Conditional Source-Term Estimation as a Method for Chemical Closure in Premixed Turbulent Reacting Flow

A Conditional Source-term Estimation (CSE) model is used to close the mean reaction rates for a turbulent premixed flame. A product-based reaction progress variable is introduced as the conditioning variable for the CSE method. Different presumed probability density function (PDF) models are studied and a modified version of a laminar flame-based PDF model is proposed. Improved predictions of the variable distribution are obtained. The conditional means of reactive scalars are evaluated with CSE and compared to the direct numerical simulation (DNS). The mean reaction rates in a turbulent premixed flame are evaluated with the CSE model and the presumed PDFs. Comparison of the CSE closure method to DNS shows promising results. This paper was presented at the 2nd ECCOMAS Thematic Conference on Computational Combustion.     

New Molecular Transport Model for FDF/LES of Turbulence with Passive Scalar

The paper addresses the issue of modelling and computation of wall-bounded turbulent flows with passive scalars. In the present approach, the large eddy simulation (LES) method is used to compute the velocity field in the near-wall zone. The LES is coupled with the Lagrangian filtered density function (FDF) model for the transport of a passive scalar. In the paper, we propose two models to account for the molecular transport near the wall and investigate their behaviour in the limit case of small filter widths. One of the models is tested numerically, and computational results for a heated channel flow are compared with the available DNS data.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach

A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is vanishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia.     

Modern turbulence and new challenges

The paper briefly reviews the progress in turbulence research in the 20th century and a number of issues are addressed based on achievements. The modern theroy of Navier-Stokes equation provides the theoretical basis for the development of turbulence research. The significance and bottle neck of DNS and the physical experiment in exploring turbulent flows are analyzed. The active manipulation of turbulence is directly guided by the knowledge of large-scale coherent structures. The existing problems in the large-eddy simulation are also pointed out. Scalar turbulence, which behaves quite different from fluid turbulence in many aspects, has drawn much attention in recent years. Besides the analysis of the difficulties in turbulence research, a number of examples are also presented to show how to use modern theory, computer and high technology to explore the nature of turbulence. The project supported by the National Natural Science Foundation of China (NSFC) (19572041 and 19732005)     

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.     

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale (SGS) stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the current second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body-fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbulent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results. The project supported by the National Natural Science Foundation of China (50779069 and 90510007), the Start-up Scientific Research Foundation of China Agricultural University (2006021) and the Beijing Natural Science Foundation (3071002).     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Second-moment closure for modelling the near-wall turbulence in 3D mean flows

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high-Reynolds-number closure remote from the wall. The closure is applied to a pressure-driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data. The project supported by the National Natural Science Foundation of China     

A new simple method of implicit time integration for dynamic problems of engineering structures

This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai’s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems. The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China (G2000048702, 2003CB716707), the National Science Fund for Distinguished Young Scholars (10025208), the National Natural Science Foundation of China (Key Program) (10532040), the Research Fund for Oversea Chinese (10228028). The English text was polished by Keren Wang.     

Analysis of high-order velocity moments in a strained channel flow

In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.     

Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases

This paper presents results of a large eddy simulation (LES) combined with Lagrangian particle tracking and a point-force approximation for the feedback effect of particles on the downward turbulent gaseous flow in a vertical channel. The LES predictions are compared with the results obtained by direct numerical simulation (DNS) of a finer computational mesh. A parametric study is conducted for particles with two response times in simulations with and without streamwise gravitational settling and elastic, binary interparticle collisions. It is shown that the classical and the dynamic Smagorinsky turbulence models adequately predict the particle-induced changes in the mean streamwise velocity and the Reynolds stresses of the carrier phase for the range of parameters studied. However, the largest discrepancies between the LES and DNS results are found in the cases of particle-laden flows. Conditional sampling of the instantaneous resolved flow fields indicates that the mechanisms by which particles directly oppose the production of momentum and vorticity of the organized fluid motions are also observed in the LES results. However, the geometric features of the near-wall quasistreamwise vortices are overestimated by the use of both turbulence models compared to the DNS predictions.     

