A Conditional Moment Closure Study of Chemical Reaction Source Terms in SCCI Combustion

The objective of this study is to evaluate conditional moment closure (CMC) approaches to model chemical reaction rates in compositionally stratified, autoigniting mixtures, in thermochemical conditions relevant to stratified charge compression ignition (SCCI) engines. First-order closure, second-order closure and double conditioning are evaluated and contrasted as options in comparison to a series of direct numerical simulations (DNSs). The two-dimensional (2D) DNS cases simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane/air mixtures in a constant volume. The cases feature two different levels of stratification with three mean temperatures in the negative-temperature coefficient (NTC) regime of ignition delay times. The first-order closure approach for reaction rates is first assessed using hybrid DNS-CMC a posteriori tests when implemented in an open source computational fluid dynamics (CFD) package known as OpenFOAM\(^{{\circledR }}\). The hybrid DNS-CMC a posteriori tests are not a full CMC but a DNS-CMC hybrid in that they compute the scalar and velocity fields at the DNS resolution, thus isolating the first-order reaction rate closure model as the main source of modelling error (as opposed to turbulence model, scalar probability density function model, and scalar dissipation rate model). The hybrid DNS-CMC a posteriori test reveals an excellent agreement between the model and DNS for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. The a priori analysis reveals that the reason for disagreement is failure of the first-order closure hypothesis in the model due to the high level of conditional fluctuations. Second-order and double conditioning approaches are then evaluated in a priori tests to determine the most promising path forwards in addressing higher levels of stratification. The a priori tests use the DNS data to compute the model terms, thus directly evaluating the model assumptions. It is shown that in the cases with a high level of stratification, even the second-order estimation of the reaction rate source term cannot provide a reasonably accurate closure. Double conditioning using mixture-fraction and sensible enthalpy, however, provides an accurate first-order closure to the reaction rate source term.     

LES/CMC Simulations of Swirl-Stabilised Ethanol Spray Flames Approaching Blow-Off

Large Eddy Simulations (LES) with the Conditional Moment Closure (CMC) combustion model of swirling ethanol spray flames have been performed in conditions close to blow-off for which a wide database of experimental measurements is available for both flame and spray characterization. The solution of CMC equations exploits a three-dimensional unstructured code with a first order closure for chemical source terms. It is shown that LES/CMC is able to properly capture the flame structure at different conditions and agrees reasonably well with the measurements both in terms of mean flame shape and dynamic behaviour of the flame evaluated in terms of local extinctions and statistics of the lift-off height. Experimental measurements of the overall (liquid plus gaseous) mixture fraction, performed using the Laser-Induced Breakdown Spectroscopy technique, are also included allowing further assessment and validation of the numerical method. The sensitivity of the simulation results to the various boundary conditions is discussed.     

RANS Simulations of a Series of Turbulent V-Shaped Flames using Conditional Source-term Estimation

In the present study, Reynolds Averaged Navier Stokes (RANS) simulations are applied to a series of turbulent V-shaped flames. Two formulations of Conditional Source-term Estimation (CSE) are developed using singly and doubly conditioned averages for turbulent premixed and partially premixed flames, respectively. Detailed chemistry is included. Conditionally averaged chemical source terms are closed by conditional averaged scalars which are obtained by inverting an integral equation. The objectives are to study a turbulent premixed V-shaped flame using the premixed CSE approach and apply the Doubly Conditional CSE (DCSE) combustion model to a case of stratified combustion. The partially premixed implementation involves double conditioning on two variables, mixture fraction and progress variable. The present study represents the first application of DCSE for a series of turbulent stratified flames. First, CSE is analysed for fully premixed conditions. A sensitivity analysis on the number of CSE ensembles and different scalar dissipation model closures is performed. Good results are obtained in terms of velocity and progress variable profiles. Finally, the partially premixed formulation is applied to the stratified case at three different conditions, corresponding to two different turbulence grids and three different profiles of the equivalence ratio, providing promising results.     

