Steam plume length diagram for direct contact condensation of steam injected into water

Direct Contact Condensation (DCC) of steam in water occurs when steam is introduced into water. It is a phenomenon of high importance in many industrial applications. An important feature of the DCC is the length of the steam plume. Correlations for a steam plume length presently available are accurate only for limited conditions. In this paper, a new two-dimensional steam plume length diagram is presented capable of predicting length accurately for a wide range of conditions. The diagram is validated against experiments. Furthermore, corrections necessary to adopt the diagram for steam injection into a water flow are discussed in the paper.     

Laminar flow of a reacting gaseous mixture through a vertical duct with catalytic walls

Numerical analysis has been performed for predicting the onset and establishment of a steady state flow of a reactive hydrogen/air/vapour mixture through a two-dimensional vertical duct of finite length with its side walls coated by catalytic material. The flow is initiated by the exothermic reaction of hydrogen with air oxygen on the catalytic wall, that causes the hot gases to flow upwards through the vertical duct and by continuity sucks fresh mixture through the lower end of the duct. The flow is always laminar and the two-dimensional governing transport differential equations are solved by means of the numerical finite volume method, using a collocated variable arrangement. Comparisons between calculated and experimental data are presented, showing good agreement between them. The method is employed for various initial mixture compositions and duct geometries.     

An investigation of two-dimensional flows of nucleating and wet steam by the time-marching method

A numerical method for the solution of two-dimensional two-phase flows of steam is described. Comparisons are with two sets of experimental results in nozzles and the agreement obtained is satisfactoryy. Some predictions of two-phase effects in blade cascades are also presented.     

Shock and blast attenuation by aqueous foam barriers: influences of barrier geometry

A Free-Lagrange CFD code is used to simulate the attenuation, by means of barriers of aqueous foam, of shocks and blast waves emerging from the open end of a two-dimensional duct. A range of foam barrier configurations is explored, comprising foam sheets that extend the effective duct length, and foam “caps” that completely obstruct the duct exit. Near-field off-axis overpressure time-histories are presented for each configuration. Two attenuation mechanisms are identified, both of which are influenced by the barrier geometry used: partial transmission at foam/air interfaces due to impedance mismatching, and delay of blast waves within the foam. Attenuation by dissipation within the foam is not simulated. Received 13 October 1997 / Accepted 31 August 1998     

On a mixed boundary value problem of diffusion type

Fluid arriving at the surface of an unevenly heated solid (such as a reactor rod) may initially be converted to steam on the higher temperature portion of the surface; and the extent of the steam covered portion shrinks when there is a continual supply of cooling fluid. A two-dimensional model diffusion problem, involving linear specifications and intended for a determination of the steady advance of the (quench) front which separates the fluid and steam covered parts of a slab face, is resolved in exact fashion and the estimates of a prior approximate calculation (Caflisch and Keller, 1981) are thereby extended.     

An efficient shock-capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.     

Experimental and numerical investigation on steady blowing flow control within a compact inlet duct

A combined experimental and numerical investigation of flow control actuation in a short, rectangular, diffusing S-shape inlet duct using a two-dimensional tangential control jet was conducted. Experimental and numerical techniques were used in conjunction as complementary techniques, which are utilized to better understand the complex flow field. The compact inlet had a length-to-hydraulic diameter ratio of 1.5 and was investigated at a free-stream Mach number of 0.44. In contrast to the baseline flow, where the flow field was fully separated, the two-dimensional control jet was able to eliminate flow separation at the mid-span portion of the duct and changed considerably the three-dimensional flow field, and ultimately, the inlet performance. A comparison between the baseline (no actuation) and forced flow fields showed that secondary flow structures dominated both flow fields, which is inevitably associated with total pressure loss. Contrary to the baseline case, the secondary flow structures in the forced case were established from the core flow stagnating on the lower surface of the duct close to the aerodynamic interface plane. High fidelity spectral analysis of the experimental results at the inlet’s exit plane showed that the baseline flow field was dominated by pressure fluctuations corresponding to a Strouhal number based on hydraulic diameter of 0.26. Not only did the two-dimensional tangential control jet improve the time-averaged pressure recovery at the inlet exit plane (13.3% at the lower half of the aerodynamic interface plane), it essentially eliminated the energy content of the distinct unsteady fluctuations which characterized the baseline flow field. This result has several implications for the design of a realistic engine inlet; furthermore, it depicts that a single non-intrusive static pressure measurement at the surface of the duct can detect flow separation.     

