Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.     

Simulation and Modelling of Turbulent Trailing-Edge Flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–ε) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Kármán vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Presumed Joint-PDF Modelling for Turbulent Stratified Flames

Flow, Turbulence and Combustion - Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function...     

Simulation and Modelling of a Skewed Turbulent Channel Flow

A time-dependent three-dimensionally skewed flow is investigated using direct numerical simulations of the incompressible Navier-Stokes equations. The effect on the instantaneous and mean turbulent field is investigated. Instantaneous flowfields reveal that the skewing has the effect of initially reducing the strength and height of quasi-streamwise vortices of both signs of rotation with respect to the skewing. A mechanism for this process is put forward. The mean flowfields show drops in turbulence quantities such as turbulence kinetic energy. In addition to this, two-equation turbulence modelling of the flow is carried out. This highlights a deficiency, in that the standard turbulence models are unable to capture the drop in turbulence intensity due to the skewing. A modification based on the exact dissipation equation is found to significantly improve the model behaviour for this flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Direct Quadrature Conditional Moment Closure for Modelling of Turbulent Combustion

We present a method of direct quadrature conditional moment closure (DQCMC) for the treatment of realistic turbulence-chemistry interaction in computational fluid dynamics (CFD) software. The method which is based on the direct quadrature method of moments (DQMOM) coupled with the conditional moment closure (CMC) equations is in simplified form and easily implementable in existing CMC formulation for CFD. The observed fluctuations of scalar dissipation around the conditional mean values are captured by the treatment of a set of mixing environments, each with its pre-defined weight. Unlike the early versions of the DQCMC method the resulting equations are similar to that of the first-order CMC, and the ??diffusion?? term is strictly positive and no correction factors are used. We present results for two mixing environments where the resulting matrices of the DQCMC can be inverted analytically. We have performed this analysis for a simple hydrogen flame using a multi species chemical scheme containing nine species. The effects of the fluctuations around the conditional means are captured accurately and the predicted results are in very good agreement with observed trends from direct numerical simulations. Furthermore, the differences between the first order CMC and DQCMC are discussed.     

Statistical Analysis and a-priori Modelling of Flame Surface Density Transport in Turbulent Stratified Flames: A Direct Numerical Simulation Study

Statistically planar turbulent premixed and stratified flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios <???> = 0.7 and <???> = 1.0 using three-dimensional simplified chemistry based Direct Numerical Simulations (DNS). The simulation parameters are chosen such that the thin reaction zones regime combustion is realised in all cases and a random bi-modal distribution of equivalence ratio ? is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity for stratified flames. The modelling of the unclosed terms (i.e. the turbulent transport term T ₁, the tangential strain rate term T ₂, the propagation term T ₃, and the curvature term T ₄) of the generalised FSD transport equation has been addressed in the context of RANS simulations. It has been found that the turbulent transport term T ₁ remains small in comparison to the leading order contributions of the tangential strain rate and curvature terms (i.e. T ₂ and T ₄, respectively) in the globally stoichiometric cases, but T ₁ begins to play a more important role in the globally fuel-lean cases. The strain rate term T ₂ remains positive throughout the flame brush and acts as a leading order source term for all the flames considered in this analysis. It is has been found that the magnitude of T ₂ decreases with decreasing root-mean-square velocity fluctuations u ^′ (<???>) for a given value of <???> (u ^′). The contribution of the propagation term T ₃ remains generally positive towards the unburned gas side of the flame brush but assumes generally negative values towards the burned gas side of the flame brush. Moreover, whilst the order of magnitude of the propagation term T ₃ is comparable in all cases, T ₃ remains small in comparison to the leading order contributors (i.e. T ₂ and T ₄) in the globally stoichiometric cases however it plays a more important role in the globally fuel-lean cases. The curvature term T ₄ acts as a leading order sink term in all cases except towards the unburned gas side of the flame brush in low u ^′ globally stoichiometric (i.e. <???> = 1.0) flames. Furthermore, it has been demonstrated that the magnitude of T ₄ decreases with decreasing u ^′ (<???>) for a given value of <???> (u ^′). Appropriate model expressions have been identified for T ₁, T ₂, T ₃ and T ₄ based on an a-priori analysis of the DNS data.     

