A mathematical model for predicting spray atomization characteristics in an Eulerian–Eulerian framework

A new mathematical model is developed for calculating droplet break-up frequency based on both drag and turbulence induced fragmentation stresses. The droplet break-up model is introduced into a CFD methodology that is based on the Eulerian–Eulerian approach. The CFD solver couples the population balance equation along with the Navier–Stokes equations for predicting the droplets diameter. Finally, preliminary results using this CFD model are presented for the case of a coaxial airblast atomizer and a good agreement with the experimental data is achieved.     

Blow-off process of highly under-expanded hydrogen non-premixed jet flame

Relationships between flame lift-off heights and reservoir pressure were experimentally investigated in order to clarify blow-off process of hydrogen non-premixed jet flames with a highly under-expanded jet structure. In this study, straight nozzles with diameters of 0.34, 0.53, 0.75 and 1.12 mm were used with maximum reservoir pressure for spouting hydrogen of 13.2 MPa. Experimental results are shown that lift-off heights in stable under-expanded jet flames do not vary significantly and are independent of the reservoir pressure in the range of studied pressure. However, the lifted heights are affected by the nozzle diameters and become smaller as the nozzle diameters increase. From experimental results, the condition for the blow-off process of under-expanded subsonic jet flames was proposed. It was concluded that the under-expanded jet flame could be blown off when the maximum waistline position, where radial distance from the jet axis to an elliptic stoichiometric contour reaches its maximum comes closer to the nozzle exit than the edge of the jet flame base.     

Estimation of turbulence intensity using rotor effective wind speed in Lillgrund and Horns Rev-I offshore wind farms

Turbulence characteristics of the wind farm inflow have a significant impact on the energy production and the lifetime of a wind farm. The common approach is to use the meteorological mast measurements to estimate the turbulence intensity (TI) but they are not always available and the turbulence varies over the extent of the wind farm. This paper describes a method to estimate the TI at individual turbine locations by using the rotor effective wind speed calculated via high frequency turbine data.The method is applied to Lillgrund and Horns Rev-I offshore wind farms and the results are compared with TI derived from the meteorological mast, nacelle mounted anemometer on the turbines and estimation based on the standard deviation of power. The results show that the proposed TI estimation method is in the best agreement with the meteorological mast. Therefore, the rotor effective wind speed is shown to be applicable for the TI assessment in real-time wind farm calculations under different operational conditions. Furthermore, the TI in the wake is seen to follow the same trend with the estimated wake deficit which enables to quantify the turbulence in terms of the wake loss locally inside the wind farm.     

Spatial and temporal variation of turbulence characteristics in combined sewer flow

Flow unsteadiness is a typical feature of both combined and storm sewer flow. The following study therefore deals with both theoretical and experimental investigations of the steady uniform and transient turbulent open-channel flows in a circular conduit with smooth walls as well as over rough sediment deposits. The aim of the study is to define the relationship between flow unsteadiness and selected flow/turbulence characteristics estimated in a circular tube running partially full using the ultrasonic velocity profiler (UVP) method. The temporal/spatial turbulence intensities and the Reynolds stress distribution were identified in the mid-vertical of the pipe. Generally, the absolute values of turbulent characteristics are larger in the rising branch of the hydrograph than in the descending one for the same flow depths. This difference in absolute values is related to the flow equilibrium parameter. Furthermore, the influence of the sediment bed on selected flow/turbulence variables was studied. The results show a strong impact of cross-section geometry on local values of friction velocity, i.e. bottom shear stress, along the wetted perimeter of the channel cross-section. Interestingly, their relative values decreased along with an increase in flow depth.     

Performance of Kenics static mixer over a wide range of Reynolds number

The present study deals with the numerical simulation of flow patterns and mixing behaviour in Kenics static mixer over a wide range of Reynolds number. Three different sets of Kenics mixer (aspect ratio = 1.5) comprised of 3, 9 and 25 elements each have been characterized. The Reynolds number was varied in the range of 1 to 25,000 (i.e., from laminar to turbulent flow regime). The numerical approach takes into account the aspects of the fluid flow at higher Reynolds number values including circumferential velocity profiles at different cross-sections within the Kenics mixer, which were neglected in previous studies. It was observed that cross-sectional mixing in the turbulent flow regime takes place up to 30% of each element length at element-to-element transition; beyond that velocity profiles were uniform. The experiments were also carried out to measure the circumferential and axial velocity profiles and pressure drop in three different Kenics Mixers using air as fluid. The pressure drop per unit element (ΔP/η) was found to be independent of the number of Kenics mixing elements used in the system. The total pressure drop across Kenics mixer obtained by CFD simulations were compared with the experimental pressure drop values and correlations available in the literature. The numerical results were found in good agreement with the experimental as well as the results reported in the literature. A new pressure drop correlation in the Kenics static mixer has been developed.     