Shock wave propagation in a branched duct

The propagation of a planar shock wave in a 90° branched duct is studied experimentally and numerically. It is shown that the interaction of the transmitted shock wave with the branching segment results in a complex, two-dimensional unsteady flow. Multiple shock wave reflections from the duct's walls cause weakening of transmitted waves and, at late times, an approach to an equilibrium, one-dimensional flow. While at most places along the branched duct walls calculated pressures are lower than that existing behind the original incident shock wave, at the branching segment's right corner, where a head on-collision between the transmitted wave and the corner is experienced, pressures that are significantly higher than those existing behind the original incident shock wave are encountered. The numerically evaluated pressures can be accepted with confidence, due to the very good agreement found between experimental and numerical results with respect to the geometry of the complex wave pattern observed inside the branched duct. Received 15 July 1996 / Accepted 20 February 1997     

Boundary layer development in an MHD duct

This study presents a method of calculation for two-dimensional, steady-state, laminar flow in the entrance region of an MHD duct. The electrically conducting fluid in the free stream is compressible whereas the medium in the boundary layer itself is taken to be incompressible. Thus, the density is variable in the axial direction of the duct only, and the momentum and energy equations for the boundary layer are uncoupled. These equations are solved using an extended Von Kármán-Pohlhausen method as described by U. P. Hwang for a compressible MHD flow with zero electric field. In this study, however, the electric field is essentially not zero and the MHD duct can work as a generator. The equations of the insulator boundary layer are solved in the assumption that the displacement thickness of the electrode boundary layer equals that of the insulator boundary layer, so the total influence of the varying effective crossection on the free stream is taken into account. In this way a quick method of calculating the MHD flow in the entrance region of a duct is obtained.     

Energy-based decomposition of friction drag in turbulent square-duct flows

The generation of friction drag in turbulent duct flows has direct connection with statistical quantities and corresponding turbulence dynamics in the duct cross-section. In this study, we generalize the RD identity (Renard and Deck, 2016) to a ‘two-dimensional’ form which we exploit to decompose the mean friction drag in turbulent square-duct flows into contributions associated with viscosity, turbulence and cross-stream convection. The friction Reynolds number of the duct flows ranges from 220 to 2000. The scaling, spatial distribution and local normalization of the contributions to friction are investigated and compared with those in pipe and channel flows. As in other canonical flows, we find logarithmic growth of the turbulent contribution in contrast to the viscous one, the former thus becoming dominant at high enough Reynolds numbers. Whereas cross-stream convection has no net effect on friction, its contribution may be locally comparable to the other two, hence may be responsible for redistribution of friction along the duct perimeter.     

Method of Lines for Transient Flow Fields

A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available in the literature. The predicted flow fields were found to be in favorable agreement with those available in the literature for laminar channel flow with sudden expansion and turbulent channel flow with Re=6600. The code was then applied to the prediction of the highly turbulent flow field in the inlet flue of a heat recovery steam generator (HRSG). The predicted flow field was found to display the same trend with the experimental findings and numerical solutions reported previously for a turbulent diverging duct. As the code uses the MOL approach in conjunction with (i) an intelligent higher-order spatial discretization scheme, (ii) a parabolic algorithm for pressure, and (iii) an elliptic grid generator using a body-fitted coordinate system for complex geometries, it provides an efficient algorithm for future direct numerical simulation (DNS) applications in complex rectangular geometries.     

Three-dimensional flow pattern visualization and bubble size distributions in stationary and transient upward flashing flow

For the first time, an experimental three-dimensional reconstruction and visualization of stationary and transient flashing flow in a vertical pipe (47 mm diameter) is presented. The measurements have been performed by means of wire-mesh sensors. This type of sensor delivers two-dimensional void-fraction distributions in the pipe cross-section where it is mounted with a maximum sampling rate of 10,000 frames per second. A sampling rate of 1200 frames per second has been used in this work. Steam bubbles have been identified from the wire-mesh data and their complete three-dimensional reconstruction has been performed by taking into account the steam bubble velocity. For the estimation of the bubble velocity, two wire-mesh sensors positioned at a small axial distance from each other have been used. The velocity has been determined by cross-correlation of the two wire-mesh signals, by direct identification of the traveling time of the steam bubbles between the two sensors and by means of a drift-flux model. A comparison between the three methods of bubbles velocity measurement is reported. Stationary and time-dependent bubble size distributions have been derived. The stationary radial void-fraction profiles have been decomposed according to bubble size classes and compared with the results obtained with an equilibrium model.     

