Presumed Probability Density Function Approach Research Articles

Wetting layer evolution and interfacial heat transfer in water-air spray cooling process of hot metallic surface

In order to respond to the increased demand for clean energy without harming the atmosphere through polluting emissions, energy production from the hydrogen combustion become largely used. This work presents a numerical study of the injection conditions effect on the structure of the H2-air diffusion flame. The aim is to reproduce a practical case of non-polluting combustion and resulting in very high temperatures. The configuration is composed of two axisymmetric coaxial jets, as can be found in the diffusion burners. A presumed probability density function approach is used to describe the chemistry-turbulence interaction. The k-? model of turbulence is used. Particular attention is given to phenomena anchoring or blowout of the flame.

Turbulent flame-wall interaction of premixed flames using Quadrature-based Moment Methods (QbMM) and tabulated chemistry: An a priori analysis

Presumed probability density function (PDF) and transported PDF methods are commonly applied to model the turbulence chemistry interaction in turbulent reacting flows. However, little focus has been given to the turbulence chemistry interaction PDF closure for flame-wall interaction. In this study, a quasi-DNS of a turbulent premixed, stoichiometric methane-air flame ignited in a fully developed turbulent channel flow undergoing side-wall quenching is investigated. The objective of this study is twofold. First, the joint PDF of the progress variable and enthalpy that needs to be accounted for in turbulence chemistry interaction closure models is analyzed in the quasi-DNS configuration, both in the core flow and the near-wall region. Secondly, a transported PDF closure model, based on a Conditional Quadrature Method of Moments approach, and a presumed PDF approach are examined in an a priori analysis using the quasi-DNS as a reference both in the context of Reynolds-Averaged Navier Stokes (RANS) and Large-Eddy Simulations (LESs). The analysis of the joint PDF demonstrates the high complexity of the reactive scalar distribution in the near-wall region. Here, a high correlation between the progress variable and enthalpy is found, where the flame propagation and quenching are present simultaneously. The transported PDF approach presented in this work, based on the Conditional Quadrature Method of Moments, accounts for the moments of the joint PDF of progress variable and enthalpy coupled to a Quenching-Flamelet Generated Manifold. In the a priori analysis both turbulence chemistry interaction PDF closure models show a high accuracy in the core flow. In the near-wall region, however, only the Conditional Quadrature Method of Moments approach is suitable to predict the flame structures.

Presumed Joint-PDF Modelling for Turbulent Stratified Flames

Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function (PDF) model of the conditioning variables. In turbulent stratified flames, a joint-PDF model for a reaction progress variable and the mixture fraction is required. The joint-PDF is often modelled by two beta functions using the first and second moments of the two conditioning variables. In this work, the performance of a joint-PDF model based on the flamelet PDF approach is compared to the double beta-PDF model. The conditional PDF of the reaction progress variable conditioned on mixture fraction is modelled with the flamelet PDF. Unlike the beta PDF, the flamelet functional form for the conditional PDF varies with the local mixture fraction. The two PDF models are coupled with a two-dimensional premixed flamelet-generated manifold chemistry model. Two stratified flames of the Cambridge–Sandia bluff-body burner are simulated using a Reynolds-Averaged Navier–Stokes (RANS) approach. The results indicate that the flamelet PDF model has a superior, albeit marginal, predictions of the temperature, major and minor species mass fractions.

Comparison between numerical and experimental data of the radiative heat transfer in a natural gas/CO2/H2 turbulent flame

Accurate computation of the radiative heat flux emitted by turbulent flames involves the challenging modeling of turbulence-radiation interactions (TRI). This study considers a non-premixed turbulent flame, in which the fuel is natural gas with CO2/H2 dilution and ambient air as the oxidant. The radiative exchange is numerically solved using the weighted-sum-of-gray-gases (WSGG) gas model, and the discrete ordinates method for directional integration of the radiative transfer equation (RTE). The steady laminar diffusion flamelet (SLDF) model is used to solve the chemical kinetics. To account for the turbulence-chemistry interaction, the mean scalars are calculated by a presumed probability density function (PDF) approach. Turbulence is treated with the k-ε standard model. The impact of TRI modeling is performed employing two methodologies. The first one is based on the correlation between the absorption coefficient and the temperature self-correlation, considering that the absorption coefficient is only dependent on the mean local temperature. The second one considers the dependence of the absorption coefficient with both the mean temperature and the species mole concentrations. The temperature variance is obtained in two ways, using a transport equation and directly from the PDF approach. Five sets of numerical results are compared with measured experimental data for the radiative heat flux. The solution is obtained using ANSYS/Fluent code coupled with user-defined functions (UDFs) to compute RTE/WSGG/TRI formulations.

