Stochastic Separated Flow Research Articles

Description of a Eulerian–Lagrangian Approach for the Modeling of Cooling Water Droplets

The present paper describes a tool developed in-house for the modeling of free-falling water droplet cooling processes. A two-way coupling model is employed to account for the interactions between the droplets and the carrier fluid, following a Eulerian–Lagrangian approach. In addition, a stochastic separated flow technique is employed, involving random sampling of the fluctuating fluid velocity. In physical modeling, two empirical correlations are considered for determining the heat and mass transfer coefficients, with the possibility of accounting for vibrations. The numerical results indicate the preponderance of the interactions between droplet and carrier fluid at various humidity ratios.

Numerical study of solid particle erosion in hydraulic spool valves

The null characteristics of hydraulic spool valves change significantly due to solid particle erosion. In the present work, a numerical model has been established to predict the material removal rate and the worn profile evolution with erosion in hydraulic spool valves. The particle trajectories are solved by a stochastic separated flow model based on eddy interaction, and the squeeze film is included as a part of a particle-wall interaction model. The erosion rates are then predicted by the particle impact characteristics, and the worn profiles are obtained by a time-discrete and spatial-discrete update method. The major influencing factors, including particle size, differential pressure, spool opening, and flow direction, are discussed. Through comparison with laboratory experiments and a field case, the model was verified. The present model and theoretical analysis are intended to elucidate the life-cycle management, life evaluation and degradation-resistant design of the spool valve.

Target Lagrangian kinematic simulation for particle-laden flows.

The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.

Prediction of soot and thermal radiation in a model gas turbine combustor burning kerosene fuel spray at different swirl levels

Combustion of kerosene fuel spray has been numerically simulated in a laboratory scale combustor geometry to predict soot and the effects of thermal radiation at different swirl levels of primary air flow. The two-phase motion in the combustor is simulated using an Eulerian–Lagragian formulation considering the stochastic separated flow model. The Favre-averaged governing equations are solved for the gas phase with the turbulent quantities simulated by realisable k–ϵ model. The injection of the fuel is considered through a pressure swirl atomiser and the combustion is simulated by a laminar flamelet model with detailed kinetics of kerosene combustion. Soot formation in the flame is predicted using an empirical model with the model parameters adjusted for kerosene fuel. Contributions of gas phase and soot towards thermal radiation have been considered to predict the incident heat flux on the combustor wall and fuel injector. Swirl in the primary flow significantly influences the flow and flame structures in the combustor. The stronger recirculation at high swirl draws more air into the flame region, reduces the flame length and peak flame temperature and also brings the soot laden zone closer to the inlet plane. As a result, the radiative heat flux on the peripheral wall decreases at high swirl and also shifts closer to the inlet plane. However, increased swirl increases the combustor wall temperature due to radial spreading of the flame. The high incident radiative heat flux and the high surface temperature make the fuel injector a critical item in the combustor. The injector peak temperature increases with the increase in swirl flow mainly because the flame is located closer to the inlet plane. On the other hand, a more uniform temperature distribution in the exhaust gas can be attained at the combustor exit at high swirl condition.

Stochastic separated flow models with applications in numerical computations of supersonic particle-laden turbulent flows

In this article, three stochastic separated flow models were applied to predict the dispersion of inertial fuel particles in the supersonic turbulent flows. The flow field of continuous phase was simulated by means of Reynolds-averaged Navier–Stokes method with a two-equation turbulence model. Clift’s expression was used to modify the drag force on the particle considering the compressibility effects. The particle-phase statistics were obtained by a secondary-order time-weighed Eulerian method. The ability of those stochastic separated flow models was then compared for predicting the mean particle velocity and the particle dispersion. For obtaining a statistically stationary solution, the stochastic separated flow model required the largest number of computational particles, whereas the improved stochastic separated flow model was found to need the least. The time-series stochastic separation flow model lay in-between. Compared with the other two models, the particle dispersion was over-predicted by the stochastic separated flow model in the supersonic particle-laden boundary layer flow, while the improved stochastic separated flow model was less predictable for the particle spatial distribution in the particle-laden strut-injection flow. Three models could well predict the mean velocities of the particle phase. This study is valuable for selecting a validated model used for predicting the particle dispersion in supersonic turbulent flows.

