Experimental study on the condensation of supersonic steam jet submerged in quiescent subcooled water: Steam plume shape and heat transfer

The condensation of supersonic steam jet submerged in the quiescent subcooled water was investigated experimentally. The results indicated that the shape of steam plume was controlled by the steam exit pressure and water temperature. Six different shapes of steam plume were observed under the present test conditions. Their distribution as a function of the steam exit pressures and water temperatures was given. As the steam mass velocity and water temperature increase, the measured maximum expansion ratio and dimensionless penetration length of steam plume were in the ranges of 1.08–1.95 and 3.05–13.15, respectively. The average heat transfer coefficient of supersonic steam jet condensation was found to be in the range of 0.63–3.44 MW/m²K. An analytical model of steam plume was found and the correlations to predict the maximum expansion ratio, dimensionless penetration length and average heat transfer coefficient were also investigated.     

Experimental investigation of over-expanded supersonic steam jet submerged in quiescent water

This study was designed to determine the behaviour of an over-expanded supersonic steam jet in quiescent water. Only two shapes of steam plume were observed and an analytical model was constructed. The axial and radial temperature distributions were measured in the steam plume and in the surrounding water. The flow pattern and temperature distributions were influenced mainly by steam mass flux and water temperature. The results confirmed the occurrence of compression and expansion waves in the steam plume, and indicated that the temperature distributions reflected the steam plume shapes. The axial temperature distributions in the forepart of the steam plume were independent of water temperature. Empirical correlations were found that predicted the dimensionless axial and radial temperatures of the turbulent jet region. Moreover, prediction of the steam plume length by the dimensionless axial temperature showed good agreement with the experimental results.     

Condensation induced water hammer: Numerical prediction

Contact of steam and subcooled water in a pipe or a pressurized vessel leads to intensive condensation accompanied by a pressure drop in the volume of condensing steam and an acceleration of the surrounding water mass towards the steam volume, which can result in a severe water hammer and plant damage. This phenomenon is known as the condensation induced water hammer (CIWH). A one-fluid model is developed for the prediction of pressure surges during CIWH. It is shown that the reliable prediction of pressure surges strongly depends on the calculation of the condensation rate, transient friction and the water column–steam interface tracking. Due to the lack of the CIWH condensation models, a new approach is derived. The one-fluid model predictions of pressure surges are compared with available measured data from a CIWH experimental facility and acceptable agreements are obtained. In addition, the ability of the developed model to simulate the water cannon event, which takes place during the steam drainage into the pool of subcooled water, is demonstrated. Experimentally observed considerable scattering of test data under the same conditions is related to the condensation rate and its dependence on the entrained droplets–steam interfacial area concentration in the vicinity of the water column head.     

Experimental and numerical analysis of steam jet pump

Steam jet pump is the best choice for pumping radioactive and hazardous liquids because it has no moving parts and so no maintenance. However, the physics involved is highly complicated because of the mass, momentum and energy transfer between the phases involved. In this study the characteristics of SJP are studied both experimentally and numerically to pump water using saturated steam. In the experimental study the static pressure, temperature along the length of the steam jet pump and the steam and water flow rates are recorded. The three dimensional numerical study is carried out using the Eulerian two-phase flow model of Fluent 6.3 software and the direct-contact condensation model developed previously. The experimental and CFD results, of axial static pressure and temperature, match closely with each other. The mass ratio and suction lift are calculated from experimental data and it is observed that the mass ratio varies from 10 to 62 and the maximum value of suction lift is 2.12 m under the conditions of the experiment.     

Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media

In this article, the numerical simulations for one-dimensional three-phase flows in fractured porous media are implemented. The simulation results show that oil displacement in matrix is dominated by oil–water capillary pressure only under certain conditions. When conditions are changed to decrease the amount of water entering into the fractured media from the boundary of the flow field, water in fracture may be vaporized to superheated steam. In these cases, the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture, which results in oil flowing from matrix to fracture. Assuming that oil is wetting to steam, the matrix steam–oil capillary pressure will decrease the matrix oil-phase pressure as the matrix steam saturation increases. After the steam–oil capillary pressure finally exceeds the pressure difference due to the appearance of superheated steam in fracture, the oil displacement in matrix will stop. It is also shown that variations of the water relative permeability curve in matrix do not result in different mechanisms for oil displacement in matrix. The simulation results suggest that the amount of liquid water supply from the boundary of flow field fundamentally influence the mechanisms for oil displacement in matrix.     

Analytical model of steam zone propagation in porous media

Steam injected into oil-bearing porous media forms a steam zone which propagates in three-dimensional space. The injected steam forms the condensation front bounding the seam zone. Simultaneous mass and the energy transfers take place through this moving boundary, between the rocks and fluids inside and outside the steam zone. The energy transfer is by conduction and convection. A new mathematical model describes the propagation growth of the steam zone subject to initial and boundary conditions, and is applicable in a general case of heterogeneous steam zone of arbitrary geometry. The model is based on the simultaneous analytical solution of the coupled overall mass and energy balance equations for a multi-phase steam zone, and is presented here for the first time. The resulting nonlinear integral equation does not have an analytical solution for a general case. The exact solution is found for a cylindrical homogeneous steam zone. For a special case of a one-dimensional, two phase steam zone, this solution shows excellent agreement with available experimental data.     

The dispersal processes within the tide‐modulated Changjiang River plume,China

The dispersal processes of the tide‐modulated Changjiang River plume, China, are studied by using a three‐dimensional hydrodynamical module of the COHERENS (A COupled Hydrodynamical–Ecological model for REgional and Shelf Seas). The model is driven by the river discharge and the M₂ tidal constituent. Modelled results show: (1) the fresh water, which forms the Changjiang River plume expanding southeastwards, is discharged mostly into the North Channel, the North Passage, and the South Passage; (2) the larger horizontal gradient outside the North Channel and the North Passage forms a strong plume front; (3) the Changjiang River plume is homogeneous vertically, and dispersing gradually within the computational domain, with an averaged propagating rate of 3.38 km/day, while the plume front is surface‐to‐bottom type, and trapped between ?10 and ?18m isobaths; and (4) both the plume length and the plume front intensity vary periodically. The maximum plume length occurs about 2 h after low slack water and the minimum plume length during high slack water. The maximum plume front intensity occurs during high slack water and the minimum plume front intensity during low slack water. Copyright © 2007 John Wiley & Sons, Ltd.     

Dimensional analysis of thermal stratification in a suppression pool

Due to complexity of direct contact condensation (DCC), it is difficult to predict the thermal hydraulic phenomenon in a suppression pool (SP) of LWRs. Especially, the momentum, induced at condensation interfaces, depends on several interrelated parameters such as the steam mass flux, subcooling, and the diameter of the injection nozzle. Complicated interaction of those parameters creates difficulties in developing a comprehensive analytical model, which applicable to various conditions. To investigate the criteria of thermal stratification created by DCC, experiments were performed using a downsized suppression pool. Time resolved temperatures were acquired by vertically aligned thermocouples. Additionally, steam bubbles were visualized by a high speed camera in order to examine bubble shapes according to the mass flux and subcooling. Both steam bubble frequency and amplitude were analyzed for different DCC regimes. Finally, Richardson number was chosen as a suitable parameter for the dimensional analysis of experimental results. Corresponding velocity at far field in synthetic jet theory was employed to calculate Richardson number. The criteria for the occurrence of the thermal stratification were clearly determined according to the Richardson number.     

