Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver

The application of the generalized Roe scheme to the numerical simulation of two-phase flow models requires a fast and robust computation of the absolute value of the system matrix. In several models such as the two-fluid model or a general multifield model, this matrix has a non-trivial eigenstructure and the eigendecomposition is often ill conditioned. We give a general algorithm avoiding the diagonalization process. It is based on an iterative approach, but turns out to be an exact computation when the eigenvalues are real. The knowledge of the characteristic polynomial gives us an easy access to the eigenvalues but however, the iterative scheme can be used with only estimates of the eigenvalues, using for example Gershgorin’s disk localization. We finally show some numerical results of two-fluid model simulations involving interfacial pressure and a virtual mass force model.     

垂直上升矩形流道内气液两相流流型图的数值模拟

两相流流型在分析换热、流动不稳定性以及临界热流密度方面具有基础性作用.本文基于VOF(Volume of Fluid)多相流模型,对垂直上升矩形流道内气液两相流动进行数值模拟,表观气速0.1～110 m/s,表观液速0.1～3.2 m/s.得到了流道内气液两相流的主要流型:泡状流、弹状流、搅混流和环状流,分析了流道内截面含气率分布与流型的对应关系,以及截面含气率与气液两相流容积含气率的关系;分析了各种流型下的压降分布特性,并绘制了基于气液表观动能通量的不同流量下气液两相流的流型图,直观的表示出各种流型的分布区域及各流型间的流型转换边界,与已发表文献的实验结果对比符合较好.     

Application of AUSM schemes to multi-dimensional compressible two-phase flow problems

This paper dicusses the extension of AUSM-type schemes to the solution of multidimensional compressible two-phase flow problems. We consider their first and second order approximations and several multidimensional problem have been analysed in order to illustrate the behaviour and performance of the schemes. Both two-fluid mixtures of water and air and phase change processes between water and steam have been considered. Thermodynamic variables have been calculated taking into account either analytical equations of state (water and air mixtures) or tabulated equations of state (water and steam mixtures). Non-conservative terms in the two-fluid system of equations have been discretized centrally. In addition, gravity forces, interfacial friction, interfacial heat and mass transfer, etc., have been taken into account using a point-wise evaluation.     

Numerical effects of the semi-conservative form of momentum equations for multi-dimensional two-phase flows

Some of the thermal hydraulics codes for multi-dimensional two-phase flow analysis use the non-conservative form of momentum equations for numerical convenience. From a mathematical point of view, these equations are equal to those in the conservative form. But, numerical integration of the non-conservative momentum equations over a control volume results in different solution characteristics, which may cause inaccurate solutions under some two-phase flow conditions. In this paper, a semi-conservative form of the momentum equations is suggested which is close to the conservative form but still maintains the feature of the non-conservative form. The numerical results of the semi-conservative and the non-conservative forms are compared against analytical solutions and the solutions of the FLUENT code that uses the conservative form. The results clearly showed that the semi-conservative form of the momentum equations provides better solutions than the non-conservative form, especially for heterogeneous two-phase flows.     

Steam-generator simulation with non-equilibrium two-phase flow models

The steam-generator model initially developed was a five-equation simulation of the transient behaviour. The present study extends the earlier work by using six field equations to simulate the two-phase flow conditions in the secondary side of the steam generator. Two versions of the six-equation model have been tested. No numerical instabilities were observed. The transient predictions with the two versions were almost identical for the PWR data used in this study.     

Numerical calculations for two-phase flow analyses in pin bundles

Two-phase flow equation systems, in which equations are defined for each phase, are discussed for use in analyzing coolant behaviors in LMFBR pin bundles. These equation systems have not yet consolidated, because of theoretical and experimental difficulties and complexities.One of the problems is the equation systems' stability. This paper shows the stability for the low Reynolds number (O(1)) system, using a one dimensional linear equation system. Based on this fact, a two-phase flow equation system is numerically solved by using the subchannel method for 19- and 37-pin bundles. The calculational examples are LOF and TOP conditions with/without the blockage, and fission gas release.     

