Prediction of losses in the flow through the last stage of low‐pressure steam turbine

In this paper, the numerical modelling of the flow through the low‐pressure steam turbine last stage was presented. On the basis of predicted wet steam flow‐field, the aerodynamic as well as thermodynamic losses were estimated. For calculations of the wet steam steady flow‐field three numerical methods were employed. The first method was a streamline curvature method (SCM). The commercial CFD code (CFX‐TACflow) and an in‐house code, both solving the 3‐D RANS equations, were the next two methods. In the wet steam region, by means of all three methods, the equilibrium flow was modelled. Additionally, the in‐house CFD code was used for modelling of the non‐equilibrium steam condensing flow. In this work, the comparison of the cascade loss coefficient for stator and rotor and selected flow parameters for the stage were presented, compared and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Calculation of spontaneously condensing steam flows in a plane turbine cascade

The results of a numerical analysis of stationary spontaneously condensing steam flows in a plane turbine cascade are presented and compared with the experimental and calculated results of other authors. The effect of the flow parameters on the position and strength of the condensation shocks is analyzed. The local and integral characteristics of superheated and wet steam flows are compared.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 144–153, November–December, 1995.     

Steam condensing flow modeling in turbine channels

The numerical method for modeling of the transonic steam flows with homogeneous and/or heterogeneous condensation has been presented. The experiments carried out for the Laval nozzles, for 2-D turbine cascades and for a 3-D flow in real turbine were selected to validate an in-house CFD code adjusted to the calculations of the steam condensing flows in complicated geometries. The sensitivity of the condensation model and difficulties in the validation process of the CFD code have been discussed. These difficulties limit the possibilities of verification and improvement of the condensation theory based on the existing experimental data.     

Exit plane and suction surface flows in an annular turbine cascade with a skewed inlet boundary layer

The flow in the exit plane and on the suction surface of an annular turbine cascade was examined experimentally for conditions of inlet boundary layer skewing similar to that found in a real turbine and for the collateral inlet as found in most cascade tests. Skewing was introduced by rotating the nose cone ahead of the cascade.At the cascade exit, the loss distribution pattern, as measured by a 3 hole cobra probe, showed that the corner vortex at the hub is displaced radially to almost a mid-span position by the skewed inlet boundary layer. This movement was attributed to the stronger endwall crossflows being radially directed as they strike and rise up onto the suction surface. The radial displacement and endwall crossflow effect was also seen in surface flow visualization studies.The overall cascade loss coefficient and deviation angle are significantly reduced by skewing. Traverses taken on the suction surface confirmed the separated flow effects seen in the flow visualization pictures.The general conclusion is that skewing plays a significant role in determining the flow phenomena in turbine cascades and that these effects should be borne in mind when interpreting the results taken from plane cascades.     

Numerical solution of single and multi‐phase internal transonic flow problems

This paper presents numerical methods for solving turbulent and two‐phase transonic flow problems. The Navier–Stokes equations are solved using cell‐vertex Lax–Wendroff method with artificial dissipation or cell‐centred upwind method with Roe's Riemann solver and linear reconstruction. Due to a big difference of time scales in two‐phase flow of condensing steam a fractional step method is used. Test cases including 2D condensing flow in a nozzle and one‐phase transonic flow in a turbine cascade with transition to turbulence are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines

This paper describes a semi-analytical solution of the polydispersed wet stream equations, valid in regions where the nucleation rate is negligible. The solution can be used in conjunction with any conventional turbomachinery calculation procedure to obtain estimates of the magnitude of departures from thermal equilibrium. For example, from an initial estimate of the pressure distribution, it is a simple matter to calculate the distribution of supercooling and wetness fraction, together with the thermodynamic losses incurred by the flow.The method differs from the usual numerical approach by providing general results which give considerable physical insight. Computational time and effort is also dramatically reduced. The controlling parameters emerge naturally from the analysis, and information concerning the fundamental fluid mechanics of wet steam is revealed. In particular, the analysis demonstrates the role played by the thermal relaxation time and the rate of expansion in controlling the deviation from equilibrium.The versatility and usefulness of the technique in furnishing results for the turbine designer are demonstrated by a number of applications including one-dimensional nozzle flows and two-dimensional blade-to-blade and hub-to-tip flows. In each case it is shown how the droplet size and expansion rate influence the thermodynamic losses and other flow variables of interest.     

