Wall function approach for boiling two-phase flows

One of the important goals of the NURESIM project is to assess and improve the simulation capability of the three-dimensional two-fluid codes for prediction of local boiling flow processes. The boiling flow is strongly affected by local mechanisms in the turbulent boundary layer near the heated wall. Wall-to-fluid transfer models for boiling flow with the emphasis on near-wall treatment are being addressed in the paper. Since the computational grid of the 3D two-fluid models is too coarse to resolve the variable gradients in the near-wall region, the use of wall functions is a common approach to model the liquid velocity and temperature profile adjacent to the heated wall.The wall function model for momentum, based on the surface roughness analogy has been discussed and implemented in the NEPTUNE_CFD code. The model has been validated on several upward boiling flow experiments, differing in the geometry, working fluid and operating conditions. The simulations with the new wall function model show an improved prediction of flow parameters over the boiling boundary layer. Furthermore, a wall function model for the energy equation, based on enhanced two-phase wall friction has been derived and validated.     

Influence of near-wall modelling on boiling flow simulation

The capability of the three-dimensional two-fluid codes to simulate the local boiling flow processes has been assessed. Boiling flow experiments of Roy et al. [Roy, R.P., Kang, S., Zarate, J.A., Laporta, A., 2002. Turbulent subcooled boiling flow—experiments and simulations, J. Heat Transfer 124, 73-93] and Lee et al. [Lee, T.H., Park, G.C., Lee, D.J., 2002. Local flow characteristics of subcooled boiling flow of water in a vertical concentric annulus. Int. J. Multiphase Flow 28, 1351-1368], both performed in annular vertical channels were used as an experimental benchmark data set. The boiling flow is strongly affected by local mechanisms in the boundary layer near the heated wall. In this paper, the influence of near-wall modelling on the distribution of flow parameters at flow boiling has been analyzed. A generic wall function model for 3D two-fluid codes, based on surface roughness analogy has been proposed instead of commonly used single-phase log-law model. The new model has been implemented in the code CFX-4.4. In general, better agreement of phase velocities with experimental data were obtained with the new model. Presented results show that the influence of nucleating bubbles on the near-wall velocity profile should be taken into account. The second goal of this paper is to compare the NEPTUNE_CFD simulations against CFX-4.4 results and experimental data.     

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.     

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow and application to fuel assembly analysis

High-thermal performance PWR (pressurized water reactor) spacer grids require both low-pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required.In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation Eddy Viscosity Models (EVM), especially the standard K-? model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional.The simulation of swirling flow generated by the mixing vanes plays an important role for the prediction of the CHF for the fuel assemblies. For this reason, according to [14] and [Mimouni et al., 2009b], rotation effects and RSTM model are more specifically addressed in the paper.Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with simpler geometries, the DEBORA case and the ASU-annular channel case. ASU-annular channel case has already been addressed in [14] and [Mimouni et al., 2009b].Then, a geometry closer to actual fuel assemblies is considered. It consists of a rectangular test section in which a 2 × 2 rod bundle equipped with a simple spacer grid with mixing vanes is inserted. The influence of the turbulence model on target variables linked to CHF limitation will be discussed. Moreover, the sensitivity to the mesh refinement will be particularly examined. The study of this case is a further step towards the modelling of the two-phase boiling flow in real-life grids and rod bundles.     

CFD analysis on subcooled boiling phenomena in PWR coolant channel

Eulerian two-fluid model coupled with wall boiling model was employed to calculate the three dimensional flow field and heat transfer characteristics in a hot channel with vaned spacer grid in PWR. The heat transfer from pellet-gap-cladding to coolant was also taken into account by a system coupled code MpCCI. The wall boiling model utilized in this study was validated by Bartolomei experiment data, and a good agreement can be observed. By solving the governing equation in a two-way coupled method, the distribution of temperature in the pellet-gap-cladding region and the distribution of temperature, void fraction and velocity of two-phase flow in coolant channel can be obtained. The influences of spacer grid and mixing vane on the thermal-hydraulic characteristics were analyzed. The heat transfer capacity was strongly improved by the spacer grid and mixing vane, while the flow resistance was also enlarged. Localized volume fraction of vapor phase decreased due to mixing vane, which will decrease the possibility of the departure from nucleate boiling (DNB) and increase the critical heat flux (CHF). By analyzing the temperature and void fraction at cladding outer surface, the critical regions where hot spot may occur were determined.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

水平管内气-液两相泡状流壁面切应力预测模型

水平管泡状流时气泡主要集中在管道的上部,在管下部只有少量的气泡.由于气泡的非均匀分布,壁面切应力沿周向变化.本文以水平管内气-液两相泡状流壁面切应力均相预测模型为基函数,在实验测量结果的基础上,建立了考虑气泡非均匀分布的水平管内气-液两相泡状流壁面切应力预测模型,预测模型能够反映不同工况下的壁面切应力沿周向的变化趋势,与实验测量结果比较,误差范围小于10%.     

