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.     

Effect of thermophoresis on fog droplet deposition on low pressure steam turbine guide blades

Deposition of droplets in the sub-micron size range, when discouraged by thermophoresis forces, has been studied by a simulation method employing uranine particles entrained in air and flowing through a cascade of full-sized low-pressure steam turbine blades. The particles, generated by a Collison atomiser, had a mass-median diameter range of 0.05–0.25 μm. The test blades were internally heated using hot air and had an output of 600 W/m² of swept surface. Circumferential tape around their surfaces provided a reception medium for the particles, the deposition density variation of which was found by fluorimetry. Prediction of the deposition on an unheated blade using the method of C.N. Davies showed acceptable agreement with the experimental results. The simulation method was validated by showing that the relevant non-dimensional numbers. Schmidt and Reynolds, can be acceptably matched for the air/particle and the steam/droplet cases. Tests on the heated blade showed that the deposition was reduced by 30–90% of the corresponding value for the unheated blade. The extent of the reduction decreased with particle size decrease.     

Modeling the evolution of droplet size distribution in two-phase flows

A theoretical model is developed in the present study to simulate droplet motion and the evolution of droplet size distribution (DSD) in two-phase air/dispersed water spray flows. The model takes into account several processes which influence DSD and droplet trajectory: droplet collision and coalescence, evaporation and cooling, gravitational settling, and turbulent dispersion of dispersed phase. The DSDs determined by the model at different locations in a two-phase flow are evaluated by comparing them to experimental observations obtained in an icing wind tunnel. The satisfactory coincidence between simulation and experimental results proves that the model is reliable when modeling two-phase flows under icing conditions. The model is applied for two particular examples in which the modification of DSD is calculated in two-phase flows under conditions describing in-cloud icing and freezing drizzle.     

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.     

Experimental determination of droplet size and density field in condensing flows

 We report a detailed experimental characterization of the process of homogeneous condensation in supersonic expanding flow. In our experiments, the supersaturated mixture expands in a Laval nozzle, where, depending on the initial conditions, a steady or periodically oscillating flow may evolve due to the non-linear interaction of nucleation and droplet growth rate with the flow field. Two experimental techniques are utilized: holographic interferometry for the determination of the density field and a time-resolved white-light extinction method. The latter is employed to derive the evolution in time of the droplet cloud (i.e., modal radius, number density, and relative width) and to measure the frequency of oscillations. In combination with the wide-field density data, droplet size measurements provide additional physical insights in the mechanism of interaction in condensing flows and serve as an excellent test case for the critical assessment of nucleation and droplet growth theories. To this purpose, the accuracy of the measurements is carefully reviewed due to the difficulties of characterizing dense sub-micron droplet clouds by means of light-scattering techniques. An important byproduct of this analysis is an evaluation of the applicability of single-scattering approximations, i.e., Lambert-Beer law, for a variety of experimental configurations. Received: 24 April 2001 / Accepted: 29 August 2001     

Particle size distribution in CPFD modeling of gas-solid flows in a CFB riser

A computational particle fluid dynamics(CPFD) numerical method to model gas-solid flows in a circulating fluidized bed(CFB) riser was used to assess the effects of particle size distribution(PSD) on solids distribution and flow.We investigated a binary PSD and a polydisperse PSD case.Our simulations were compared with measured solids concentrations and velocity profiles from experiments,as well as with a published Eulerian-Eulerian simulation.Overall flow patterns were similar for both simulation cases,as confirmed by experimental measurements.However,our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser,as seen in other numerical studies.Above this bottom region,distributions of particle volume fraction and particle vertical velocity were consistent with our experiments,and the simulated average particle diameter decreased as a power function with riser height.Interactions between particles and walls also were successfully modeled,with accurate predictions for the lateral profiles of particle vertical velocity.It was easy to implement PSD into the CPFD numerical model,and it required fewer computational resources compared with other models,especially when particles with a polydisperse PSD were present in the heterogeneous flow.     