Turbulence Modelling of Unsteady Turbulent Flows Using the Stress Strain Lag Model

This paper reports the application of a recently developed turbulence modelling scheme known as the C _as model. This model was specifically developed to capture the effects of stress-strain misalignment observed in turbulent flows with mean unsteadiness. Earlier work has reported the approach applied within a linear k-ε modelling framework, and some initial testing of it within the k-ω SST model of Menter (AIAA J 32:1598–1605, 1994). The resulting k-ε-C _as and SST-C _as models have been shown to result in some of the advantages of a full Reynolds Stress transport Model (RSM), whilst retaining the computational efficiency and stability benefits of a eddy viscosity model (EVM). Here, the development of the the high-Reynolds-number version of the C _as model is outlined, with some example applications to steady and unsteady homogeneous shear flows. The SST-C _as form of the model is then applied to further, more challenging cases of 2-D flow around a NACA0012 aerofoil beyond stall and the 3-D flow around a circular cylinder in a square duct, both being flows which exhibit large, unsteady, separated flow regions. The predictions returned by a range of other common turbulence modelling schemes are included for comparison and the SST-C _as scheme is shown to return generally good results, comparable in some respects to those obtainable from far more complex schemes, for only moderate computing resource requirements.     

A-Priori Direct Numerical Simulation Modelling of Co-variance Transport in Turbulent Stratified Flames

Three-dimensional Direct Numerical Simulations of statistically planar turbulent stratified flames at global equivalence ratios <???>?=?0.7 and <???>?=?1.0 have been carried out to analyse the statistical behaviour of the transport of co-variance of the fuel mass fraction Y _F and mixture fraction ξ (i.e. $\widetilde{Y_F^{\prime\prime} \xi ^{\prime\prime}}={\overline {\rho Y_F^{\prime\prime} \xi^{\prime\prime}} } \Big/ {\overline \rho })$ for Reynolds Averaged Navier Stokes simulations where $\overline q $ , $\tilde{q} ={\overline {\rho q} } \big/ {\overline \rho }$ and $q^{\prime\prime}= q-\tilde{q}$ are Reynolds averaged, Favre mean and Favre fluctuation of a general quantity q with ρ being the gas density and the overbar suggesting a Reynolds averaging operation. It has been found that existing algebraic expressions may not capture the statistical behaviour of $\widetilde{Y_F^{\prime\prime} \xi^{\prime\prime}}$ with sufficient accuracy in low Damköhler number combustion and therefore, a transport equation for $\widetilde{Y_F^{\prime\prime} \xi^{\prime\prime}}$ may need to be solved. The statistical behaviours of $\widetilde{Y_F^{\prime\prime} \xi^{\prime\prime}}$ and the unclosed terms of its transport equation (i.e. the terms originating from turbulent transport T ₁ , reaction rate T ₄ and molecular dissipation $\left( {-D_2 } \right))$ have been analysed in detail. The contribution of T ₁ remains important for all cases considered here. The term T ₄ acts as a major contributor in <???>?=?1.0 cases, but plays a relatively less important role in <???>?=?0.7 cases, whereas the term $\left( {-D_2 } \right)$ acts mostly as a leading order sink. Through an a-priori DNS analysis, the performances of the models for T ₁ , T ₄ and $\left( {-D_2 } \right)$ have been addressed in detail. A model has been identified for the turbulent transport term T ₁ which satisfactorily predicts the corresponding term obtained from DNS data. The models for T ₄ , which were originally proposed for high Damköhler number flames, have been modified for low Damköhler combustion. Predictions of the modified models are found to be in good agreement with T ₄ obtained from DNS data. It has been found that existing algebraic models for $D_2 =2\overline {\rho D\nabla Y_F^{\prime\prime} \nabla \xi^{\prime\prime}} $ (where D is the mass diffusivity) are not sufficient for low Damköhler number combustion and therefore, a transport equation may need to be solved for the cross-scalar dissipation rate $\widetilde{\varepsilon }_{Y\xi } ={\overline {\rho D\nabla Y_F^{\prime\prime} \nabla \xi^{\prime\prime}} } \big/ {\overline \rho }$ for the closure of the $\widetilde{Y_F^{\prime\prime} \xi^{\prime\prime}}$ transport equation.     

