Large eddy simulation of particle response to turbulence along its trajectory in a backward-facing step turbulent flow

In order to understand particle response to turbulence along its path, properties of the particle phase and gas phase are compared and analyzed for a turbulent flow over a backward-facing step. The turbulent gas phase is simulated numerically using large eddy simulation and the particle phase is modeled by means of Lagrangian methods. The particle Stokes number ranges from 0.01 to 111.18 and the Reynolds number is 18,400, based on the step height and the inlet mean velocity. Particle velocities, fluid velocities and vorticity along particle trajectory as well as particle dispersion are obtained so as to provide information on particle response to turbulence. Results show that particle behavior depends heavily on the local fluid turbulence along its path, especially for small particles. Particles follow a path along which the gas-phase vorticity is small. However, large particles maintain the inertia along their trajectories without responding to the fluid fluctuations.     

Modeling nonadiabatic turbulent premixed reactive flows including tabulated chemistry

A two-scalar probability density function (PDF) is used to evaluate the mean chemical rate in turbulent combustion. This presumed PDF is based on an original closure model which has previously been validated for adiabatic partially premixed combustion. This model is now extended to nonadiabatic premixed combustion in a turbulent reactive flow and only requires transport equations for means and variances of two independent thermodynamical quantities, i.e., fuel mass fraction and enthalpy. Numerical simulations of a turbulent propane/air flame stabilized in the vicinity of recirculation kernels generated by a sudden expansion are performed. Heat losses at the combustion chamber walls are incorporated and depend on the wall material thermal characteristics. Two chemical mechanisms are investigated: (i) a global one-step reaction following an Arrhenius law and (ii) a tabulated chemistry (FPI technique) predicting intermediate species (carbon monoxide, OH and CH radicals, etc.). Numerical simulations on the mean velocity and temperature fields are compared to experimental data. In particular, the capability of the model to predict the temperature field, a quantity depending on both fuel mass fraction and enthalpy, is clearly demonstrated.     

A statistical model for predicting the fluid displaced/added mass and displaced heat capacity effects on transport and heat transfer of arbitrary-density particles in turbulent flows

The objective of the paper is twofold: (i) to present a new statistical model for predicting the transport and heat transfer of arbitrary-density particles suspended in turbulent flows and (ii) to examine the performance of this model in an isotropic velocity flow field without and with a mean temperature gradient as well as in a near-wall turbulent flow. The model presented is based on a kinetic equation for the probability density function (PDF) of velocity and temperature distributions and coves the entire range of the particle-to-fluid density ratio (from heavy particles in a gas to bubbles in a liquid).     

A mesoscopic description of polydispersed particle laden turbulent flows

Turbulent polydispersed multiphase flows are encountered in many engineering and environmental applications and particularly in combustion applications, spray polydispersity is the norm rather than the exception. In this review we summarize the current state of Eulerian transport models for turbulent polydispersed particulate flows without size class discretization. The stochastic nature of both carrier and dispersed phase justifies a stochastic approach to describe the behavior of such systems. In this regard Brownian motion of a single microscopic particle is discussed to intuitively introduce the subject and point out the need for a stochastic representation of the phenomena based on stochastic differential equations (SDEs). Understanding the stochastic tools and mathematical framework based on Langevin equation is compulsory for the rest of this review but here we restrict our coverage to definitions and general remarks and give references for further readings. A stochastic foundation based on Langevin equation is defined for fluid and particle and derivation of the transport equation up to third order statistics without binning the particle diameter is discussed based on corresponding Fokker–Planck equation. Terms that appear in the process of contracting a probability density function (PDF) causing closure problems are identified. The Maximum entropy method is discussed as a tool for closure of particle acceleration terms in Eulerian transport equations followed by current closure issues such as realizability and generality.     

Turbulent collision rates of arbitrary-density particles

The paper deals with collisions resulting from the interaction between particles (droplets, bubbles) and turbulent eddies of the continuous fluid medium (gas or liquid). A statistical model is developed for predicting the collision rate. This model is valid for arbitrary values of the particle-to-fluid density, the particle inertia parameter, and the ratio between the particle size and the fluid turbulent lengthscale.     

An improved mixing model providing joint statistics of scalar and scalar dissipation

For the calculation of nonpremixed turbulent flames with thin reaction zones the joint probability density function (PDF) of the mixture fraction and its dissipation rate plays an important role. The corresponding PDF transport equation involves a mixing model for the closure of the molecular mixing term. Here, the parameterized scalar profile (PSP) mixing model is extended to provide the required joint statistics. Model predictions are validated using direct numerical simulation (DNS) data of a passive scalar mixing in a statistically homogeneous turbulent flow. Comparisons between the DNS and the model predictions are provided, which involve different initial scalar-field lengthscales.     