Flux schemes based finite volume method for internal transonic flow with condensation

This paper describes the development of numerical method for the solution of condensing steam flow in internal aerodynamics problems. The numerical method is based on the fractional step method, where the resulting set of ODEs is solved by the two‐stage Runge–Kutta method and the homogeneous set of PDEs by a finite volume method. The flow does not contain both phases (gas and liquid) in the whole domain, therefore we discuss properties of used finite volume methods in several cases of single‐phase transonic flow in a channel and a turbine cascade. We present numerical results of two‐phase flow of condensing steam in 2D nozzle achieved by several numerical methods and show the differences in results caused by numerical diffusion. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydrodynamic and Thermal Fields in a Porous Medium with Injection of Superheated Steam

The plane one-dimensional and radially symmetric problems of injection of superheated steam into a porous medium saturated with gas are considered. Self-similar solutions are constructed on the assumption that in this case four zones are formed in the porous medium, namely, a gas flow zone, superheated and wet steam zones, and a water slug zone formed due to steam condensation. On the basis of the solution obtained, both the effects of the boundary pressure, mass flow rate, and temperature of the injected superheated steam and the effect of the initial state of the porous medium on the propagation of the hydrodynamic and thermal fields in the porous medium are studied.     

Direct simulation of two‐dimensional turbulent flow over a surface‐mounted obstacle

Two‐dimensional turbulent flow over a surface‐mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier–Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12 518. Instantaneous streamline patterns are shown that give a complete picture of the flow phenomena. Energy and enstrophy spectra yield the dual cascade of two‐dimensional turbulence and the ?1 power law decay of enstrophy. Mean values of velocities and root mean square fluctuations are compared with the available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behaviour of turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical study of the spontaneous nucleation of self-rotational moist gas in a converging–diverging nozzle

Spontaneous nucleation is the primary way of droplet formation in the supersonic gas separation technology, and the converging–diverging nozzle is the condensation and separation unit of supersonic gas separation devices. A three-dimensional geometrical model for the generation of self-rotational transonic gas flow is set up, based on which, the spontaneous nucleation of self-rotational transonic moist gas in the converging–diverging nozzle is carried out using an Eulerian multi-fluid model. The simulated results of the main flow and nucleation parameters indicate that the spontaneous nucleation can occur in the diverging part of the nozzle. However, different from the nucleation flow without self-rotation, the distributions of these parameters are unsymmetrical about the nozzle axis due to the irregular flow form caused by the self-rotation of gas flow. The nucleation region is located on the position where gas flows with intense rotation and the self-rotation impacts much on the nucleation process. Stronger rotation delays the onset of spontaneous nucleation and yields lower nucleation rate and narrow nucleation region. In addition, influences of other factors such as inlet total pressure p ₀, inlet total temperature T ₀, the nozzle-expanding ratio ? and the inlet relative humidity ф ₀ on the nucleation of self-rotational moist gas flow in the nozzle are also discussed.     

A robust ‘time-marching’ solver for one-dimensional nucleating steam flows

A mixed Lagrangian/Eulerian ‘time-marching’ solver capable of predicting one-dimensional nucleating steam flows is described. Simple nucleation and droplet growth models are employed which avoid the use of variable empirical factors and which have been validated using existing experimental data from nozzle experiments performed in the steam tunnel of the Central Electricity Research Laboratories. Theoretical predictions are compared against experimental results encompassing all flow regimes likely to be encountered in a one-dimensional analysis of flow in a low pressure steam turbine. These include supercritical heat addition cases which display both steady and unsteady shock wave formation.     

Numerical simulation of heat transfer performance of an air-cooled steam condenser in a thermal power plant

Numerical simulation of the thermal-flow characteristics and heat transfer performance is made of an air-cooled steam condenser (ACSC) in a thermal power plant by considering the effects of ambient wind speed and direction, air-cooled platform height, location of the main factory building and terrain condition. A simplified physical model of the ACSC combined with the measured data as input parameters is used in the simulation. The wind speed effects on the heat transfer performance and the corresponding steam turbine back pressure for different heights of the air-cooled platform are obtained. It is found that the turbine back pressure (absolute pressure) increases with the increase of wind speed and the decrease of platform height. This is because wind can not only reduce the flowrate in the axial fans, especially at the periphery of the air-cooled platform, due to cross-flow effects, but also cause an air temperature increase at the fan inlet due to hot air recirculation, resulting in the deterioration of the heat transfer performance. The hot air recirculation is found to be the dominant factor because the main factory building is situated on the windward side of the ACSC.     

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.     