Calculation of spray-type steam evaporator

For the understanding of the different thermodynamic and gasdynamic processes in a spray-type evaporator, a theory is developed to calculate the two phase flow with change of phase with any change of evaporator cross section. Firstly the calculation model for the problem is given. The control volume is divided into three control volumes: For water droplets in preheating phase, for water droplets in saturation state, and for the steam phase. The fundamental equations were formulated under different assumptions for the steam- and water control volumes. After the transformation of the fundamental equations, they are solved numerically. The number of drop groups and the number of drops in every group are determined. The distribution of the drop spectrum, the end steam wettness, and the steam temperature along the evaporator are calculated. The numerical results have shown, that the steam temperature, and the steam wettness decrease very strongly at the beginning of the evaporator. This is a result of the high degree of steam superheat, and due to the high steam wettness. After the initial strong decrease of steam temperature and steam wettness, it is varied by a smaller rate along the evaporator, so that it lead to a strong increase of the evaporator length, especially when small values for end steam wettness and end steam superheat are prescribed at the evaporator outlet.     

Tabular method of estimating nucleating steam flows

In the pressure range 0.04–1 bar the time necessary for steam to revert from a series of initial degress of supercooling to thermodynamic equilibrium and the resulting fluid parameters have been tabulated. Application to practical flow conditions is discussed.     

Experimental study on the direct contact condensation of the steam jet in subcooled water flow in a rectangular channel: Flow patterns and flow field

Direct contact condensation (DCC) of steam jet in subcooled water flow in a channel was experimentally studied. The main inlet parameters, including steam mass flux, water mass flux and water temperature were tested in the ranges of 200–600 kg/(m² s), 7–18 × 10³ kg/(m² s), 288–333 K, respectively. Two unstable flow patterns and two stable flow patterns were observed via visualization window by a high speed camera. The flow patterns were determined by steam mass flux, water mass flux and water temperature, and the relationship between flow patterns and flow field parameters was discussed. The results indicated that whether pressure or temperature distributions on the bottom wall of channel could represent different flow patterns. And the position of pressure peak on the bottom wall could almost represent the condensation length. The upper wall pressure distributions were mainly dependent on steam and water mass flux; and the upper wall temperature distributions were affected by the three main inlet parameters. Moreover, the bottom wall pressure and temperature distributions of different unstable flow patterns had similar characteristics while those of stable flow patterns were affected by shock and expansion waves. The underlying cause of transition between different flow patterns under different inlet parameters was reflected and discussed based on pressure distributions.     

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed.     

Effect of the nonmonotonic temperature dependence of water density on free convection from a linear heat source

This paper presents the results of experimental studies of free convection from a heated wire in water for the two cases where the water temperature is higher or lower than the temperature at which water has maximum density. It is shown that, in the first case, the convective plume formed by heating rises, reaching the free surface. In the second case, the height of the convective plume is limited because water in the plume head reaches maximum density and becomes heavier than the surrounding water.     

An experimental study of steam injection into a uniform water flow through porous media

An experimental study of steam injection into a porous media was carried out in a 2-dimensional plane porous channel. The steam was injected into a uniform downward water flow in a vertically aligned porous channel. The steam-water interface was carefully observed to understand the underlying physics. Two steam injection rate bounds were found for a given water flow rate and water subcooling. The upper bound is the steam flow rate at which the steam zone grows without limit and the lower bound is the steam flow rate at which a steam zone is just initiated. The bounds were determined experimentally for a porous channel with different permeabilities and thermal conductivities. For large particle size, chaotic oscillation of steam water interface was observed. The oscillation is believed to enhance heat and momentum transfer mechanisms. The steam zone size and shape were measured to evaluate heat transfer characteristics. The average Nusselt number is presented in terms of steam and water Reynolds numbers and the Stefan number.     

A note on mixed convection of laminar plane water plumes at temperatures around the density extremum

In all studies concerning mixed convection in plane laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the water density-temperature relationship is non-linear at low temperatures with a density maximum at 3.98°C for pure water. In this note the problem of plane laminar water plume in a coflowing vertical free stream has been investigated taking into account the non-linearity between density and temperature. This is the first work in the literature which treats plane mixed convection plumes with nonlinear relation between density and temperature. Both rising and descending plumes have been investigated. It was found that the ambient water temperature plays an important role on the results. When the ambient temperature is greater than maximum density temperature (T _a > T _m), the water plume behavior is similar to that of the classical plume with linear density-temperature relationship. However, when the ambient temperature is equal or lower than the maximum density temperature the water plume behavior is completely different from the classical plume with linear density-temperature relationship. The centerline velocity shows a series of maxima and minima which are produced by the combination of the nonlinear density-temperature relation and the free stream.     