Equilibrium Eulerian approach for predicting the thermal field of a dispersion of small particles

The equilibrium Eulerian method [J. Ferry, S. Balachandar, A fast Eulerian method for disperse two-phase flow, Int. J. Multiphase Flow 27 (7) (2001) 1199–1226] provides an accurate approximation to the velocity field of sufficiently small dispersed particles in a turbulent fluid. In particular, it captures the important physics of particle response to turbulent flow, such as preferential concentration and turbophoresis. It is therefore employed as an efficient alternative to solving a PDE to determine the particle velocity field. Here we explore two possible extensions of this method to determine the particle temperature field accurately and efficiently, as functions of the underlying fluid velocity and temperature fields. Both extensions are theoretically shown to be highly accurate for asymptotically small particles. Their behavior for finite-size particles is assessed in a DNS of turbulent channel flow (Re_τ = 150) with a passive temperature field (Pr = 1). Here it is found that although the order of accuracy of the two extensions is the same, the constant factor by which one is superior to the other can be quite large, so the less accurate extension is appropriate only in the case of a very small mechanical-to-thermal response time ratio.     

颗粒扩散的三个效应分析及其数值模拟

在对均匀各相同性湍流中的颗粒进行研究时，目前通常采用拉氏方法描述两相湍流中的颗粒相运动，用的较多的就是基于颗粒所见气体速度的Langevin方程。此方程的封闭必须考虑颗粒扩散的轨道穿越效应、连续性效应和惯性效应。在仔细分析几个效应的基础上，提出了一种改进的漂移系效模型，综合考虑颗粒在均匀各向同性湍流内扩散所遇到的三种效应的影响，并进行数值模拟分析了几个效应对于效值模拟结果的影响。     

Modeling of heat transfer and differential diffusion in transported PDF methods

In order to model the conditional diffusive heat and mass fluxes in the joint probability density function (PDF) transport equation of the thermochemical variables, the diffusive fluxes are decomposed into their Favre mean and fluctuation. While the mean flux appears to be closed, the contributions of fluctuating fluxes are modeled with the interaction by exchange with the mean (IEM) model. Usually, the contribution of the Favre averaged diffusive fluxes is neglected at high Reynolds numbers. Here, however, this term is included to account for molecular mixing in regions, where turbulent mixing is negligible. This model approach is applied in steady state Reynolds Averaged Navier–Stokes (RANS)/transported PDF calculations to simulate the heat transfer of wall bounded flows as well as the stabilization of a hydrogen–air flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes. In wall bounded flows this is the case in the viscous sublayer. Heat transfer studies show, that “mixing models” based on the high Reynolds number assumption fail to compute correctly the temperature field and the heat flux close to the wall. A similar situation occurs at the flame root of the investigated turbulent hydrogen-air jet flame, where turbulent mixing is still too weak to achieve a fast mixing of reactants. In this area differential diffusion effects are observed in the experiment, i.e. superequilibrium temperatures and nonlinear relations between the elemental mixture fractions of hydrogen and oxygen. It will be shown, that the presented model can successfully reproduce these effects, which underlines the necessity to include Favre averaged molecular diffusive fluxes in transported PDF methods.     

Simulations of transient n-heptane and n-dodecane spray flames under engine-relevant conditions using a transported PDF method