Aerosol nucleation and growth in a turbulent jet using the Stochastic Fields method

The Stochastic Fields transported PDF method for turbulent reacting flows has been used to model the nucleation and growth of dibutyl phthalate particles in a hot, turbulent jet in a colder background for which experimental data is available. The aerosol population is modelled using an assumed log-normal size distribution. It has been found that neglecting the effect of turbulent fluctuations leads to the peak particle concentration being predicted too close to the jet and the concentration downstream underpredicted. However, this effect was small compared to that of adjusting modelled surface tension. Only by adjusting this was it possible to reproduce correctly the downstream evolution of particle number found in experiment. Particle mass mean diameter was significantly underpredicted at the centre of the jet, which may be due to the inability of log-normal size distribution to capture the distribution in detail. Taking account of turbulent fluctuations leads to increased mean particle size at the edge of the plume. The extent of this increase is strongly dependent on the choice of micromixing timescale.     

Multicompartment hydrodynamic model for slurry bubble columns

A core-annulus multicompartment two-dimensional two-bubble class model accounting for slurry recirculation and coupled with catalyst transport was developed as a part and parcel of the analysis of the behavior of slurry bubble column reactors at high gas throughputs corresponding to the churn turbulent flow regime. The model analyzed the contributions of bubble-induced turbulence closures, bubble coalescence and breakup phenomena, and catalyst axial distribution as the resultant of sedimentation, advection via liquid-solid slip, per-compartment axial dispersion and core-annulus lateral exchange of catalyst by bubble-induced turbulence. The model was also used to analyze the effects of catalyst loading, gas density and superficial velocity, and column diameter and vessel aspect ratio on the hydrodynamics of slurry bubble column reactors, namely, the per-compartment phase holdups and interstitial velocities, pressure gradient, bubble coalescence and break-up rates, and loci of velocity inversion for the gas and slurry profiles.     

Mass transfer across the falling film: Simulations and experiments

Mass transfer across the thin falling film gas-liquid interface is a very important process as in chemical engineering and other fields, and yet there is still a lack of general predictability of the transfer quantity based on basic hydrodynamic parameters and independent of the geometrical setup. In this work, a numerical simulation is carried out for a vertical falling film arrangement. The wave dynamics and the associated mass transfer phenomena are discussed and compared with previous experimental empirical relationships. Based on the validity of the simulated results for wave parameters, numerical experiments for mass transfer were carried out with the aim of comparing to the empirical relation based on a single hydrodynamic parameter β (the gradient of the vertical fluctuating velocity at the interface) established previously by Law and Khoo [2002. Transport across a turbulent gas-liquid interface. A.I.Ch.E. Journal 48(9), 1856-1868.] and Xu et al. [2006. Mass transfer across the turbulence gas-water interface. A.I.Ch.E. Journal 52, 3363-3374] with various non-falling film experiments. Separately, experiments in an inclined plate thin falling film apparatus were carried out to determine the β distribution and associated mass transfer. It is found that there is reasonable concurrence with the mentioned empirical relation, hence suggesting the general applicability of β characterizing the scalar transport across the gas-liquid interface independent of the means of turbulence generation.     

CFD simulation of Taylor–Couette flow in scraped surface heat exchanger

The flow between two concentric cylinders which is termed as Taylor–Couette flow has been studied in scraped surface heat exchanger with and without blades. Shear rate in annular flow with and without blades was measured by Dumont et al. (2000a) using electrochemical method and determined the onset of Taylor vortices at specific Taylor number in both cases for Newtonian flow. CFD simulations have been carried out to determine the transition zone from laminar Couette flow to Taylor vortex flow using the same geometry for which Dumont et al. (2000a) had carried out the experiments. The Reynolds stress model (RSM) and k–? model are used for Taylor vortex flow (Ta > 300) to characterize the flow pattern in annular flow and SSHE respectively. The aim of the present work is to analyze the effect of rotating scraper on the existing flow patterns in simple annular flow using CFD simulations.     

Numerical simulation of mass transport in a filter press type electrochemical reactor FM01-LC: Comparison of predicted and experimental mass transfer coefficient

This paper studies flow characteristics and their effect on local mass transfer rate to a flat plate electrode in a FM01-LC electrochemical reactor. 3D reactor simulations under limiting current and turbulent flow conditions were performed using potassium ferro-ferricyanide electrochemical system with sodium sulfate as supporting electrolyte. The model consists of mass-transport equations coupled to hydrodynamic solution obtained from Reynolds-averaged Navier–Stokes equations using standard k–? turbulence model, where the average velocity field, the turbulence level given by the eddy kinetic energy and the turbulent viscosity of the hydrodynamic calculation were used to evaluate the convection, turbulent diffusion and the concentration wall function. The turbulent mass diffusivity was evaluated by Kays–Crawford equation using heat and mass transfer analogies, while wall functions, for mass transport, were adapted from Launder–Spalding equations. Simulation results describe main flow properties, concentration profiles throughout the entire volume of the reactor and local diffusion flux over the electrode. Overall mass transfer coefficients estimated by simulation, without fitting parameters, agree closely with experimental coefficients determined from limiting current measurements (1.85% average error) for Re between 187 and 1407.