Modeling of nonreacting and reacting turbulent spray jets using a fully stochastic separated flow approach

Numerical modeling of several turbulent nonreacting and reacting spray jets is carried out using a fully stochastic separated flow (FSSF) approach. As is widely used, the carrier-phase is considered in an Eulerian framework, while the dispersed phase is tracked in a Lagrangian framework following the stochastic separated flow (SSF) model. Various interactions between the two phases are taken into account by means of two-way coupling. Spray evaporation is described using a thermal model with an infinite conductivity in the liquid phase. The gas-phase turbulence terms are closed using the k– ε model. A novel mixture fraction based approach is used to stochastically model the fluctuating temperature and composition in the gas phase and these are then used to refine the estimates of the heat and mass transfer rates between the droplets and the surrounding gas-phase. In classical SSF (CSSF) methods, stochastic fluctuations of only the gas-phase velocity are modeled. Successful implementation of the FSSF approach to turbulent nonreacting and reacting spray jets is demonstrated. Results are compared against experimental measurements as well as with predictions using the CSSF approach for both nonreacting and reacting spray jets. The FSSF approach shows little difference from the CSSF predictions for nonreacting spray jets but differences are significant for reacting spray jets. In general, the FSSF approach gives good predictions of the flame length and structure but further improvements in modeling may be needed to improve the accuracy of some details of the predictions.

EVALUATION OF PARTICLE STOCHASTIC SEPARATED FLOW MODELS VIA LARGE EDDY SIMULATION

This paper evaluates three widely used particle stochastic separated flow (SSF) models through large eddy simulation (LES) of gas-particle two-phase turbulent flows over a backward-facing step. The ability of the models to predict mean velocities, fluctuating velocities, and spatial dispersion of particles are carefully examined in comparison with LES reference results. Evaluation shows that the improved time-series SSF model produces good predictions on mean and fluctuating velocities in the particle phase which highly agree with LES results. However, the time-series SSF model has higher computational cost. Further, compared with the two other models, the time-series SSF model predicts better results on the spatial dispersion of particles. It has an overall advantage in terms of accuracy and efficiency in predicting velocity moments and particle dispersion even without the presence of so many particles. The dependence of different SSF models on the number of computational particles in a converged flow field is also discussed. This paper is useful for the selection and application of SSF models in numerical simulations of practical two-phase turbulent flows.

Numerical Simulation of the Cooling Effect by Air Conditioner and Spraying in High-Temperature Working Face

A multicomponent turbulent model of the airflow in working face was modeled.And the simulation result is compared with the measured temperature.The temperature of the airflow along the transportation channel of working face goes up,and the gradient of the temperature curve is flat.Then the low-temperature droplets are simulated by stochastic separated flow model.The interaction between grains and fluid are simulated by adding source terms in conservation equations.The temperature curves of the airflow under different cooling schemes are investigated.If the air conditioner is in front of the nozzles,the temperature of the air near the inlet is low and uniform,and the cooling effect of the outlet is obvious.

Simulations of Evaporating Spray Jet in a Uniform Co-Flowing Turbulent Air Stream

Numerical simulations are performed on the flow of fine, polydisperse droplets of acetone ejected from a round jet of air into an ambient turbulent, uniform co-flowing air stream. The objective is to validate the numerical model by comparing the predictions with experimental measurements of a well defined evaporating spray configuration (Chen et al., Int. J. Multiphase Flow 32(2006), 389–412). The carrier-phase is considered in the Eulerian context, while the dispersed phase is tracked in the Lagrangian framework. Various interactions between the two phases are taken into account by means of a two-way coupling. The stochastic separated flow (SSF) model is adopted for the spray calculations. The gas-phase turbulence terms are closed using the standard k-ε model. The spray evaporation is described using a thermal model with an infinite-conductivity. Overall, very good agreement is observed in the comparisons of the computational predictions and experimental measurements. The predicted droplet number-mean axial velocity, r.m.s. of fluctuating velocity for the various droplet classes at different downstream locations exhibit a self-similarity downstream of the nozzle exit. Near the nozzle-exit (around z/djet = 5), the r.m.s. of droplet number mean axial fluctuating velocity attains a maximum within the shear layer near r/djet = 0.4–0.6 for different droplet classes. Further downstream, the peak shifts towards the axis. A similar variation is noticed in the Sauter mean diameter (SMD) distribution of the droplets. It is concluded that, a higher level of turbulence leads to a faster depletion of the smaller droplets, resulting in an increase in the local droplet-SMD in those regions.

A Time-Series Stochastic Separated Flow (TSSSF) Model for Turbulent Two-Phase Flows

A time-series stochastic separated flow (TSSSF) model is proposed to obtain more reasonable statistical characteristics of two-phase turbulent flows. The sampled instantaneous fluctuating velocities of the gas phase u i ′(t) are imposed on the particle's motion for n time steps determined by the calculation of the auto-correlation coefficient between u i ′(t) and u i ′(t − n Δt) at each time step. An application of the model is performed in a turbulent two-phase flow over a backward-facing step. The statistical particle-phase velocities and particle concentration contours agree well with the experimental data and large-eddy simulation results, respectively. The present model can represent the unsteady flow mechanisms and therefore improves the prediction of particle dispersion.