Time-dependent Reynolds-averaged CFD is performed for transient turbulent spray flames in a high-pressure, constant-volume chamber for two single-component fuels using skeletal chemical mechanisms. The simulations span a range of initial pressures, temperatures and compositions that correspond to conventional and advanced (e.g., low-temperature) compression-ignition engine combustion. The objectives are to establish the extent to which turbulent fluctuations in composition and temperature influence ignition delays and lift-off lengths and turbulent flame structure under engine-relevant conditions, and to provide insight into turbulence-chemistry interactions. This is done by comparing results from a model that accounts for turbulent fluctuations using a transported composition probability density function (PDF) method with those from a model that ignores the influence of turbulent fluctuations on local mean reaction rates (a locally well-stirred reactor – WSR – model). For robust diesel combustion conditions, the WSR and PDF computed ignition delays and lift-off lengths are close to each other, and both are in good agreement with experiment. For lower initial temperatures, ignition delays and lift-off lengths from the two models are significantly different, and the results from the PDF model are in better agreement with experiment. The differences are especially striking for n-dodecane. There the PDF-model computed ignition delays and lift-off lengths are within 10% of measured values for initial temperatures of 900 K and higher (for 22.8 kg/m³ density, 15% oxygen), while the WSR model predicts an ignition delay that is three times the measured value at 900 K. At an initial temperature of 800 K, the WSR model fails to ignite, whereas the PDF model computed ignition delay and lift-off length are within 30% of the measured values. In all cases, the WSR and PDF models produce significantly different turbulent flame structures, and the differences increase with decreasing initial temperature and oxygen level. The WSR model produces a thin laminar-like flame, while the PDF model gives a broadened turbulent flame brush that is qualitatively more consistent with what is expected for these highly turbulent flames and what is observed experimentally. Thus, while it may be possible to reproduce some global ignition characteristics using a WSR model (depending on the choice of chemical mechanism), turbulent fluctuations play an increasingly important role at lower initial temperatures and oxygen levels.     

Evaluation and modification of gas-particle covariance models by Large Eddy Simulation of a particle-laden turbulent flows over a backward-facing step

Three-dimensional numerical investigation of a low speed particle-laden turbulent flow over a backward-facing step has been carried out. An assumption of incompressibility of the flow is used due to low Mach number of the flow. The gas phase is performed by Large Eddy Simulation (LES) and the particle phase is solved by a Lagrangian particle tracking model. The simulation results such as mean streamwise velocities and fluctuation velocities for the both phase are validated by experimental results performed by Fessler and Eaton (1999) [1]. Reynolds number of the gas phase over the backward-facing step with an expansion ratio of 5:3 is 18,400, based on the maximum inlet velocity and step height. The flow is considered as dilute. Hence a one-way coupling method is applied, in which we only consider the effect of fluid on the particle. Particle–particle collisions are also neglected. The success of simulation in predicting a particle-laden turbulent flow using LES and Lagrangian trajectory model provides a numerical basis for revisiting the gas-particle correlations models. Four second-order closure models for gas-particles covariance are evaluated in the present study. A modified better gas-particle covariance model is proposed in this paper.     

Formulation for predicting deposition velocity of particles in turbulence

Relationships for the particle concentration and convection velocity profile has been obtained by the adaptation of the random surface renewal model [1], [2], [3], [4], [5] to the particle continuity and momentum equations of the nonisothermal turbulence boundary-layer flows; particle transport mechanisms of Brownian and turbulent diffusion, eddy impaction, particle inertia, and thermophoresis are included. This proposed model provides a useful framework for coupling these modeling parameters with analytical equation of the particle deposition velocity. The predictions obtained on the basis of this equation have been found to be in good agreement with experimental values of deposition velocity for fully-developed turbulent pipe flow.     

Time response characteristics of microcapsulated liquid-crystal particles

Microcapsulated liquid-crystal particles are widely used as temperature sensors in the field of heat transfer engineering. Conventionally, these particles are painted on a surface of a heated plate for temperature measurements. The temperature is measured by tracing the color changes of the microcapsulated liquid-crystal particle through the color digital image processing technique. Recently, these particles are often suspended in thermal fluid flows as temperature tracers of the flows. For the use of a microcapsulated liquid-crystal particle itself as a temperature sensor in the suspending method, the heat capacity of the capsule covering the liquid crystal should be regarded as an important factor in predicting the time response of the microcapsulated liquid-crystal particle which is directly injected into a thermal fluid flow. The heat capacity of the liquid crystal and the capsule can produce a delayed time response for the temperature change of the outside fluids and eventually produce erroneous measurement data. Without a new temperature sensor smaller than the particle, it is very difficult to measure the time response of the microcapsulated liquid-crystal particle since the particles move with the working thermal fluid in different flow conditions. Therefore, a numerical simulation for the time response of the particle is made and its usable limit is discussed in detail for the measurement of turbulent thermal flows. Responses for a temperature step change, fluctuating temperature changes, and the thermal inertia of the working fluid temperature are considered. The response time of the microcapsulated liquid-crystal particle has been evaluated to be as much as 150 ms time delay for a step change of the working fluid temperature, which means the physical properties of the particle itself must be considered for outside temperature changes. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 390–398, 1998     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.     