Assessment of Presumed/Transported Probability Density Function Methods for Rocket Combustion Simulations

Combustion models of different fidelity are applied to a seven-element gaseous methane/oxygen subscale rocket combustion chamber. The covered region of thermo-chemical states is analyzed for two non-adiabatic flamelet-based methods, from which one is well established and the other one has just recently been proposed for hydrogen/oxygen combustion. Of particular interest is their applicability in situations with strong heat losses. Consequently, the tabulated combustion models are linked with a presumed probability density function approach, and the results are assessed using a transported probability density function method. An analytically reduced chemical reaction mechanism with 13 species and 73 reactions is used for all models in order to allow for direct comparison of turbulence–chemistry interaction. The results are evaluated with respect to temperature, gas composition, and wall heat transfer and they are brought in context with their respective computational costs. Finally, the results are compared to available experimental data in terms of wall heat flux and pressure measurements. Locally and temporally resolved results provide additional insights to the experiment.

Lean Flame Root Dynamics in a Gas Turbine Model Combustor

ABSTRACTA swirl-stabilised flame close to blow-off conditions in a gas turbine model combustor is investigated using large eddy simulation. The sub-grid combustion is modelled using a presumed probability density function approach along with flamelets. Good comparisons between the computed and measured statistics are observed. This allows for a detailed investigation of the flame behaviour. Two distinct stages are noted for the flame behaviour. The flame has a steady and stable flame root anchored near the entrance to the burner, yielding a “V” shaped flame in Stage 1, and a transient lift-off event is observed in Stage 2. These two stages switch from one to the other, giving the unstable flame behaviour, as observed in the experimental studies. Further analysis of the simulations shows that large-scale scalar mixing plays a prominent role in the stabilisation of the flame and the entrainment of inflammable mixtures near the flame root location initiates the lift-off event.

Modeling of the Influence of Mixture Fraction Fluctuations on Burning Rate in Partially Premixed Turbulent Flames

A common approach to modeling the influence of turbulent fluctuations in the mixture fraction f on the burning rate in a partially premixed flame consists of invoking a presumed Favre (mass-weighted) probability density function (PDF) . In the present work, two issues relevant to such an approach are addressed. First, averaging of a dependence q(f), where q is an arbitrary quantity, e.g., the laminar flame speed SL, requires modeling of the canonical PDF P(f) if q is not proportional to the density . Second, because the shape of is not known a priori in a typical case, the presumed PDF approach can be a predictive tool only if the mean quantities are weakly sensitive to the PDF shape. To study the two issues, dependencies of and , computed for gasoline surrogate-air mixtures under elevated temperatures and pressures, associated with the conditions in a gasoline direct injection spark ignition engine, are averaged invoking either beta function or double-Dirac delta function Favre or canonical PDFs. Moreover, a simpler approach is proposed to evaluate . The approach consists of expanding in Taylor series with respect to , followed by averaging. The mean quantities and obtained for various Favre first and second moments using the aforementioned alternative methods are compared with each other and with and , respectively. The following conclusions are drawn. First, when averaging under conditions of the present study, the difference between the Favre and canonical beta-function PDFs may be disregarded for simplicity. Second, is sensitive to the shape of presumed PDF if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently large. Third, if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently low in order for the mean laminar flame speeds obtained invoking the beta-function and double-Dirac delta-function PDFs to be approximately equal to one another, then, can also be evaluated using the Taylor-expansion approach.