Development of a Hybrid Turbulent Particle Dispersion Model and Implementation in the Gasflow Code

Abstract Dust mobilization in a vacuum vessel is one of the key issues endangering the security of the International Thermonuclear Experimental Reactor (ITER) in case of loss of vacuum accidents. The turbulent behavior of particles in turbulent flows has to be modeled for successful numerical simulations about particle mobilization. In this study a Lagrangian approach is adopted to formulate the particle transport especially for dust-dilute flows mostly encountered in the vacuum vessel of ITER. Based on the logic frame of the approach and the used computational fluid dynamics (CFD) computer code in the study, a hybrid turbulent particle dispersion model is proposed. The hybrid model features both a deterministic separated flow model and a stochastic separated flow (SSF) model, which are two popular turbulent dispersion models applied in particle simulations, and takes the advantages of the both models. The proposed model is implemented into the particle model of the CFD code successfully and the simulation results are verified against the experimental data. The verifications manifest the validities of the proposed model. In this paper general information about the work of dust mobilization is introduced and the particle turbulent dispersion models are reviewed briefly at first. The hybrid model is then proposed based on the SSF model. An experiment about particle dispersions in an advective wind channel flow with decaying turbulence in the streamwise direction is reviewed in the third section. In the following section about model verification, the decaying turbulence parameters in the channel flow are verified against the experimental data as the first step, and the parameters about the particle dispersions in the verified flow field are then verified against the data. The work is concluded finally.

Large-eddy simulation of two-phase spray combustion for gas turbine combustors

In three-dimensional arbitrary curvilinear coordinates, an Eulerian–Lagrangian formulation is applied to large-eddy simulation (LES) of instantaneous gas–liquid two-phase turbulent combustion flows in gas turbine combustors. Three dimensional block-structured grids are generated by zone method and solving a system of elliptic partial differential equations. The k-equation sub-grid scale model is used to simulate the sub-grid eddy viscosity and the EBU combustion sub-grid scale model is employed to predict the chemical reaction rate. The gas-phase governing equations are solved with SIMPLE algorithm and hybrid scheme in non-staggered grid system. A stochastic separated flow formulation is used to track the droplet trajectories velocities, size and temperature history by Lagrangian equations of motion and thermal balance. Multi-zone coupling method is employed to transport data between interfaces. The influences of two different primary hole positions and three different fuel–air ratios on turbulent two-phase reacting flows are calculated. Predictions are in reasonable agreement with the measured velocity using PIV system and temperature, species concentration measurements at the exit. It is shown that the present approach may be used to study spray combustion flow fields for guiding the design of advanced gas turbine combustors.

Effect of initial conditions of modeled PDFs on droplet characteristics for coalescing and evaporating turbulent water spray used in fire suppression applications

Parametric studies were conducted for a coalescing and evaporating turbulent water spray using a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet binary collisions. While the initial droplet size distribution, in general, is not known due to the difficulty in the optical access to the nozzle exit region, the size distribution is modeled using the analytical PDFs (probability density functions) such as log-normal, Rosin–Rammler, Gaussian, and Nukiyama–Tanasawa distribution model. Standard deviation of the PDFs is varied and their effects on droplet size and speed distribution in the downstream are reported. The arithmetic mean droplet size at the nozzle exit, which is used as input for simulations, was extrapolated using the existing experimental data obtained at downstream locations.

Self-consistency and the use of correlated stochastic separated flow models for prediction of particle-laden flows

Computational fluid dynamics (CFD) is being used increasingly in the design and analysis of particle-laden flows. A significant challenge of this work is in correctly predicting the interaction of the fluid turbulence with the particulate phase. Typically, Lagrangian tracking is used to calculate the particle trajectories with stochastic treatments used to provide an instantaneous turbulent flow field. The stochastic calculations are based on the mean velocities and turbulence quantities calculated by the CFD solver. The current work examines the correlated stochastic separated flow (SSF) model used to synthesize the instantaneous fluid velocity field. Two functional forms of the Eulerian spatial correlation are considered: exponential, and Frenkiel with loop parameter m equal to unity. It is well known that the use of a Frenkiel function is incorrect due to the Markovian nature of the model. Nonetheless, a literature review indicates that the Frenkiel function is still being used in the CFD community. In order to illustrate the implications of this, numerical predictions are compared to Taylor's analytical result for fluid particle dispersion in homogeneous isotropic turbulence. Excellent predictions are obtained with the exponential correlation and recommendations on timestep requirements are made. In contrast, predictions from the Frenkiel model are in poor agreement with Taylor's solution. This poor agreement results from an inconsistency between the effective correlation of fluid velocities arising from the model and the original intended correlation.