Direct Numerical Simulation of a Recirculating, Swirling Flow

A direct numerical simulation (DNS) of a recirculating, swirling flow is performed at a Reynolds number of 5000. Detailed one and two point statistics are presented in this paper. Flow visualization and frequency analysis are used to identify a precessing vortex core and to characterize its position, extent and influence on the flow field. The results are compared with laser Doppler velocimetry (LDV) measurements as well as large eddy simulation (LES) data reported in the literature. The present work constitutes a first step in setting up a DNS data base for complex flows.     

On the Relationship Between the Statistics of the Resolved and True Rate of Dissipation of Mixture Fraction

The relationship between the one-point probability-density-function (PDF) of the dissipation rate of mixture fraction fluctuations and the corresponding resolved quantity available in large eddy simulation (LES) is analyzed. The investigation pursues two fronts: an a priori study using direct numerical simulation (DNS), and an analytic development that, using common turbulence physics simplifications, relates the one-point statistics of the resolved and true scalar dissipations. Particularly, the analysis reveals the connection between the multi-point correlations of the mixture fraction gradient and the one-point PDF of the resolved scalar dissipation. A DNS of a temporally evolving shear layer with and without heat release is used to quantify the accuracy of the analytical result. It is verified, both by filtering the DNS and from the theory, that increasing the filter cutoff width reduces the magnitude of the resolved scalar dissipation fluctuations, as expected and observed experimentally. Comparison with DNS indicates that the analytical relationship predicts the behavior of the resolved scalar dissipation PDF well at the center planes of the shear layer, where turbulence is locally more isotropic and homogeneous. Large-scale anisotropy and inhomogeneities in the DNS degrade the accuracy of the approximate analytical result close to the edges of the shear layer. These results may be improved with future investigations to account fully for the missing statistics in LES, which have the potential to allow a more accurate quantification of finite-rate chemistry effects in reacting flows.     

Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined. The project supported by the National Natural Science Foundation of China (10372007, 10002003) and CNPC Innovation Fund     

The nonlinear galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows

Using results of DNS in the case of two-dimensional homogeneous isotropic flows, we first analyze in detail the behavior of the small and large scales of Kolmogorov-like flows at moderate Reynolds numbers. We derive several estimates on the time variations of the small eddies and the nonlinear interaction terms; these terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, we propose a multilevel scheme which treats the small and the large eddies differently. Using mathematical developments, we derive estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptative procedure. Finally, we perform realistic simulations of (Kolmogorov-like) flows over several eddy-turnover times. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.This work was partially supported by NFS Grant DMS 9024769 and DOE DE-FG02-92ER25120. The computations were made on the Cray-2 of the National Center for Supercomputing Applications (NCSA, Illinois). Part of the work was done while T. Dubois was visiting the Institute for Computer and Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001, U.S.A.     

Simulating turbulent Dean flow in Cartesian coordinates

A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier–Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher‐order terms are neglected. The curvature terms are implemented in a conventional Navier–Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier–Stokes model. It is particularly rewarding that also distinct pairs of counter‐rotating streamwise‐oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd.     

A car-following model with the anticipation effect of potential lane changing

In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.     

Studies on stability and dynamics of a swirling jet

The temporal instability and nonlinear evolution of the swirling jet near a nozzle exit are studied by both normal-mode method and three dimensional direct numerical simulation (3D DNS). It is found that the swirl enhances the maximum linear growth rates for negative helical modes, while decreases the growth rate for axisymmetric mode. Numerical simulations show that the evolution in early stage is compared well with the linear stability theory. In nonlinear stage, the swirl promotes the breakup of 3D large scale organized structures in the flow into small eddies. The project supported by the National Natural Science Foundation of China (19772052)