Presumed Probability Density Function Research Articles

Numerical Study of a Turbulent Burner by Means of RANS and Detailed Chemistry

The present paper shows a numerical study of the Co-flow turbulent flame configuration using the Reynolds Averaged Navier-Stokes (RANS) modelling with detailed chemistry. The presumed Probability Density Function (PDF) model combined with the k-Ɛ turbulence model is adopted. The GRI Mech-3.0 mechanism that involves 53 species and 325 reactions is used. The effect of the turbulent Schmidt number Sct and the C1ε constant in the turbulent dissipation transport equation is highlighted. Despite the simplicity of RANS approach compared to other complex models such as LES and DNS, the results show that this approach is still able to simulate the turbulent flame.

A Novel In Situ Flamelet Tabulation Methodology for the Representative Interactive Flamelet Model

ABSTRACTA priori flamelet tabulation methods have been used extensively to model premixed and non-premixed combustion in Reynolds-averaged Navier–Stokes (RANS) and large Eddy simulations (LES). Pre-tabulation of flamelet libraries have led to significant cost reduction of Computational Fluid Dynamics (CFD) simulations. However, these tabulation methods rely on certain simplifying assumptions. The dimensionality of the flamelet manifolds and size of flamelet libraries are also constrained due to memory and computational limitations. This limits the applicability and predictive capability of flamelet models. The traditional representative interactive flamelet (RIF) approach with multiple flamelets on the other hand involves online solution of flamelet equations and presumed probability density function (PDF) integration at each computational cell, making it attractive but computationally expensive and not suitable for LES with large cell counts. The current work discusses the development of a novel methodology that combines the advantages of an online flamelet solver along with the computational efficacy of tabulated models. The novel in situ tabulation approach consists of creating a flamelet table at each computational time step using the unsteady flamelet equations. The flamelets are then integrated in real time based on their respective scalar dissipation rate histories. This approach is capable of including history effects and unsteady chemical kinetic effects as it involves the online solution of unsteady flamelets. Implementation and comprehensive validation of the new framework is carried out against gas-jet flames as well as spray flames at high pressures. The approach is first validated for a partially premixed methane gas-jet flame in a RANS framework. The temperature and species mass fractions are compared against experimental results at different locations of a lifted flame. The approach is able to capture the transient flame characteristics. The model is then validated against an n-dodecane spray flame at high pressures in an LES framework with a 103-species n-dodecane chemistry mechanism. The model is able to capture ignition delays and flame liftoff of the n-dodecane spray over varying ambient temperature conditions. Due to the offsetting of presumed PDF integration cost, the proposed framework is shown to be faster than the traditional RIF approach, and the speedup over RIF increases with an increase in the cell count. This framework enables use of the RIF model for large cell count LES simulations.

Numerical Investigation of an OxyfuelNon-Premixed CombustionUsing a Hybrid Eulerian Stochastic Field/Flamelet Progress Variable Approach: Effects of H2/CO2Enrichment and Reynolds Number

In the present paper, the behaviour of an oxy-fuel non-premixed jet flame is numerically investigated by using a novel approach which combines a transported joint scalar probability density function (T-PDF) following the Eulerian Stochastic Field methodology (ESF) and a Flamelet Progress Variable (FPV) turbulent combustion model under consideration of detailed chemical reaction mechanism. This hybrid ESF/FPV approach overcomes the limitations of the presumed- probability density function (P-PDF) based FPV modelling along with the solving of associated additional modelled transport equations while rendering the T-PDF computationally less demanding. In Reynolds Averaged Navier-Stokes (RANS) context, the suggested approach is first validated by assessing its general prediction capability in reproducing the flame and flow properties of a simple piloted jet flame configuration known as Sandia Flame D. Second, its feasibility in capturing CO2addition effect on the flame behaviour is demonstrated while studying a non-premixed oxy-flame configuration. This consists of an oxy-methane flame characterized by a high CO2 amount in the oxidizer and a significant content of H2 in the fuel stream, making it challenging for combustion modelling. Comparisons of numerical results with experimental data show that the complete model reproduces the major properties of the flame cases investigated and allows achieving the best agreement for the temperature and different species mass fractions once compared to the classical presumed PDF approach.

Simulations of a Turbulent Line Fire with a Steady Flamelet Combustion Model and Non-Gray Gas Radiation Models