An experimental study of ice-layer transition phenomena in a rectangular duct containing water flow

Measurements of both the velocity and turbulence-intensity distributions above an ice-layer surface along flow direction have been performed to clarify the ice-layer transition phenomena observed in a rectangular duct. The test duct which has a lower cooled wall kept less than the freezing temperature of water with cross-sectional dimension of 50 mm by 19 mm was used in the present measurements. The velocity and turbulence-intensity distributions in the test duct were measured using Laser Doppler Velocimeter set up on the two-dimensional traversing table. The freezing experiments were carried out under the condition of uniform water-flow rate even after the ice layer has developed in the test duct. It was found that inlet water flow tended to be laminarized under an influence of developing ice layer, and that onset of the ice-layer transition phenomena might be closely related to an increase in turbulence intensity in the water flow above the developing ice-layer surface.     

Steam chugging in a boiling water reactor pressure-suppression system

Results of a transient analysis predicting the general characteristics of steam chugging compare well with the results of two large scale experiments: GKM II, test 21 and GKSS, test 16. Predicted fundamental periods of chugging are within 5 and 16 per cent of the respective experimental values. The results of the analysis include effects of air in the drywell, momentum loss and heat transfer in the condensation pipe, direct contact condensation heat transfer at the gas-water interface and momentum and heat transfer in the wetwell water pool. Bubble shape is calculated in two-dimensional cylindrical coordinates.Required inputs to the analysis include the geometry, initial conditions and constants to determine both the steam inlet mass flowrate to the drywell as a function of time and conduction heat transfer through the wall of the condensation pipe. There are no arbitrary free parameters which must be specified to predict specific experiments. Rather, the analysis is based on fundamental physical phenomena, experimental coefficients documented for general heat transfer and fluid mechanics characteristics and standard analytical techniques.The random nature of steam chugging observed in some experiments is partially explained by predicted regimes of chugging and changes in the maximum extent of a bubble below the condensation pipe exit during each regime.     

大型汽轮机部件低周疲劳安全寿命的设计和评定

文中提出了汽轮机部件低周疲劳安全寿命的设计和评定方法。介绍了汽轮机部件低周疲劳安全寿命的含义和计算方法。该方法以概率论和统计学为基础，把汽轮机部件的低周疲劳寿命处理为随机变量，对低周疲劳试验数据进行统计分析来确定材料低周疲劳寿命的分布参数，使用可靠性理论来确定汽轮机部件的低周疲劳安全寿命。文中给出了低周疲劳寿命服从正态分布和对数正态分布时汽轮机部件低周疲劳安全寿命的计算方法和应用实例。该方法考虑了汽轮机运行参数随机性和材料低周疲劳特性离散性的影响，为汽轮机部件低周疲劳寿命的设计、评定和诊断提供了科学的依据。     

The effects of rate of expansion and injection of water droplets on the entropy generation of nucleating steam flow in a Laval nozzle

The entropy generation due to irreversible heat transfer between vapor and liquid phases in a nucleating steam flow in a Laval nozzle is studied. To calculate the entropy generation due to self-condensation in transonic steam flow, a thermodynamic model is presented. The calculations of nucleating steam flow and the predictions of entropy generation rely on one-dimensional two-phase model. This model shows that the most of the thermodynamic losses take place during the nucleation phenomena. The effect of rate of expansion on the exergy losses is considered by decreasing the divergent angle of nozzle. Also micro-sized pure water droplets is injected theoretically to supercooled steam right after the nozzle throat at the onset of divergent section and the effects of injected droplets on thermodynamic losses and nucleation phenomena are investigated. The results indicate that decreasing the divergent angle and also injection of droplets diminishes the pressure rise in transonic steam flow and decreases the thermal entropy generation due to nucleation.     

Interaction of Rarefaction Waves and Vacuum in a Convex Duct

The motion of the supersonic compressible flow governed by the Euler system in a two-dimensional convex duct is studied. The rarefaction waves in the compressible flow propagate and reflect on the walls of the convex duct, so that interaction occurs and a vacuum may appear. The existence of the global piecewise smooth solution to the steady Euler system in the interaction region is established. Meanwhile, the appearance of a vacuum is carefully considered. It is found that a vacuum is always adjacent to one of the walls and the appearance of a vacuum depends on the limit of the slope of the wall at the infinity.     

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.