Numerical research on oscillation of two-phase flow in multichannels under rolling motion

Two-phase flow instability and dynamics of a parallel multichannels system has been theoretically studied under periodic excitation induced by rolling motion in the present research. Based on the homogeneous flow model considering the rolling motion, the parallel multichannels model and system control equations are established by using the control volume integrating method. Gear method is used to solve the system control equations. The influences of the inlet, upward sections, heating power and rolling amplitudes on the flow instability under rolling motion have been analyzed. The marginal stability boundary (MSB) under the rolling motion condition is obtained. The unstable regions occur in both low and high equilibrium quality and inlet subcooling regions. The multiplied period phenomenon occurs in the high equilibrium quality region and the chaos phenomenon appears on the right of MSB. The concept of stability space is presented.     

Type of flow, pressure drop, and critical heat flux of a two-phase sodium flow

Little is known about the two-phase pressure loss, the flow pattern, and the critical heat flux conditions for boiling sodium under forced convection. The specific thermohydraulic properties of sodium prohibit extrapolation to sodium of experimental data obtained for other liquids. Therefore, some new test series were carried out in a sodium loop with an induction heated test section of 9 mm inner diameter and 200 mm heated length. The two-phase pressure loss and the film thickness were measured up to the critical cooling conditions. The experimental results are compared with values predicted by known models on annular flow and annular mist flow, respectively. Satisfactory predictions of the flow pattern and the critical heat flux conditions could only be obtained using the measured two-phase pressure losses.     

Fluid-to-fluid modeling of two-phase flow critical heat flux in horizontal helically coiled tubes

The new similarity laws for fluid-to-fluid modeling of two-phase flow critical heat flux (CHF) in horizontal helically coiled tubes were derived based on the dimensional analysis and similarity theory considering the effect of the geometrical parameters on CHF. A generalized factor D_n was introduced to the new similarity laws, and all the new dimensionless numbers were derived from the classical theorem of Buckingham π for dimensional analysis. The obtained dimensionless parameter sets were a reasonable extension to Ahmad's compensated distortion model, which may be considered as a special case of the new dimensionless parameter sets when the variable n is equal to unity. Based on the experimental data, the specific similarity numbers were determined for CHF phenomena in horizontal helically coiled tubes. A new equivalent characteristic parameter D_e-helix was developed, which could reflect the influence of complex flow channels on the occurrence of CHF. The equivalent characteristic parameter consists of the essential geometrical parameters of tubes and the fluid thermophysical properties. The new fluid-to-fluid modeling methods were proposed for CHF of R134a-water in horizontal helically coiled tubes, which could be used readily to derive the CHF data of water through the CHF data of R134a at the corresponding experimental conditions.     

蒸汽发生器二次侧两相流传热特性数值研究

以AP1000核电站蒸汽发生器为原型,建立蒸汽发生器二次侧"平均通道"模型,利用计算流体动力学软件ANSYS CFX,基于相界面模型对蒸汽发生器二次侧两相流流动和沸腾换热过程进行研究。结果表明:数值模拟计算方法能准确模拟蒸汽发生器二次侧汽液两相流沸腾和传热过程;满负荷运行时,流体由预热区经过泡核沸腾区过渡到稳定沸腾区,含汽率和传热系数沿流动方向逐渐增大,出口含汽率与该型号蒸汽发生器设计值符合较好,平均传热系数的模拟结果和JensLottes经验关联式的预测值基本一致。     

Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena

For the investigation of stratified two-phase flow, two horizontal channels with rectangular cross-section were built at Forschungszentrum Dresden-Rossendorf (FZD). The channels allow the investigation of air/water co-current flows, especially the slug behaviour, at atmospheric pressure and room temperature. The test-sections are made of acrylic glass, so that optical techniques, like high-speed video observation or particle image velocimetry (PIV), can be applied for measurements. The rectangular cross-section was chosen to provide better observation possibilities. Moreover, dynamic pressure measurements were performed and synchronised with the high-speed camera system.CFD post-test simulations of stratified flows were performed using the code ANSYS CFX. The Euler–Euler two fluid model with the free surface option was applied on grids of minimum 4 × 10⁵ control volumes. The turbulence was modelled separately for each phase using the k–ω-based shear stress transport (SST) turbulence model. The results compare very well in terms of slug formation, velocity, and breaking. The qualitative agreement between calculation and experiment is encouraging and shows that CFD can be a useful tool in studying horizontal two-phase flow.     

