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.     

Origin of droplet size underprediction in modeling of low pressure nucleating flows of steam

This article examines deficiencies in nucleation rate and droplet growth models that impair modeling of low pressure (LP) nucleating flows of steam. It is shown that classical nucleation theory (CNT) exhibits excessive dependence on supersaturation in the operating range of LP condensing (wet-steam) flows. The complex mechanisms of the nucleation-growth model are explained with regard to discrepancies in the modeling results. The discrepancy between modeling results and LP wet-steam experiments is attributed to imprecision in CNT and inadequacies in the employed droplet growth equation. The link between the excessive dependence of CNT on supersaturation and underprediction of the mean droplet size is explained. Two examples are given demonstrating that the inverse correlation between mean droplet size and nucleation rate can be moderated by rectifying and reducing the dependence of CNT on supersaturation. Moreover, prediction of mean droplet size is improved without modifying the location and magnitude of the condensation shock.     

Experimental determination of the speed of sound in cavitating flows

This paper presents measurements of the speed of sound in two-phase flows characterized by high void fraction. The main objective of the work is the characterization of wave propagation in cavitating flows. The experimental determination of the speed of sound is derived from measurements performed with three pressure transducers, while the void fraction is obtained from analysis of a signal obtained with an optical probe. Experiments are first conducted in air/water mixtures, for a void fraction varying in the range 0–11%, in order to discuss and validate the methods of measurement and analysis. These results are compared to existing theoretical models, and a nice agreement is obtained. Then, the methods are applied to various cavitating flows. The evolution of the speed of sound according to the void fraction α is determined for α varying in the range 0–55%. In this second configuration, the effect of the Mach number is included in the spectral analysis of the pressure transducers’ signals, in order to take into account the possible high flow compressibility. The experimental data are compared to existing theoretical models, and the results are then discussed.     

Experimental determination of three-dimensional finite-time Lyapunov exponents in multi-component flows

We present an experimental approach for estimating finite-time Lyapunov exponent fields (FTLEs) in three-dimensional multi-component or multi-phase flows. From time-resolved sequences of particle images, we directly compute the flow map and coherent structures, while avoiding and outperforming the computationally costly numerical integration. Performing this operation independently on each flow component enables the determination of three-dimensional Lagrangian coherent structures (LCSs) without any bias from the other components. The locations of concurrent LCSs for different flow elements (e.g., passive tracers, inertial particles, bubbles, or active particles) can provide new insight into the interpenetrating FTLE structure in complex flows.     

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.     

Laser reflection method for determination of shear stress in low density transitional flows

The details of laser reflection method (LRM) for the determination of shear stress in low density transitional flows are presented. The method is employed to determine the shear stress due to impingement of a low density supersonic free jet issuing out from a convergent divergent nozzle on a flat plate. The plate is smeared with a thin oil film and kept parallel to the nozzle axis. For a thin oil film moving under the action of aerodynamic boundary layer, the shear stress at the air–oil interface is equal to the shear stress between the surface and air. A direct and dynamic measurement of the oil film slope generated by the shear force is done using a position sensing detector (PSD). The thinning rate of the oil film is directly measured which is the major advantage of the LRM. From the oil film slope history, calculation of the shear stress is done using a three-point formula. The range of Knudsen numbers investigated is from 0.028 to 0.516. Pressure ratio across the nozzle varied from 3,500 to 8,500 giving highly under expanded free jets. The measured values of shear, in the overlapping region of experimental parameters, show fair agreement with those obtained by force balance method and laser interferometric method.     

Measurement of local size and velocity probability density distributions in two-phase suspension flows by Laser-Doppler technique

A technique is presented for the simultaneous measurement of the local number and velocity probability densities of a dilute two-phase suspension which has a distribution of particle sizes and a predominate direction of flow orientation such as in the cases of pipe and boundary-layer flows. It is shown that by a suitable scheme of discrimination on the amplitude as well as the residence time and frequency of the individual Laser-Doppler bursts, one can obtain the statistics on the size number density distribution and, for each size range, velocity distribution of the particulate phase together with the velocity probability distribution of the fluid phase.Results have been obtained for experiments conducted on a laminar uniform flow and a turbulent shear flow of a dilute glass particle-water suspension having a particle size distribution. Calibration needed for the scheme was accomplished by analyzing particle size and number density distribution data obtained from a Coulter particle sizing counter on a sample taken with an isokinetic probe.     