Modeling of combustion and flow in a single element GH2/GO2 combustor

A single element gaseous H2/O2 combustion test case set up by the Pennsylvania State University is investigated using the new Reynolds Averaged Navier–Stokes (RANS) code, Rocflam3. There are considerable numbers of publications on this test case. Some of the publishing authors assume that it is not possible to achieve good results for this test case with simple RANS methods whereas others demonstrate the opposite. This is a reason for discussion which continues in this work. To obtain a reasonable solution for the test case, different simulation settings have been examined. This includes a grid study, a comparison of various $$k{\text{-}} \epsilon$$ type turbulence models and the variation of the turbulent Prandtl and Schmidt numbers. Turbulent combustion is treated via an equilibrium-based, presumed probability density function approach with a mixture fraction formulation. The 2D steady state simulations show good agreement with the experimentally measured heat flux. However, a discrepancy between the computed chamber pressure and the measured one is observed and is discussed incorporating considerations about combustion efficiency. This discussion shows that the experimental data are inconsistent. Computations performed with the chemical equilibrium code by Gordon and McBride are used to support the statements.

Simulation of a MILD combustion burner using ILDM chemistry

A numerical study was performed to accommodate mathematical simplification of kinetics and non-premixed reactants in three-dimensional computations. Specifically, the ILDM technique was combined with the presumed probability density function approach to simulate turbulent combustion in a burner operating at MILD combustion, which was characterised by relatively uniform temperatures with no visible flame and sound. An Eulerian solution strategy was implemented in a CFD code on a structured mesh. Predictions of the mean flow field, turbulence kinetic energy, mixture fraction and its variance, temperature, and mass fraction of CO2 and H2O were presented. It is found that the flow near the burner exhibited strong anisotropy and, thus, k – ε turbulence model has over predicted the spread of the jets. Nevertheless, the calculated mean velocities and temperatures reproduce experimental data reasonably well. The mixing mechanism in the near field of the burner was fully described with remarks on the entrainment of flue gas. Low levels of turbulence in the lifted reaction zone were particularly emphasised with relevance to the homogeneity of the temperature field.

Probability density function approach coupled with detailed chemical kinetics for the prediction of knock in turbocharged direct injection spark ignition engines

In this work a new knock model is derived which accounts for the inherent feature of knocking combustion, namely that it is a stochastic phenomenon. It provides the probability of autoignition and distinct criteria to determine the mean knock onset as well as the relative number of knocking cycles. For modeling purposes an ignition progress variable is proposed to determine the reactive state of the unburnt fuel–air mixture and the occurrence of autoignition. Statistical information of this quantity is introduced by presuming a clipped Gaussian probability density function (PDF). Its shape is defined by the Favre mean and variance of the ignition progress variable for which transport equations are derived. The chemical source terms that appear in these equations are closed by employing a presumed PDF approach to account for turbulence chemistry interaction. A clipped Gaussian PDF distribution for temperature and a β-PDF for mixture fraction are employed. Hence, the impact of temperature and mixture fraction fluctuations on the ignition progress variable is accounted for. The chemical source terms are evaluated based on tabulated chemistry incorporating detailed chemical kinetics. For the assessment of the knock model a spark timing sweep was performed on the engine test bench for a full-load operating point at n=2000rpm. In-cylinder flow simulations including gas exchange, mixture formation, combustion, and knock were carried out and the results are compared with experimental data. It is shown that the knock model is able to predict the mean knock onset with reasonable accuracy and that the impact of a spark timing sweep on the number of knocking cycles is well captured.

Evaluation of combustion models based on tabulated chemistry and presumed probability density function approach for diesel spray simulation

Two combustion models of different complexity have been implemented in a RANS solver in the CFD platform OpenFOAM®. Both models rely on the flame prolongation of ILDM (FPI) method, which allows the use of detailed chemistry mechanisms at relatively low computational costs. The homogeneous auto-ignition (HAI) model, directly using the chemical data from the FPI tabulation, does not take into account subgrid turbulence-chemistry interaction. Therefore, the second, more advanced model combines the FPI method with a presumed conditional moment approach. This auto-ignition-presumed conditional moment (AI-PCM) model accounts for the fluctuations of the mixture fraction and the progress variable caused by the turbulent flow. Both models have been evaluated by means of a parametric study of a single diesel spray at varying initial temperatures and oxygen concentration levels. The results obtained with the CFD models have been compared with experimental data from the engine combustion network (ECN). The comparison of the two models demonstrates the important role of the subgrid turbulence-chemistry interaction on the accuracy of the auto-ignition process and the diesel flame structure, as indicated by the agreement of the AI-PCM predictions with the measured data.

