关;相同截面平均流速条件下,加速情况下的中心流体速度小于稳态的,且加速流动使沿程流动损失增加,减速流动则恰好相反,实验验证结果与理论分析结果符合良好。