Numerical simulation of lateral phase distribution in turbulent upward bubbly two-phase flows

New constitutive models for the interfacial forces acting on bubbles were developed for accurately predicting the lateral phase distribution in turbulent bubbly two-phase flow in vertical channels. Several experimental measurements have revealed that the lateral void profile in bubbly two-phase flow varies from the void peaking near the wall to the almost flat distributions as the liquid velocity increases. However, within the authors' knowledge, the effect of liquid velocity on the void profile has not been successfully predicted by the existing models; this would indicate the strong limitation of the existing multidimensional two-phase flow models. In view of these, the validity of the present constitutive models was tested in varied conditions of the liquid velocity as well as the bubble size. Since several assumptions were required in the models mainly due to the insufficient knowledge of the bubble motion, further improvements should still be needed. Nevertheless, the predicted lateral phase distributions were found to be in reasonably good agreement with available experimental data. It is hence expected that the present constitutive models can effectively be used in the practical applications and also be the base of the more sophisticated ones.     

Numerical simulation of secondary flow in bubbly turbulent flow in sub-channel

Secondary flow in bubbly turbulent flow in sub-channel was simulated by using an algebraic turbulence stress model. The mass, momentum, turbulence energy and bubble diffusion equations were used as fundamental equation. The basis for these equations was the two-fluid model: the equation of liquid phase was picked up from the equation system theoretically derived for the gas-liquid two-fluid turbulent flow. The fundamental equation was transformed onto a generalized coordinate system fitted to the computational domain in sub-channel. It was discretized for the SIMPLE algorithm using the finite-volume method. The shape of sub-channel causes a distortion of the computational mesh, and orthogonal nature of the mesh is sometimes broken. An iterative method to satisfy a requirement for the contra-variant velocity was introduced to represent accurate symmetric boundary condition. Two-phase flow at a steady state was simulated for different magnitudes of secondary flow and void fraction. The secondary flow enhanced the momentum transport in sub-channel and accelerated the liquid phase in the rod gap. This effect was slightly mitigated when the void fraction increased. The acceleration can contribute to effective cooling in the rod gap. The numerical result implied a phenomenon of industrial interest. This suggested that experimental approach is necessary to validate the numerical model and to identify the phenomenon.     

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.     

基于图像法的气液两相稀疏泡状流气泡参数分析

采用图像法对垂直上升管气液两相流中稀疏上升气泡进行实验测量研究。该方法使用高速摄像机拍摄气泡运动图像,经图像处理后,提取气泡的特征参数,分别绘制稀疏气泡上升过程中速度变化曲线和单个气泡上升过程中面积变化及形心位置变化曲线,分析气泡参数,总结运动规律。实验结果表明,采用图像法可以很好地完成对气泡参数的分析。     

基于修正AIAD模型的稳压器波动管CCFL现象数值模拟

现阶段采用的第三代核电技术广泛引入非能动自动卸压系统,提高了反应堆的安全性,但是破口事故后可能引发的气液相向流动限制现象(Counter-Current Flow Limitation,CCFL)会增加稳压器波动管自身的安全风险,因此对稳压器波动管中CCFL现象的研究非常重要。本文采用自由表面模型结合修正的AIAD(Algebraic Interfacial Area Density)模型对稳压器波动管CCFL现象进行了三维数值模拟。通过与之对应的实验现象比较,结果分析表明:所使用的模型可以正确模拟该现象下汽液两相的相间作用;并通过对气相流速和倾斜角的敏感性分析,可以得到如下结论:阻塞的推进主要受初始气相流速和稳压器波动管倾斜角的影响,在靠近管道起始点的位置主要受初始气相流速影响,远离管道起始点的位置主要受倾斜角的影响。     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.