DNS of a premixed turbulent V flame and LES of a ducted flame using a FSD-PDF subgrid scale closure with FPI-tabulated chemistry

Two complementary simulations of premixed turbulent flames are discussed. Low Reynolds number two-dimensional direct numerical simulation of a premixed turbulent V flame is first performed, to further analyze the behavior of various flame quantities and to study key ingredients of premixed turbulent combustion modeling. Flame surface density, subgrid-scale variance of progress variables, and unresolved turbulent fluxes are analyzed. These simulations include fully detailed chemistry from a flame-generated tabulation (FPI) and the analysis focuses on the dynamics of the thin flame front. Then, a novel subgrid scale closure for large eddy simulation of premixed turbulent combustion (FSD-PDF) is proposed. It combines the flame surface density (FSD) approach with a presumed probability density function (PDF) of the progress variable that is used in FPI chemistry tabulation. The FSD is useful for introducing in the presumed PDF the influence of the spatially filtered thin reaction zone evolving within the subgrid. This is achieved via the exact relation between the PDF and the FSD. This relation involves the conditional filtered average of the magnitude of the gradient of the progress variable. In the modeling, this conditional filtered mean is approximated from the filtered gradient of the progress variable of the FPI laminar flame. Balance equations providing mean and variance of the progress variable together with the measure of the filtered gradient are used to presume the PDF. A three-dimensional larger Reynolds number flow configuration (ORACLES experiment) is then computed with FSD-PDF and the results are compared with measurements.     

Detailed modeling of soot formation in a partially stirred plug flow reactor

The purpose of this work is to propose a detailed model for the formation of soot in turbulent reacting flow and to use this model to study a carbon black furnace. The model is based on a combination of a detailed reaction mechanism to calculate the gas phase chemistry, a detailed kinetic soot model based on the method of moments, and the joint composition probability density function (PDF) of these scalar quantities.Two problems, which arise when modeling the formation of soot in turbulent flows using a PDF approach, are studied. A consistency study of the combined scalar-soot moment approach reveals that the molecular diffusion term in the PDF-equation can be closed by the IEM and Curl-type mixing models. An investigation of different kernels for the collision frequency of soot particles shows that the influence of turbulence on particle coagulation is negligible for typical flame conditions and the particle size range considered.The model is used as a simple tool to simulate a furnace black process, which is the most important industrial process for the production of carbon blacks. Despite the simplifications in the modeling of the turbulent flow reasonable agreement between the calculated soot yield and data measured in an industrial furnace black reactor is achieved although no adjustments were made to the kinetic parameters of the soot model. The effect of the mixing intensity on soot yield and different soot formation rates is investigated. In addition the influence of different operating conditions such as temperature and equivalence ratio in the primary zone of the reactor is studied.     

Simulation of Swirling Turbulent Flow and Combustion in a Combustor

An algebraic concentration moment (ACM)-PDF turbulent combustion model is proposed. It is formulated by jointly utilizing the explicit algebraic expressions for the second-order-moment of concentration fluctuation and the presumed probability density function (PDF) of gas instantaneous temperature. A set of analytical expressions for the time-averaged temperature relevant quantity is obtained for the closure of the time-averaged reaction rate. The model is applied to the simulation of turbulent flow and combustion in a swirl combustor. The calculated gas velocity, temperature, species concentrations, and turbulent fluctuating velocity are in agreement with the measured data. They are much improved over those obtained by the EBU-Arrhenius model.     

Experimental and numerical investigation of premixed acetylene flame

In this paper, the mean velocity, turbulence intensity and temperature profiles in different cross-sections of premixed acetylene flame are given. A mathematical model for prediction of velocity, temperature and concentration fields of axisymmetric free premixed turbulent flame is presented in this paper. A second-order closure for turbulent reacting flows is used. Special attentions is paid to model behavior with the respect to the prediction correlation coefficients of turbulent diffusion of the scalar components. Conditional and unconditional statistics of the LDA signals were performed using jet and/or air seed. Compared to commonly used unconditional statistics, conditional statistics of velocity fluctuations can give us more data about intensity of turbulent mixing in the flame.     

钝体驻定湍流扩散火焰局部熄火的PDF模拟

用标量联合的概率密度函数(PDF)方法对钝体驻定的湍流射流扩散Sydney火焰HM3进行数值模拟,速度场用一个修正的LRR-IP雷诺应力模型求解.采用3种不同层次的甲烷反应动力学机理对火焰的宏观结构和熄火特征进行比较研究,并结合当地自适应建表方法加速化学反应计算.结果表明,计算值和实验数据吻合较好,在回流区内,不同反应机理的预测值差别不大,但在"颈部"区域,C2机理相对C1机理可以更准确地模拟标量场的变化和局部熄火现象.