Vortex motion in a rotating barotropic fluid layer

To study vortex motion and the mechanisms of geostrophic adjustment (i.e. the equilibrium between pressure gradient and Coriolis force, which leads to the weakening of inertio-gravity waves) in large scale geophysical flows, we simulate the dynamics of a shallow-water layer in uniform rotation, without any forcing other than the initial injection of energy and potential enstrophy. Such a flow generates inertio-gravity waves which interact with the rotational eddies. We found that both inertio-gravity waves and rotation reduce the non-linear interactions between vortices, namely the condensation of the vorticity field into isolated coherent vortices, corresponding to the inverse rotational energy cascade, and the associated production of vorticity filaments, due to the direct potential enstrophy cascade. Rotation also inhibits the direct inertio-gravitational energy cascade for scales larger than the Rossby deformation radius. Therefore, if inertio-gravity waves are initially excited at large enough scales, they will remain trapped there due to rotation and there will be no geostrophic adjustment. On the contrary, if inertio-gravity waves are only present at scales smaller than the Rossby deformation radius, which are insensitive to the effect of rotation, they will non-linearly interact and cascade towards the dissipative scales, leaving the flow in geostrophic equilibrium.     

Nonequilibrium homogeneous condensation of gases in high-velocity flows

This paper discusses questions of the homogeneous condensation of water vapors in high-velocity flows. Special attention is paid to agreement between the results of calculations and experimental data in a wide range of temperatures and pressures in the condensation zone and of the gradients of the gasdynamic parameters. The article proposes a relationship enabling a sufficiently exact determination of the value of the maximal supercooling. A parametric investigation is made, showing that the value of the maximal supercooling of the flow, as well as the drop size, are determined above all by the saturation temperature of the flow and the rate of change of the temperature along the line of flow in the condensation zone. The isentropic index of a mixture of gases and the concentration of the condensing component have a relatively weak effect on the value of the maximal supercooling, but the presence of other gases can appreciably affect the drop size. The Mach number of the flow with M > 1.5 has no effect on the value of the maximal supercooling and the drop size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–88, November–December, 1978.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

The mechanism of violent condensation shocks

In direct-contact steam condensers, violent condensation shocks (VCSs) occur at low steam flow rates. This phenomenon was also observed in the pressure-suppression system of nuclear boiling water reactors. Thus, the phenomenology of condensation in this type of condenser has been investigated. The main design feature of the Plexiglas test apparatus used here is that the events of rapid steam-water condensation are observed in a sectional view instead of an external view. This allows the phenomena at the phase interfaces to be observed in detail. In our experiments we found that a characteristic feature of VCSs is the appearance of considerable entrainment inside so-called steam pockets, which is characterized by atomization and is correlated to the extremely high rate of condensation. This avalanche-like increase in water atomization is induced by the Kelvin—Helmholtz instability and occurs because of the increasing steam flow velocity along the freely movable surface of water, primarily in the bottle-neck of the steam pocket. Detailed examination of the experimental data shows that the entrainment causes the temporary high condensation rates, which were previously observed but not understood. This is in agreement with the conditions of a sonic steam jet blowing into a subcooled pool of water where entrainment stimulates the condensation process in a similar way. The extraordinarily high condensation rates in the steam pocket induce very high steam velocities in the vent pipe, so that the entrainment often propagates outside the steam pocket in the vent pipe. We conclude that the initiating mechanism of VCSs is this self-amplifying feedback process which lasts until the initiating steam pocket has disappeared. The induced state of rapid condensation outside the steam pocket decays with a time constant in the range of 0.1 s.     

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.     

局部弹性翼型非定常分离的动力学特性

对在低雷诺数下局部弹性翼型绕流中, 局部弹性导致的自激振动所产生的复杂非定常流动分离现象和描述方法进行了分析. 采用ALE-CBS方法数值模拟了具有可动边界的绕流流场问题, 同时采用Galerkin方法求解局部弹性结构的控制方程. 着重研究了翼型的局部弹性对流动分离和翼型性能的影响, 并分别从Eulerian和Lagrangian的角度分析了局部弹性结构导致的不同非定常分离现象, 其中Lagrangian角度可以方便地揭示出局部弹性翼型大幅度提高升力的机理和流动中的能量迁移. 结果表明翼型的局部弹性对非定常分离和分离泡的演化过程有着明显的影响, 可以使得流体质点由主流获取动量实现再附, 并且在一定的攻角下可以将固定分离转变为移动分离, 从而明显地提高了翼型的升力.      

Reynolds stress modelling of jet and swirl interaction inside a gas turbine combustor

Influences of the inlet swirl levels on the interaction between the dilution air jets and the swirling cross‐flow to the interior flow field inside a gas turbine combustor were investigated numerically by Reynolds stress transport model (RSTM). Due to the intense swirl and jet interaction, a high level of swirl momentum is transported to the centreline and hence, an intense vortex core is formed. The strength of the centreline vortex core was found to depend on the inlet swirl levels. For the higher swirling inlet, the decay of the swirling motion causes strong streamline variation of pressure; and consequently leads to an elevated level of deceleration of its axial velocity. Predictions contrasted with measurements indicate that the stress model reproduces the flow correctly and is able to reflect the influences of inlet swirl levels on the interior flow structure. Copyright © 1999 John Wiley & Sons, Ltd.