Numerical investigation of secondary flows in a high-lift low pressure turbine

In turbomachines, secondary flows (or endwall flows) typically originate at the junction between endwalls and the blade surface. Within the blade passage, the strength of the secondary flows is amplified by the crossflow from the pressure to the suction surface of the blade. The enhanced mixing due to secondary flows induce additional losses into the system. This decreases the overall work output and also changes the flow incidence onto the downstream blade rows. Using a series of high-fidelity eddy resolving simulations, the current study attempts to provide an improved understanding for the complex flow physics over the endwalls of a high-lift Low Pressure Turbine (LPT) blade. The effect of three different inflow conditions has been studied. These include a laminar boundary layer (LBL), a turbulent boundary layer (TBL) and wakes with secondary flow (W&S) from an upstream blade row. For the simulations with TBL and W&S, precursor eddy resolving simulations were used to prescribe realistic inflows. The loss generation mechanisms were subsequently studied both at the endwall and the midspan, which includes evaluating the mass-averaged total pressure loss coefficient (Y_p) and the loss generation rate.When compared to LBL, additional disturbances from an incoming TBL and wakes with secondary flows enhanced the mixing within the blade passage resulting in a substantial increase in the total pressure loss. Prior to flow transition, incoming wakes with secondary flows increased the local loss generation rate at both the endwall and the midspan in the front portion of the blade passage (x/C_x < 0.84). In contrast, in the aft portion of the passage (x/C_x > 0.8), the incoming wakes effectively suppressed the separation bubble at the midspan thereby decreasing the local loss generation rate. It is also demonstrated that the wakes shed from the trailing edge at the mid-span mix out rapidly when compared to the passage vortex at the endwall.     

Numerical modeling of viscoelastic counter flows using the pressure correction method

Counter flows of a viscoelastic fluid described by the rheological Oldroyd model in crossshaped channels are investigated. The modeling is based on the pressure correction method in a convenient-in-use form and with a simple topology of the computation grid and formally proved convergence. It is shown that, starting from certain threshold values of the Weissenberg numbers, the flow pattern in the stabilization stage exhibits considerable changes following two different mechanisms, depending on the Reynolds number. In particular, at low Reynolds numbers (less than 0.1) the flows involve vortex-like structures near the central point, where at the same time anomalies in normal stress distributions are observable. The similarity of these structures with the elastic instability phenomena, which were previously observed in the experimental realizations of the counter flows of this type and in other processes, is shown. To demonstrate the numerical procedure convergence, the results of calculations with different computation grid steps varied on a wide range are presented. In the context of the problem considered the general features of elastic instability are discussed.     

Theory of pressure swirl atomisation and study on the characteristic of droplet size in atomisation

Based on the observation of the working condition in pressure swirl atomisationexperiments,this article tries to suggest a model of the mechanism of pressure swirlatomisation—the atomisation theory of pressure swirl spray of conical film.Under somebasic assumptions,the formula for the characteristic of droplet size of pressure swirlatomisation is derived:The above theory agrees basically with the actual working conditions in atomisation,andgives the latter a compratively good interpretation.In this article,theoretical calculations are worked out for the characteristic ofatomised droplet size of some Oil atomising nozzles used in power plants in our country(thePeople＇s Republic of China)and are compared with actual test data.The results show thatthe theory is of some value to preactice,and it is recommended to those concerned forreference.     

Wet steam flows in industrial large-diameter pipes: flowrate, moisture and pressure drop measurements

The flowrate, moisture and pressure drop were measured in a water-steam mixture flowing at a pressure of I MPa in pipes with 0.3 and 1.2 m dia. The results are presented here, along with an original method for assessing pressure drops in a water-steam mixture flowing in such industrial pipes.     

Numerical modeling of three-dimensional viscous flows using a space-marching method with pressure iterations

A method of calculating steady three-dimensional compressible and incompressible flows on the basis of simplified Navier-Stokes equations is examined. Some calculation results are presented. These relate to the problem of supersonic flow past blunt bodies and to incompressible channel flows.Based on paper read at the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August I991. Presented by V. I. Polezhaew.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 132–147, September–October, 1992.     

A random simulation of droplet distribution in nozzle and plume flows

A simple entrainment model is used to estimate droplet streamlines, velocity and mass flux in rocket exhaust plumes. Since droplet mass flux constitutes only about 1% of the exhaust mass flux, the effect of droplet entrainment on the gas flow is neglected. The novelty of the present model is in obtaining the droplet distribution within the nozzle by assuming a small radial random velocity component for droplets at the throat. Gas flow in the nozzle is approximated as isentropic plus a correction for the boundary layer. The computed distribution of droplet mass flux is found to be in good agreement with experimental data. Received 15 January 1996 / Accepted 11 September 1996     

Experimental results for nucleating steam flow in a two-dimensional supersonic duct and comparison with theory

Results are presented of experiments conducted in a two-dimensional duct carrying a supersonic flow of condensing steam. The measurements comprised static pressure readings along the profiled surfaces of the duct and ‘fog’ droplet sizing using a light attenuation technique. Three sets of results for dry supercooled and nucleating steam flows are presented, are are compared with the predictions of a two-dimensional numerical calculation method.     