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit, (II)

The authors have developed a measurement system which is composed of an ultrasonic velocity profile monitor and a video data processing unit in order to clarify its multi-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for multi-dimensional two-phase flow. In this paper, the measurement system was applied for bubbly countercurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. Next, turbulence intensity in a continuous liquid phase was defined as a standard deviation of velocity fluctuation, and the two-phase multiplier profile of turbulence intensity in the channel was clarified as a ratio of the standard deviation of flow fluctuation in a bubbly countercurrent flow to that in a water single phase flow. Finally, the distribution parameter and drift velocity used in the drift flux model for bubbly countercurrent flows were calculated from the obtained velocity profiles of both phases and void fraction profile, and were compared with the correlation proposed for bubbly countercurrent flows.     

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit, (III)

The authors have developed a new measurement system which consisted of an Ultrasonic Velocity Profile Monitor (UVP) and a Video Data Processing Unit (VDP) in order to clarify the two-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for two-dimensional two-phase flow. In the present paper, the proposed measurement system is applied to fully developed bubbly cocurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. In addition, the two-phase multiplier profile of turbulence intensity, which was defined as a ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow, were examined. Next, these flow characteristics were compared with those in bubbly countercurrent flows reported in our previous paper. Finally, concerning the drift flux model, the distribution parameter and drift velocity were obtained directly from both bubble and water velocity profiles and void fraction profiles, and their results were compared with those in bubbly countercurrent flows.     

压水堆子通道欠热沸腾数值验证及交混翼研究

为改善压水堆交混翼格架在欠热沸腾工况下的热工水力特性,以子通道为研究对象验证了所使用的欠热沸腾数值模型在不同工况下的有效性。基于已验证的数值模型,对含不同偏折角交混翼格架的子通道模型在不同工况下进行了两相流数值模拟,研究交混翼及其偏折角对子通道中两相流动、传热及气泡分布的影响。结果表明：交混翼在增大压降的同时明显强化了冷却剂的交混、降低了近壁面气泡份额、提高了换热效率,且在一定范围内偏折角越大影响越明显。相对较高的气泡份额将导致更大的压力损失、减弱冷却剂的交混、降低传热效率。当交混翼偏折角达25°时,继续增大其偏折角对降低近壁面气泡份额和提高传热效率的作用不再明显,反而造成压降的快速增大,因此建议其偏折角在25°左右。     

Two-phase flow in an annulus with a rotating inner cylinder (flow pattern in bubbly flow region)

The two-phase flow pattern in a concentric annulus with a rotating inner cylinder have been investigated experimentally. The observed flow patterns were dispersed bubbly, ring-form, single-spiral, double-spiral, triple-spiral flows and transition regions. When the rotational speed was at a relatively low level, the buoyancy effect of bubbles dominated the flow field and a dispersed bubbly flow was formed. On the other hand, when the rotational speed was at a high level, the vortex motion induced by the rotation dominated the flow field and ring-form and spiral flows were formed.     

Analysis of subcooled boiling flow with one-group interfacial area transport equation and bubble lift-off model

To enhance the multi-dimensional analysis capability for a subcooled boiling two-phase flow, the one-group interfacial area transport equation was improved with a source term for the bubble lift-off. It included the bubble lift-off diameter model and the lift-off frequency reduction factor model. The bubble lift-off diameter model took into account the bubble's sliding on a heated wall after its departure from a nucleate site, and the lift-off frequency reduction factor was derived by considering the coalescences of the sliding bubbles. To implement the model, EAGLE (elaborated analysis of gas-liquid evolution) code was developed for a multi-dimensional analysis of two-phase flow. The developed model and EAGLE code were validated with the experimental data of SUBO (subcooled boiling) and SNU (Seoul National University) test, where the subcooled boiling phenomena in a vertical annulus channel were observed. Locally measured two-phase flow parameters included a void fraction, interfacial area concentration, and bubble velocity. The results of the computational analysis revealed that the interfacial area transport equation with the bubble lift-off model showed a good agreement with the experimental results of SUBO and SNU. It demonstrates that the source term for the wall nucleation by considering a bubble sliding and lift-off mechanism enhanced the prediction capability for the multi-dimensional behavior of void fraction or interfacial area concentration in the subcooled boiling flow. From the point of view of the bubble velocity, the modeling of an increased turbulence induced by boiling bubbles at the heated wall enhanced the prediction capability of the code.     