Experimental investigation of a maximum entropy assumption for acceleration terms within a poly‐disperse moment framework

Moment transport methods are being developed to model poly‐dispersed multiphase flows by transporting statistical moments of the particle size–velocity joint probability density function (JPDF). A common feature of these methods is the requirement to reproduce or approximate the form of the JPDF from the transported moments for calculation of body force terms and other source terms. This paper examines the application of a maximum entropy technique against phase Doppler anemometry data sets from an electrostatically charged kerosene spray and also an automotive pressure swirl atomizer. An assessment of which moments are required to reproduce the JPDFs using a maximum entropy assumption to a sufficient level of accuracy is made. It is found that it is possible to reproduce the JPDFs to a high level of accuracy using a large number of moments; however, this incurs large computational overheads. If the moments to be transported are chosen on the basis of physical reasoning (such as the relationship between size and velocity due to drag) it is possible to reduce the number of moments to those which would be conserved via balance equations. This permits an approximation to the JPDF commensurate with the closure level of the moment transport method and thus the closure model method is naturally scalable with the degree of information from available conservation equations. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of Mixing Models for use in Simulations of Turbulent Spray Combustion

The present study concerns the investigation of different mixing models for use in the transported probability density function (PDF) modeling of turbulent (reacting) spray flows. The modeling of the turbulent mixing and other characteristic scalar variables such as gas enthalpy using transported (joint) PDFs has become an important method to describe turbulent (reacting) spray flows since the evaporation process causes the PDF of the mixture fraction to deviate from the widely used β function, which is typically used in models for turbulent gas flows. In the PDF transport equation, the molecular mixing does not appear in closed form so that modeling strategies are required. For gas combustion, the interaction-by-exchange-with-the-mean (IEM) model, the modified Curl (MC) model, and the Euclidean minimum spanning tree (EMST) models are used. More recently, a new mixing model, the PSP model, which is based on parameterized scalar profiles has been developed. The present study focuses on the use and analysis of the IEM, MC and PSP models for turbulent spray flames. For this purpose, the models are reconsidered with respect to the evaporation process that must be included and evaluated if spray combustion is considered. For model evaluation, turbulent ethanol/air spray flames are simulated, and the results are compared to experimental data by A. Masri, University of Sydney, Australia.     

Reduced coupled flapping wing-fluid computational model with unsteady vortex wake

Insect flight research is propelled by their unmatched flight capabilities. However, complex underlying aerodynamic phenomena make computational modeling of insect-type flapping flight a challenging task, limiting our ability in understanding insect flight and producing aerial vehicles exploiting same aerodynamic phenomena. To this end, novel mid-fidelity approach to modeling insect-type flapping vehicles is proposed. The approach is computationally efficient enough to be used within optimal design and optimal control loops, while not requiring experimental data for fitting model parameters, as opposed to widely used quasi-steady aerodynamic models. The proposed algorithm is based on Helmholtz–Hodge decomposition of fluid velocity into curl-free and divergence-free parts. Curl-free flow is used to accurately model added inertia effects (in almost exact manner), while expressing system dynamics by using wing variables only, after employing symplectic reduction of the coupled wing-fluid system at zero level of vorticity (thus reducing out fluid variables in the process). To this end, all terms in the coupled body-fluid system equations of motion are taken into account, including often neglected terms related to the changing nature of the added inertia matrix (opposed to the constant nature of rigid body mass and inertia matrix). On the other hand—in order to model flapping wing system vorticity effects—divergence-free part of the flow is modeled by a wake of point vortices shed from both leading (characteristic for insect flight) and trailing wing edges. The approach is evaluated for a numerical case involving fruit fly hovering, while quasi-steady aerodynamic model is used as benchmark tool with experimentally validated parameters for the selected test case. The results indicate that the proposed approach is capable of mid-fidelity accurate calculation of aerodynamic loads on the insect-type flapping wings.

     

Spray impact onto flat and rigid walls: Empirical characterization and modelling

An experimental study of spray impact onto horizontal flat and rigid surfaces is presented and used as input data for a new empirical model. A phase Doppler instrument has been used to measure drop size and two components of velocity directly above the target. The average film thickness formed due to spray impact has been measured using a high-speed CCD camera. The spray–wall interaction has been characterized in terms of correlations for the velocity and trajectory of secondary droplets and the mass and number ratio of the secondary spray. The novel aspect of the model is that the correlations are based on mean statistics over many events and not on the outcome of single drop impact experiments. Furthermore a rather large range of oblique impact angles have been studied and incorporated into the empirical models as an influencing factor.     