Drop coalescence and deposition in turbulent wet steam pipe flows

The numerical turbulent coalescence/deposition model of Crane and Williams has been used to indicate likely trends in the development of drop size distribution and entrained water flow rate in the cross-over pipes of a nuclear wet steam turbine. Large increases in mean drop diameter have been shown to be possible, the results being very sensitive to the width of the initial size distribution, the entrained wetness fraction and the turbulence intensity. Deposition rate was also found to be strongly dependent on turbulence intensity, but inertial deposition onto and re-entrainment from the turning vanes of a bend did not significantly influence subsequent coalescence and turbulent deposition rates in the single example computed     

Atomization of viscous and non-newtonian liquids by a coaxial,high-speed gas jet. Experiments and droplet size modeling

This paper describes a collaborative theoretical and experimental research effort to investigate both the atomization dynamics of non-Newtonian liquids as well as the performance of coaxial atomizers utilized in pharmaceutical tablet coating. In pharmaceutically relevant applications, the coating solutions being atomized are typically complex, non-Newtonian fluids which may contain polymers, surfactants and large concentrations of insoluble solids in suspension. The goal of this investigation was to improve the understanding of the physical mechanism that leads to atomization of viscous and non-Newtonian fluids and to produce a validated theoretical model capable of making quantitative predictions of atomizer performance in pharmaceutical tablet coaters. The Rayleigh–Taylor model developed by Varga et al. has been extended to viscous and non-Newtonian fluids starting with the general dispersion relation obtained by Joseph et al. The theoretical model is validated using droplet diameter data collected with a Phase Doppler Particle Analyzer for six fluids of increasing rheological complexity. The primary output from the model is the Sauter Mean Diameter of the atomized droplet distribution, which is shown to compare favorably with experimental data. Critical model parameters and plans for additional research are also identified.     

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.     

Some developments in computational modeling of turbulent flows

In this paper, some recent developments of two turbulence closure schemes at ICOMP, NASA Lewis will be discussed. One is the Reynolds-stress algebraic equation model and the other is the Reynolds-stress transport equation model. Various model constraints required by the rapid distortion theory, the invariant theory and the realizability principle, etc. will be described in the model development. The models discussed are for high-turbulent Reynolds number flows, so that the near-wall turbulence and the low-Reynolds-number turbulence are not discussed here.     

Numerical modeling of the dynamics of a viscous-fluid droplet

A numerical model developed on the basis of the level set method is proposed. This makes it possible to describe both the nonlinear oscillations of a single viscous-fluid droplet and the fragmentation and coalescence processes. The Navier-Stokes equations written in “velocity-pressure” variables on a rectangular uniform grid in cylindrical coordinates are solved using the method of splitting into physical processes. Non-oscillating solutions for two-phase media with a characteristic density ratio of less than 10⁻³ and Re > 1000 are obtained. The possibilities of the approach proposed are demonstrated with the reference to the problem of a droplet falling from a capillary (detachment from the capillary, formation of a “Plato ball”, droplet motion, collision with a plane wall, droplet oscillations on the wall, and droplet spreading). A comparison of the numerical results with the known calculation models and experimental data shows satisfactory agreement with respect to both the phases and the shape of the droplet.     

Droplet heat transfer on micro-post arrays: Effect of droplet size on droplet thermal characteristics

Heat transfer towards a water droplet from hydrophobic micro-post array surface is considered while mimicking the environmental temperatures. Micro-post arrays are created on a silicon wafer surface via lithography technique. The textured surfaces are replicated by polydimethylsiloxane (PDMS) to achieve an optical transmittance. The droplet adhesion on micro-post array surface is presented and the influence of droplet size on the heat transfer and droplet internal flow characteristics is examined. The flow predictions are validated via the particle image velocimetry data. It is found that adhesion force between the water droplet and the micro-post arrays surface depends on the geometric size and the orientation of the micro-post arrays on the surface. Temperature and flow fields are influenced by the droplet size. The Nusselt and the Bond numbers increase with the droplet volume; however, the Bond number remains less than unity indicating that the Marangoni current dominates over the buoyancy current in the droplet. The Nusselt number attains larger values for micro-post array surface than that of the plain surface. This is because of temperature and velocity oscillations along the contact lines at the droplet bottom due to the pitches of the micro-post arrays.