AN IMPROVEMENT TO THE SSF MODEL FOR PREDICTION OF LIGHT PARTICLE DISPERSION

This study investigates the predicted motion of small, light particles using the stochastic separated flow models proposed by Shuen et al. (1983) and Lightstone and Raithby (1998). Model predictions are compared to the benchmark experiment of Snyder and Lumley (1971) for particles released from a point source in grid-generated turbulence. It is found that the predictions of particle velocity variance and dispersion exhibit nonphysical waves. This behavior is explored in order to understand its mathematical basis arising from the model formulation. A modification to the model is presented. The modified model is successful in removing the characteristic waves.

Analysis of tracer particle migration in inhomogeneous turbulence

Previous studies [J.M. Maclnnes, F.V. Bracco, Stochastic particle dispersion modeling and the tracer particle limit, Physics of Fluids A 4 (1992) 2809–2824; X.Q. Chen, Heavy particle dispersion in inhomogeneous, anisotropic, turbulence flows, International Journal of Multiphase Flow 26 (2000) 635–661; T.L. Bocksell, E. Loth, Random walk models for particle diffusion in free-shear flows, AIAA Journal 29 (2001) 1086–1096] have shown that the commonly applied stochastic separated flow (SSF) model predicts unphysical results when dealing with the dispersion of tracer particles in inhomogeneous flows. This problem is explored, with regards to the discontinuous random walk model, by considering an idealized flow with constant mean velocity with two regions of constant turbulent kinetic energy. Using the probability density functions (PDFs) for the turbulent velocities it is shown that there is a higher probability of particles traveling into the low kinetic energy region than there are traveling to the region of high kinetic energy, thus resulting in a net migration of particles to the region of low kinetic energy. Corrections that apply a correction velocity and/or adjust the fluctuating velocity based on the local value of the turbulent kinetic energy are analyzed and tested.

Numerical modeling and experimental measurements of water spray impact and transport over a cylinder

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.

Influences of inlet air pressure, air temperature and secondary air swirl on penetration histories of pulverized coal particles in a tubular combustor

A numerical model has been developed to predict the penetration histories of poly-dispersed pulverized coal particles undergoing the process of devolatilization and subsequent combustion into a turbulent swirling flow of air in a typical tubular combustor. The computation scheme is based on the typical stochastic separated flow model of the gas-particle flow within the combustor. A k– ɛ model with wall function treatment for near wall region has been adopted for the solution of conservation equations in gas phase on a Eulerian frame. The initial size parameters of coal particles are specified by a suitable pdf size distribution. The combustion chemistry has been considered by the typical ‘conserved scalar mixture fraction approach’. The information of pulverized coal particles are generated by the solution of conservation equations of discrete coal particles on a Lagrangian scheme. The temperature and mass histories of coal particles along their trajectories in the combustor have been evaluated at different values of inlet pressure and temperature of air and secondary air swirl. It has been recognized that penetration of particles in the combustor is reduced with pressure and secondary air swirl. While the coarser particles exhibit a relatively larger mass depletion in a situation of air flow without swirl, the finer particles exhibit the same in a flow with swirl.

Droplet distributions at the liquid core of a turbulent spray

Initial droplet distributions at the liquid core are examined for various Weber number and pulsing conditions. While experimental investigation in the liquid core region is nearly impossible due to difficulty in the optical access to the region, the distribution at the region is investigated computationally, and typical droplet distributions are identified. It is found that the Nukiyama–Tanasawa and log-normal distributions can best describe the droplet size and velocity distributions, respectively. By comparing computational results obtained at the liquid core (0<x<8mm) and experimental data collected at x=48mm, it is suspected that the droplet gradation occurs immediately after droplets are separated from the liquid core. Thus, the distribution shape changes rapidly in both axial and radial directions. Such droplet–gradation behavior is numerically confirmed when the Nukiyama–Tanasawa droplet size distribution is used as an initial condition for the stochastic separated flow model. When the jet velocity is increased, the width of the droplet-size distribution becomes narrower, while the droplet velocity distribution becomes broader. Possible physical mechanism for that behavior is discussed in detail. Pulsing injection prominently influences the external spray shape near the nozzle exit. However, the overall droplet size and velocity distributions of the liquid core due to the pulsing injection are relatively insignificant for a turbulent spray in the atomization regime.

Modelling spray impingement using linear stability theories for droplet shattering

This paper compares several linear-theory-based models for droplet shattering employed for simulations of spray impingement on flat wall surface or a circular cylinder. Numerical simulations are conducted using a stochastic separated flow (SSF) technique that includes sub-models for droplet dynamics and impact. Results for spray impingement over a flat wall indicate that the linear theory applicable for a single droplet impact over-predicts the number of satellite (or secondary) droplets upon shattering when compared to experimental data. The causes for the observed discrepancies are discussed. Numerical simulation results for spray impingement over a circular cylinder in cross flow are obtained and discussed. Copyright © 2005 John Wiley & Sons, Ltd.