A Generalised Multiple Mapping Conditioning Approach for Turbulent Combustion

This paper follows the evolution in understanding of the multiple mapping conditioning (MMC) approach for turbulent combustion and reviews different implementations of MMC models. As the MMC name suggests, the original version represents a consistent combination of CMC-type conditional equations (conditional moment closure) and generalised mapping closure. It seems that the strength of the MMC model, and especially that of its stochastic version, lies in a more general (and much more transparent) interpretation. In this new generalised interpretation, we can replace complicated derivations by physical reasoning and the model appears to be a natural extension of modelling approaches developed in recent decades. MMC can be seen as a methodology for enforcing certain known characteristics of turbulence on a conventional mixing model. This is achieved by localising the mixing operation in a reference space. The reference space variables are selected to emulate the properties of a turbulent flow which have a strong effect on reactive quantities. The best and simplest example is an MMC model which has a single reference variable emulating the mixture fraction. In diffusion flames turbulent fluctuations of reacting quantities are strongly correlated with fluctuations of the mixture fraction. By making mixing local in the reference mixture fraction space a CMC-type mixing closure is enforced. In the original interpretation of MMC the reference variables are modelled as Markov processes. Since the reference variables should emulate properties of turbulent flows as realistically as possible the next step, and the basis of generalised MMC, is to remove the Markovian restriction and set reference variables equal to traced Lagrangian quantities within DNS or LES flow fields. Indeed, no Markov value can emulate the mixture fraction better than the mixture fraction itself. (Using a Markov vector process of dimension higher than the number of conditioning variables represents a more economical alternative for producing reference variables in generalised MMC.) The generalised MMC approach effectively incorporates the mixture fraction-based models, the PDF methods and LES/DNS techniques into a single methodology with possibility of blending useful features developed previously for conventional models. The generalised approach to MMC stimulates a more flexible understanding of simulations using sparsely placed Lagrangian particles as tools that may provide accurate joint distributions of reactive scalars at relatively low computational cost. The physical reasoning behind the new interpretation of MMC is supported by example computations for a partially premixed methane/air diffusion flame (Sandia Flame D). The scheme utilises LES for the dynamic field and a sparse-Lagrangian filtered density function method with MMC mixing for the scalar field. Two different particle mixing schemes are tested. Simulations are performed using only 35,000 Lagrangian particles (of these only 10,000 are chemically active) on a single workstation. The relatively low computational cost allows the use of realistic chemical kinetics containing 34 reactive species and 219 reactions. Intended for publication in the special issue of Flow, Turbulence and Combustion arising from the 2nd ECCOMAS Thematic Conference on Computational Combustion held at Delft in mid-2007.     

A consistent,scalable model for Eulerian spray modeling

Despite great practical interest in how sprays emanate from fuel injectors, the near-nozzle region has remained a challenge for spray modelers. Recently, Eulerian models have shown promise in capturing the fast gas-liquid interactions in the near field. However, with the inclusion of compressibility, it can be difficult to maintain consistency between the hydrodynamic and thermodynamic variables. In order to resolve numerical inconsistencies that occur in segregated solutions of Eulerian spray model equations as well as to provide good scalability and stability, a new construction of a Σ-Y model is introduced. This construction is built around an IMEX-RK3 algorithm which offers accuracy and efficiency. The new algorithm is compared to an existing implementation for speed and is validated against experimental measurements of spray evolution in order to test the accuracy. The predictions of the new construction are slightly more accurate and, when tested on 256 processors, are 34 times faster.     

A finite element solution to turbulent diffusion in a convective boundary layer

A second-order closure turbulence model is used to simulate the plume behaviour of a passive contaminant dispersed in a convective boundary layer. A time-splitting finite element scheme is used to solve the set of partial differential equations. It is shown that the second-order closure model compares favourably with recent findings from laboratories, wind-tunnel experiments and large-eddy simulations. We also compare the second-order closure model with the commonly used K-diffusion model for the same meteorological conditions. Case studies also show the effects of model parameters and turbulence variables on the plume behaviour.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Towards the optimization of a pulsatile three-stream coaxial airblast injector

A large-scale parametric air–water test stand (AWTS) study involving more than 40 evaluations was carried out for the purposes of three-stream airblast reactor feed injector characterization and optimization; a subset of seven air stream combinations is discussed here. The role of CFD as a supplement to, or a replacement for, air–water testing is of great industrial interest. To this end a set of CFD simulations was carried out to complement the AWTS study. Pressure responses, spray opening characteristics near the feed injector face, and spray distribution were primary measures for both the AWTS and CFD programs. It was found that, over the range of variables studied, there was somewhat of a match between CFD and AWTS results. A self-exciting, pulsatile spray pattern was achieved in CFD and AWTS (frequencies between 75 and 600 Hz), and an interesting transition in spray bursting character occurred at moderate inner air flows. The oscillatory flow pattern mimics prior work in terms of the energy of the fluctuations, but the fact that the present fluctuations occur at an order of magnitude lower frequency is apparently related to the comparatively low gas/liquid momentum ratio in the current study. Overall, it is shown that the CFD method contained herein can be used to supplement, but not replace, air–water testing for said injector configuration.     