Modelling of Two-Component Turbulent Mass and Heat Transfer in Air-Fed Pressurised Suits

In this paper the modelling of an important industrial problem is addressed, which involves the two-component turbulent flow with heat transfer that takes place inside protective clothing. The geometry of the flow boundaries is reconstructed in a CAD system from photogrammetry scan data. The overall model is sufficiently realistic to allow, after validation, design improvements to be tested. Those presented here allow the reduction of hotspots over the worker’s body surface and increase thermal comfort.     

DNS and Modelling of Passive Scalar Transport in Turbulent Channel Flow with a Focus on Scalar Dissipation Rate Modelling

A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation. The Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half width is 265. Budgets are presented for the passive scalar variance and its dissipation rate, as well as for the individual scalar flux components. These form a basis for a discussion of modelling issues related to explicit algebraic scalar flux modelling. This revised version was published online in July 2006 with corrections to the Cover Date.     

确定非线性隔振装置参数的一种方案

对单自由度刚度可调非线性隔振模型进行数学建模仿真和实验，对于待训练的神经网络模型，将数值仿真结果作为学习样本，将实验结果作为检验样本，训练成功的神经网络模型具有较好的内延能力和一定的外推能力，在设定非线性隔振装置要求的隔振效能参数后，可以给出隔振装置对应的刚度和阻尼参数，从而为设计非线性隔振装置提供了一种方案。     

Statistics and Modelling of Turbulent Kinetic Energy Transport in Different Regimes of Premixed Combustion

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants.     

Modelling Turbulent Premixed Combustion Using the Level Set Approach for Reynolds Averaged Models

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described in terms of the G-equation. The numerical instabilities of the G-field are resolved using a reinitialisation procedure. For the G-points near the flame surface an algorithm proposed by Russo and Smereka [1] and modificated by Düsing [2] is presented. For all other points the standard Sussman algorithm is employed. Fluid properties are conditioned on the flame front position using a burnt-unburnt probability function across the flame front. Computations are performed using the code FASTEST-3D [3] which is a flow solver for a non-orthogonal, block-structured grid. The computational examples include two test cases, the first containing the propagation of two circular merging flames and the second one containing the simulation of the ORACLES-burner [4].     

Subgrid Linear Eddy Mixing and Combustion Modelling of a Turbulent Nonpremixed Piloted Jet Flame

A linear eddy model for subgrid mixing and combustion has been coupled to a large eddy simulation of the turbulent nonpremixed piloted jet flame (Sandia Flame D). For the combustion reaction, simplified, single-step, irreversible, Arrhenius kinetics are used. The large scale and the subgrid structure of the flow are compared with experimental observations and, where appropriate, with a flamelet model of the flame. The main objective of this work is to demonstrate the feasibility of the LES-LEM approach for determining the structure of the subgrid scalar dissipation rate and the turbulence-chemistry interactions. The results for the large- and subgrid-scale structure of the flow show a reasonable agreement with the experimental observations.     

Flamelet Based NO x -Radiation Integrated Modelling of Turbulent Non-premixed Flame using Reynolds-stress Closure

A methodology of extending laminar flamelet model in its adiabatic form to a non-adiabatic form which can account for radiative heat loss as well as its effect on NO _x pollutant has been developed. Coupling of radiation submodel with flamelet model is based on the enthalpy defect concept. Pollutant NO _x has been calculated from solution of its transport equation containing source term which is derived from flamelet calculations. Flamelet calculations adopted GRI 2.11 reaction mechanism which accounts for detailed carbon and NO _x chemistry. Depending on consideration of variation in scalar dissipation within flamelet calculations, the non-adiabatic form has been further divided into non-adiabatic model with single (NADS) and multiple scalar dissipation rates (NADM). Bluff-body stabilized CH₄/H₂ flame has been chosen as the test case to assess the capability of non-adiabatic models. Turbulence closure has been achieved with a Reynolds stress transport model. Calculations have also been carried out with a modified k-ε model for evaluation of relative performance of the two turbulence closures. Performance of non-adiabatic flamelet models in regard to the overall structure of the flame is reasonably good and the agreement is similar to that of the adiabatic flamelet model thereby indicating weakly radiating nature of the flame. However, the NADM model results in minor but encouraging improvement in NO mass fraction predictions by reducing the extent of overprediction observed with the adiabatic model. In contrast, the NADS model results in overprediction over and above the adiabatic predictions thereby showing that, it is imperative to consider variation in scalar dissipation rate in flamelet calculations to capture the effect of radiation on NO. The results also show that employing the modified k-ε model instead of the Reynolds stress transport model for turbulence closure in NADM calculations results in considerable overprediction in centerline NO mass fractions.     