Effect of the steam compressibility on the stability of a phase interface in geothermal systems with constant temperature

The stability of vertical steady-state flows in geothermal water-above-steam systems is considered. The steam compressibility and the capillary forces on a phase interface are taken into account. A domain of the physical parameters of the geothermal system, where vertical steady-state flows exist, is found. The linear stability of these flows is analyzed, namely, the dispersion relation is obtained, the stability diagram is constructed, and the possible types of loss of stability are found using asymptotic and numerical methods. The effect of the steam compressibility and other physical parameters on vertical steady-state flows and their stability is analyzed.     

Entrainment and condensation effects in the upward acceleration of a liquid column

The instability-governed entrainment rate of the lower surface of a subcooled water column accelerated upwards by an expanding steam mass is measured. It is found that the entrainment rate is approximately proportional to the fourth root of the acceleration. This would be the case if the characteristic length scale in the late stages of Taylor instability were governed by linear instability theory. In addition to the linear displacement measurements, the steam pressure in the lower driver section was monitored as a function of time. Estimates of the concentration, radius and age distribution of the entrained droplet population were made by modeling the bubble-and-spike breakup into discrete droplets. This allows the steam condensation rate, and hence the steam pressure, at each instant of time to be computed. This is compared with the observed steam pressure history. Reasonable agreement is found. One can thus estimate the reduction in work potential in the case of a steam explosion in the lower plenum of a pressurized-water nuclear reactor.     

A comparison between a plume path model and a virtual point source model for a stack plume

Some years ago we developed a theoretical model for the calculation of the rise of a stack plume in the atmosphere. Recently we have extended this model in such a way that the ground level concentration of gases emitted by a stack can also be calculated. The cross-section of the plume, which was originally assumed to be a circle, is now assumed to be an ellipse. The height-to-width ratio of the ellipse is chosen in accordance with full-scale data. The entrainment of air into the plume due to atmospheric turbulence can now be calculated not only for neutral atmospheric conditions, but also for stable and unstable conditions.Predictions of the ground level concentration made with this model have been compared with predictions made with the often used virtual point source model. For neutral and unstable atmospheric conditions the agreement is rather good. For stable conditions the differences can be rather large. The sensitivity of the ground level concentration with respect to the atmospheric stability condition, the stack height, the plume exit momentum flux and the plume exit buoyancy flux has also been investigated with the aid of the model. The influence of the plume exit momentum flux is negligible; however, the influence of the other parameters can be large.     

火箭剩余推进剂排放过程的分析与模拟

为了减少空间碎片的产生,星箭分离后,需要在轨排放火箭末级贮箱内的剩余推进剂,分析表明,排放条件下的推进剂射流进入太空后,立即失稳破碎为大量液滴;液滴在高真空环境下扩散,它们的表面不断有气体分子蒸发,逐渐在箭体周围形成了一个由液滴和蒸气分子组成的羽流场.采取Lagrange方法追踪该流场中每个液滴的运动轨迹以及表面蒸发冷凝过程,利用直接模拟Monte Carlo方法计算蒸气分子的运动和碰撞,然后通过微观量的统计平均获得感兴趣的宏观流场、箭体表面的压力和剪应力分布等.为了检验稀薄蒸气算法、模型和程序,模拟了真空水射流周围水蒸气羽流场,获得的径向Pitot压力分布与Fuchs和Legge的实验数据的符合。在此基础上,分别模拟了CZ-4B火箭末级剩余燃料偏二甲肼在不同排放方式下的三维稀薄蒸气与液滴羽流场。计算表明:原排放方式的扰动力矩相当大,超出了火箭姿控范围,新排放方式的扰动力矩很小,处于火箭姿控范围之内。这些预测得到了飞行遥测数据的支持。