Predicting turbulent flow in a staggered tube bundle

This paper presents the results of calculations performed for the turbulent, incompressible flow around a staggered array of tubes for which carefully obtained experimental results are available as part of an established ERCOFTAC-IAHR test case. The Reynolds-averaged Navier–Stokes equations are solved using a pressure-based finite volume algorithm, using collocated cell vertex store on an unstructured and adaptive mesh of tetrahedra. Turbulence closure is obtained with a truncated form of a low-Reynolds number k– model developed by Yang and Shih. The computational domain covers all seven rows of tubes used in the experimental study and periodic flow is allowed to develop naturally. The results of the computations are surprisingly good and compare favourably with results obtained by others using a wide range of alternative k– models for a single cylinder with periodic inflow and outflow boundaries on structured meshes.     

CFD modeling and experimental validation of heat and mass transfer in wood poles subjected to high temperatures: a conjugate approach

In this article, a coupling method is presented in the case of high thermal treatment of a wood pole and a three-dimensional numerical simulation is proposed. The conservation equations for the wood sample are obtained using diffusion equation with variables diffusion coefficients and the incompressible Reynolds averaged Navier–Stokes equations have been solved for the flow field. The connection between the two problems is achieved by expressing the continuity of the state variables and their respective fluxes through the interface. Turbulence closure is obtained by the use of the standard k–ɛ model with the usual wall function treatment. The model equations are solved numerically by the commercial package ANSYS-CFX10. The wood pole was subjected to high temperature treatment under different operating conditions. The model validation is carried out via a comparison between the predicted values with those obtained experimentally. The comparison of the numerical and experimental results shows good agreement, implying that the proposed numerical algorithm can be used as a useful tool in designing high-temperature wood treatment processes. A parametric study was also carried out to determine the effects of several parameters such as initial moisture content, wood aspect ratio and final gas temperature on temperature and moisture content distributions within the samples during heat treatment.     

An approach formulated in terms of conserved variables for the characterisation of propellant combustion in internal ballistics

A model formulated in terms of conserved variables is proposed for its use in the study of internal ballistic problems of pyrotechnical mixtures and propellants. It is a transient two‐phase flow model adapted from the non‐conservative Gough model. This conversion is mathematically attractive because of the wide range of numerical methods for this kind of systems that may be applied. We propose the use of the AUSM+, AUSM + up and Rusanov schemes as an efficient alternative for this type of two‐phase problem. A splitting technique is applied, which solves the system of equations in several steps. A second‐order approach based on Monotonic Upstream‐Centred Scheme for Conservation Laws (MUSCL) is also used. Some tests are used to validate the code, namely a shock wave test, a contact discontinuity problem and an internal ballistics problem. In this last case, one‐dimensional numerical results are compared with experimental data of 155‐mm gunshots. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessment of the SSG pressure-strain model in two-dimensional turbulent separated flows

Data from a number of benchmark two-dimensional turbulent separated flows are used to assess the performance of the Speziale, Sarkar and Gatski model [28] for the fluctuating pressure-strain correlations and, in particular, to determine whether the model can reproduce the effects of rigid boundaries without recourse to ad-hoc corrections. Comparative predictions are also obtained with a standard Reynolds-stress closure in which such correlations are necessary and these serve to distinguish the models' true performance from spurious computational artifacts. The models were implemented in a finite-volume method which solves the Navier-Stokes equations on non-orthogonal grids with colocated storage arrangement. Details of the numerical treatments adopted to obtain stable and fast-converging solutions are described and the outcome of rigorous grid-independence checks are reported for each test case. It is found that both models yield essentially similar results for the mean flow and turbulence fields. The implications of this result to the choice of Reynolds-stress closure for complex engineering simulations are discussed.     

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.