Transient film boiling under transient conditions related to vapor explosion (effects of transient flow and fragmentation under a shock pressure)

Two fundamental phenomena are significant when a shock pressure interacts with the large scale coarse mixing state. One is an intensive flow and the other is the surface area enhancement due to the disintegration of the hot drops. The effects of these phenomena on the transient heat transfer and behavior of vapor film under a shock pressure are investigated. Transient heat transfer of film boiling from an electrically heated platinum ribbon 2.5 mm wide and 0.15 mm thick was measured immediately after passage of a shock pressure from 0.1 to 0.7 MPa. The heater was set horizontally in a vertical shock tube which was filled with vapor liquid bubbly mixture and kept initially in the film boiling state. That is, the heater corresponds to a typical hot drop and the bubbles around it correspond to the coarse mixture around the drop. The liquid was Freon-113 with an initial void fraction in the range from 0 to 3%. When the shock wave arrives at the heater, intensive transient flow occurs due to collapse of bubbles around the heater. First, the effects of the initial void fraction, the intensity of the shock and the heated wall temperature on the transient heat fluxes and collapse of the vapor film were investigated experimentally and analytically under the shock pressure. Compared with a heated wall in the liquid alone, the transient heat flux at the heated wall increases and the collapse of the vapor film becomes easier in the bubbly mixture due to the transient flow. Effects of surface enhancement during the fragmentation process on the heat transfer rate and transient behavior of vapor film are investigated analytically by application of the newly proposed surface stretch model. It is made clear when the surface area is increasing, the vapor film is apt to collapse and the transient heat transfer is enhanced by the surface stretch.     

Two-phase Flow Patterns in a Four by Four Rod Bundle

Air-water two-phase flow patterns in a four by four square lattice rod bundle consisting of an acrylic channel box of 68mm in width and transparent rods of 12mm in diameter were observed by utilizing a high speed video camera, FEP (fluorinated ethylene propylene) tubes for rods, and a fiberscope inserted in a rod. The FEP possesses the same refractive index as water, and thereby, whole flow patterns in the bundle and local flow patterns in subchannels were successfully visualized with little optical distortion. The ranges of gas and liquid volume fluxes, {J_G} and {J_L}, in the present experiments were 0:1 ? {J_L} < 2:0 m/s and 0:06 < {J_G} < 8:85 m/s, which covered typical two-phase flow patterns appearing in a fuel bundle of a boiling water nuclear reactor. As a result, the following conclusions were obtained: (1) the region of slug flow in the {J_G}-{J_L} flow pattern diagram is so narrow that it can be regarded as a boundary between bubbly and churn flows, (2) the boundary between bubbly and churn flows is close to the boundary between bubbly and slug flows of the Mishima and Ishii's flow pattern transition model, and (3) the boundary between churn and annular flows is close to the Mishima and Ishii's model.     

A mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model

In this paper, we present an analytical methodology to predict forced convective CHF (Critical Heat Flux) for DNB (Departure from Nucleate Boiling) type boiling transition that occurs inside of uniformly heated round tubes. Axial directional two-phase flow analysis was conducted based on one-dimensional two-fluid model and typical constitutive models. At the same time, the radial directional distribution of void fraction at any axial location was calculated based on the bubble diffusion model, which was coupled with two-phase turbulence model for boiling bubbly flow. The calculated void fraction showed the wall peak distribution, and was compared with experimental data, which was derived from subcool boiling experiments. IPNVG (Incipient Point of Net Vapor Generation), which means the starting point of two-phase flow analysis, was also investigated well, since it was revealed that IPNVG had a significant influence on CHF prediction. By using this methodology for calculating radial directional void fraction distribution, we carried out CHF prediction for water on the assumption that DNB would occur when the local void fraction near the heated wall exceeds a critical value. The predicted CHF agreed well with experimental data, and the accuracy was within about 20%.     

内螺纹管临界热流密度预测与数值计算

基于壁面汽泡壅塞理论,针对近临界压力区两相流动沸腾的偏离泡核沸腾(DNB)现象,对垂直上升内螺纹管的DNB型临界热流密度(CHF)进行了数值计算研究。以内螺纹管为分析对象改进已有的汽泡壅塞模型,计算了汽泡层区与主流区的极限传递质量流量、湍流速度分布、汽泡层区临界截面含气率等本构关系,汽泡脱离直径的计算考虑了汽泡接触角的影响。本文模型还根据大量CHF实验数据拟合得到了新的α_b关联式。最后,基于Fortran语言编制了CHF的理论预测数值模型程序,研究分析了压力、质量流速、热平衡干度及进口欠焓对CHF的影响,并根据CHF查表值对本文模型进行评估,同时将实验得到的内螺纹管CHF数据与采用Bowring模型、Katto模型、Shah模型和本文模型计算的CHF进行比较,发现本文模型的误差最小,与实验值吻合结果较好,说明本文模型能较好地对垂直上升内螺纹管DNB型CHF进行预测。