Numerical study of cryogenic liquid nitrogen jets at supercritical pressures

This paper discusses numerical modeling of the mixing and flow processes of cryogenic liquids that are encountered in liquid propellant rocket engines. In the present approach, turbulence is represented by an extended k–ɛ turbulence model. A conserved scalar approach together with a presumed probability density function approach is utilized to account for scalar fluctuation effects on the turbulent mixing processes of real fluids over transcritical and supercritical states. The two real-fluid equations of state (EOS) and dense-fluid correction schemes incorporated into our real-fluid code are validated for thermodynamic and transport properties over a wide range of pressures and temperatures. In this study, computations are made for four cryogen nitrogen jets at near-critical and supercritical pressures. Special emphasis is given to sensitivity analyses for two different equations of state. Based on our numerical results, the real fluid behaviors and precise structures of cryogenic nitrogen jets are discussed in detail. Numerical results indicate that the present real-fluid model has the predicative capabilities to simulate the essential features of the cryogenic liquid nitrogen jets. The PR equation predicts the slightly better conformity with measured nitrogen density profiles, compared to the SRK equation. It is also found that increases in pseudo-boiling strength result in increases in the cold potential core length as well as decreases in the decay rate of the axial velocity.

Computational Methodology for Carbon Monoxide Emission for Aeroengine Combustor Design

Design of lean combustion technologies will have to face the problem of the increasing difficulty to control carbon monoxide emission. To help the designer, a 91 species and 1329 elementary reactions chemical mechanism for Jet Al kerosene is tabulated and coupled with the turbulent flow through a presumed probability density function approach. The capacities of the methodology for finite rate chemistry prediction are assessed by the computation of several operating conditions of an experimental combustor. The first case corresponds to high-power operating conditions and a good agreement is achieved between the predicted and measured carbon monoxide emissions and temperature profile at the combustor outlet. The second case corresponding to low-power operating conditions for which finite rate chemistry effects are important is focused on the study of carbon monoxide emissions variations with respect to the global fuel air ratio of the combustor, while keeping constant the inlet air mass flow rate and the airflow split. A detailed discussion is provided to carefully check the coherence of the obtained results, then the full relevance of this tabulated approach regarding the prediction of finite rate chemistry effects for turbulent combustion in aeronautical combustors with liquid injection is concluded.

3d Modeling of Mixing, Ignition and Combustion Phenomena in Highly Stratified Gasoline Engines

The present paper describes recent developments realised at IFP on the 3D modeling of combustion in spark ignition engines. They consist in improvements made to the classical coherent flame model (CFM) to yield the extended coherent flame model (ECFM), specifically adapted to simulating the combustion process in direct injection-spark ignition (DI-SI) engines. The principal idea of this extension consists in describing locally the fuel/air (F/A) equivalence ratio in fresh gases, composition (including residual gases) and temperature, allowing to improve the description of large scale stratification. A generalisation of this approach to multi-component fuels is proposed. The effect of small scale stratification is included into the ECFM model via a variance/scalar dissipation model in combination with a presumed probability density function approach for the fuel stratification. The spark ignition model AKTIM, developed to represent the initiation of combustion at the spark plug, has been modified here in order to account for the flame wrinkling by turbulence. It is shown that this effect is essential in the case of high turbulence levels. Finally, a model to predict knock in SI engines is briefly described. These developments are then validated on two engine configurations: an optical access engine, for which LIF (laser induced fluorescence) measurements are available and the gasoline direct injection Mitsubishi engine for global validations.

Response of the dynamic LES model to heat release induced effects

The response of the dynamic large eddy simulation (LES) subgrid model to heat release effects is investigated. Nonpremixed turbulent flames are considered in the case of large Damköhler number combustion in homogeneous and isotropic flows. The subgrid fluctuations of mixture fraction are accounted for through a presumed probability density function approach. In this work, dynamic LES includes a procedure minimizing, over flow path lines, the error in the determination of the parameters entering the turbulence model [Meneveau, Lund, and Cabot, Proceedings of the 1994 Summer Program (CTR, Stanford, CA, 1994), pp. 271–299]. Both direct numerical simulation (DNS) and LES are performed. It is found that the flux of turbulent kinetic energy toward the subgrid is correctly represented by the dynamic LES model in the presence of heat release.