Experimental investigation of the probability density of temperature fluctuations in nonisothermal turbulent flows

The results of measuring the probability density of the temperature fluctuations in a weakly heated submerged turbulent jet are given for the range of Reynolds numbers extending from 7.7·10³ to 5·10⁵. It is shown that for large positive fluctuations the probability density is independent of the Reynolds number and is formed by bursts with a characteristic length of the order of the integral scale.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 59–68, September–October, 1996.     

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     

The influence of phase-averaging window size on the determination of turbulence quantities in unsteady turbulent flows

 The phase-averaging window size is shown to affect the measurement of phase-averaged turbulence quantities in unsteady turbulent flows. The flow turbulence is usually estimated on the assumption of quasi-constant flow velocity during the duration of the phase-averaging window. The calculated turbulence level then consists of two parts: one due to the turbulent velocity fluctuations and the other due to the changes in the mean flow velocity. This second part is shown to be directly proportional to the averaging window size. In order to determine the true turbulence the averaging window size has to be made as small as possible, especially if the unsteady flow exhibits large temporal gradients and the flow turbulence itself is small. Received: 9 April 1996/Acceped: 17 August 1996     

Wave dynamics of mixed,periodically nonstationary flows of a spontaneously condensing vapor

A study is made of the dynamics of mixed flows of a condensing vapor with nonequilibrium phase transitions and gas-dynamic discontinuities in channels of variable area in the presence of periodically nonstationary boundary conditions at the entrance. The results are given of a numerical investigation of the flows of superheated and spontaneously condensing water vapor in a supersonic nozzle. It is shown that the periodic nonstationarity of the flow at the entrance can lead to a qualitative rearrangement of the flow structure in the presence of spontaneous condensation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–121, November–December, 1980.     

Application of a droplet cluster to visualize microscale gas and liquid flows

The possibility of using microdroplets, which form a dissipative droplet-cluster structure, as tracers localized in the boundary layer of a gas adjoining a liquid-gas interface is experimentally demonstrated. Examples of the visualization of boundary layer flow fields generated by both processes in the gaseous phase and liquid convection are considered.     

Uniformization of the density in reacting magnetohydrodynamic flows

Ionization and recombination provide a transfer between species in a partially ionized plasma. These phenomena modify the continuity equation for each species by linking them together in a common system. The consequences are specially clear when the velocities of ions and neutrals coincide and the flow is weakly compressible: the densities along each trajectory tend to a definite limit depending only on the initial total density and not on the ion/neutral rate. For the general case a weaker global estimate on the final rate between species may be proved.     

Optical density and velocity measurements in cryogenic gas flows

This paper presents the application of optical measurement techniques in dense-gas flows in a heavy-gas channel to determine planar two-component (2C) velocity profiles and two-dimensional (2D) temperature profiles. The experimental approach is rather new in this area, and represents progress compared with the traditional techniques based on thermocouple measurements. The dense-gas flows are generated by the evaporation of liquid nitrogen. The optical measurement of both the velocity and density profiles is accomplished by the implementation of particle image velocimetry (PIV) and background-oriented schlieren (BOS) systems. Supplemental thermocouple measurements are used as independent calibrations to derive temperatures from the density data measured with the BOS system. The results obtained with both systems are used to quantify the dilution behavior of the propagating cloud through a global entrainment parameter . Its value agrees well with the results obtained by earlier studies.     

Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution

A theoretical model of a two-phase air/dispersed water spray flow in an icing wind tunnel is presented here. The mutual interactions taking place within the dispersed phase known as binary droplet collisions, as well as gravitational sedimentation are considered. Where large droplets and low air stream velocities are concerned, the effect of gravity on droplet dynamics is considerable. Gravity causes the vertical deflection of droplet trajectories and an increase in liquid water content (LWC) in the bottom half of the wind tunnel. Droplet collision tends to influence the size, trajectory and velocity of droplets thus affecting the characteristics of the flow and, thereby, the formation of ice on the object placed in the wind tunnel. The present model simulates droplet motion and droplet collision in an icing wind tunnel, where it may be observed that bouncing, stable coalescence, or coalescence followed by separation are the possible outcomes of collision. In the theoretical examination, firstly, the effect of gravity on the vertical deflection of droplet trajectories and on the vertical distribution of the LWC near the icing object are taken into account, while droplet collision is disregarded. Then both factors are considered and collision outcome is determined together with the size and velocity of post-collision droplets. The initial droplet size distribution (DSD), as it occurs at the nozzle outlet, is estimated by a curve in accordance with previous experimental results. The DSD is determined theoretically near the icing object, which makes it possible to calculate the median volume diameter and the LWC of the aerosol cloud. The simulation results with regard to the LWC are compared to the experimental results obtained in this research and a satisfactory qualitative coincidence is to be found between them.     

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.