Computational Modelling of Turbulent Mixing in Confined Swirling Environment Under Constant and Variable Density Conditions

A high-intensity swirling flow in a model combustor subjected to large density variations has been examined computationally. The focus is on the Favre-averaged Navier–Stokes computations of the momentum and scalar transport employing turbulence models based on the differential second-moment closure (SMC) strategy. An updated version of the basic, high-Reynolds number SMC model accounting for a quadratic expansion of both the pressure–strain and dissipation tensors and a near-wall SMC model were used for predicting the mean velocity and turbulence fields. The accompanied mixing between the annular swirling air flow and the central non-swirling helium jet was studied by applying three scalar flux models differing mainly in the model formulation for the pressure-scalar gradient correlation. The computed axial and circumferential velocities agree fairly well with the reference experiment [So et al., NASA Contractor Report 3832, 1984; Ahmed and So, Exp. Fluids 4 (1986) 107], reproducing important features of such a weakly supercritical flow configuration (tendency of the flow core to separate). Although the length at which the mixing was completed was reproduced in reasonable agreement with the experimental results, the mixing activity in terms of the spreading rate of the shear/mixing layer, that is its thickness, was somewhat more intensive. Prior to these investigations, the model applied was validated by computing the transport of the passive scalar in the non-swirling (Johnson and Bennet, Report NASA CR-165574, UTRC Report R81-915540-9, 1981) and swirling (Roback and Johnson, NASA Contractor Report 168252, 1983) flow in a model combustor.     

Modelling of a Premixed Swirl-stabilized Flame Using a Turbulent Flame Speed Closure Model in LES

This paper proposes a combustion model based on a turbulent flame speed closure (TFC) technique for large eddy simulation (LES) of premixed flames. The model was originally developed for the RANS (Reynolds Averaged Navier Stokes equations) approach and was extended here to LES. The turbulent quantities needed for calculation of the turbulent flame speed are obtained at the sub grid level. This model was at first experienced via an test case and then applied to a typical industrial combustor with a swirl stabilized flame. The paper shows that the model is easy to apply and that the results are promising. Even typical frequencies of arising combustion instabilities can be captured. But, the use of compressible LES may also lead to unphysical pressure waves which have their origin in the numerical treatment of the boundary conditions.     

Statistical Analysis of Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Study

Turbulent combustion of mono-disperse droplet-mist has been analysed based on three-dimensional Direct Numerical Simulations (DNS) in canonical configuration under decaying turbulence for a range of different values of droplet equivalence ratio (?_d), droplet diameter (a_d) and root-mean-square value of turbulent velocity (u^′). The fuel is supplied in liquid phase and the evaporation of droplets gives rise to gaseous fuel for the flame propagation into the droplet-mist. It has been found that initial droplet diameter, turbulence intensity and droplet equivalence ratio can have significant influences on the volume-integrated burning rate, flame surface area and burning rate per unit area. The droplets are found to evaporate predominantly in the preheat zone, but some droplets penetrate the flame front, reaching the burned gas side where they evaporate and some of the resulting fuel vapour diffuses back towards the flame front. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for ?_d > 1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets and this predominantly fuel-lean mode of combustion exhibits the attributes of low Damköhler number combustion and gives rise to thickening of flame with increasing droplet diameter. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion and the relative contribution of non-premixed combustion to overall heat release increases with increasing droplet size. The statistical behaviours of the flame propagation and mode of combustion have been analysed in detail and detailed physical explanations have been provided for the observed behaviour.