The general objective of this project is to develop an accurate combustion and radiation modeling framework for high-fidelity large eddy simulations (LES) of well-controlled turbulent laboratory-scale fires for which the fuel composition and fuel oxidation chemistry are known. This modeling framework is aimed at providing a solid basis for the development and validation of engineering-level models used in simulations of real-world fire problems for which the sources of fuel are diverse, complex, and in many cases, poorly characterized. The combustion model features a library of flamelet solutions corresponding to one-dimensional, steady, laminar, counterflow diffusion flames simulated with specialized software, a chemical kinetic mechanism and an equi-diffusive molecular transport model (i.e., unity Lewis numbers). Two different flamelet libraries are considered here: a first library generated with a solver called libOpenSMOKE and a detailed chemical kinetic mechanism developed for C1-C3 combustion chemistry and a second library generated with a solver called FlameMaster and the GRI-Mech v3.0 chemical kinetic mechanism developed for methane combustion chemistry. The radiation model features a banded Weighted-Sum-of-Gray-Gases model but (so far) no description of subgrid-scale turbulence-radiation interactions (TRI). This modeling framework is incorporated into a LES solver developed by FM Global and called FireFOAM, and is evaluated in simulations of a two-dimensional, plane, buoyancy-driven, methane-air, turbulent diffusion flame experimentally studied at the University of Maryland. The configuration corresponds to an intermediate validation step in our model development strategy without the complications of flame extinction. The flame structure is characterized by new micro-thermocouple measurements of the temporal mean and root-mean-square gas temperatures. Comparisons between simulated and measured temperatures show significant discrepancies that are explained by the large values of the width of the presumed probability density function (PDF) representing subgrid-scale variations of mixture fraction and by the absence of a model for subgrid-scale TRI.

The effects of flue-wall design modifications on combustion and flow characteristics of an aluminum anode baking furnace-CFD modeling

A modern aluminum smelter has a capacity of 1–2 million tons of aluminum per annum which requires more than 0.5–1.0 million tons of heat treated (baked) carbon anodes per year. The anode baking process is very energy intensive, approximately requires 2 GJ of energy per ton of carbon anodes which will be approximately 1–2 million GJ of energy per year. Since the plant testing is very expensive, anode baking furnace modeling is imperative to investigate the effects of different operational and geometrical parameters on the furnace energy consumption.In the numerical modeling of turbulent reactive flows, the accuracy of the model highly depends on the description of turbulence-chemistry interaction, and the robustness of the radiative transfer equation solver. Hence, the present study tested different turbulence-chemistry interaction frameworks and radiative transfer equation solvers for confined turbulent diffusion flames and results are compared with the experimental data. It was observed that the k-ε realizable turbulence model combined with the presumed probability density function method as turbulence-chemistry interaction, and discrete ordinates method as radiative transfer equation solver illustrate excellent agreement with the experimental data.Anode baking homogeneity is an important consideration in the design of the anode baking furnace, which requires appropriate flow distribution in the flue-wall cavity. Hence, the developed numerical framework was employed to investigate the effects of flue-wall design modifications on combustion and heat transfer characteristics of anode baking furnace energy consumption. It was observed that the modified design results in a higher thermal efficiency (lower energy consumption), and more homogenous temperature and flow fields which result in the baking of anodes more uniformly which consequently result in the evolution of more homogenous material properties. Consequently, the energy consumption in the aluminum reduction cell will also be significantly reduced. The present study also investigated the effect of flue-wall flow blockage due to packing coke infiltration on baking energy consumption for the aged anode baking furnaces and introduced three modified flue-wall designs.

OpenCrys: Open-Source Software for the Multiscale Modeling of Combined Antisolvent and Cooling Crystallization in Turbulent Flow

The open-source software, called openCrys, is provided for the multiscale simulation of antisolvent and combined antisolvent-cooling crystallization. It simulates the macro- and micromixing scales, and the complete energy and population balance equations during crystal nucleation and growth. The model is based on the Reynolds-Averaged-Navier–Stokes equation, coupled with a three-environment presumed probability density function model, and the spatially varying population balance equation semidiscretized using a high resolution finite-volume method. openCrys is implemented in C++ object oriented programming language using the open-source CFD package OpenFOAM. The software is used to compare the performance of dual impinging jet, coaxial, and radial crystallizers. It is shown that improving the micromixing does not necessarily result in a narrower crystal size distribution when temperature effects are taken into account. The complex interplay of crystallizer kinetics and momentum, mass, and heat transfer makes the selection of the best mixer for a particular application to be nonobvious, which motivates the development and application of high-fidelity multiscale simulations for the design of antisolvent crystallizers.

Large-eddy simulation of multiphase combustion jet in cross-flow using flamelet model

In this work, large-eddy simulations of pulverized coal combustion are conducted using the flamelet model, in which the devolatilization, char surface reactions, radiation and flame-wall interactions (FWI) are all considered. The mixings between the oxidizer and the volatiles/char off-gases are described with two mixture fractions Zvol and Zchar, while the interphase heat transfer and progress of reactions are described with the manifolds of total enthalpy He and reaction progress variable YPV, respectively. The turbulence-chemistry interactions are considered with the presumed probability density functions. Standard pulverized coal combustion submodels are used to characterize the coal combustion sub-processes of devolatilization, char surface reactions, radiation, etc. Characteristics of pulverized coal combustion jet in cross-flow (JICF) are analyzed in detail. Particularly, the effects of the flame-flame interactions (FFI) and the wall heat losses (WHL) on the pulverized coal flame structure and thermo-chemical quantities distributions are studied through both qualitative and quantitative analyses. The results show that the overall flame temperature with twin jets in cross-flow (TJICF) is higher than that with single jet in cross-flow (SJICF) due to the FFI. The gas velocities in different directions have different sensitivities to the FFI, and the particle residence time/trajectory is influenced by the FFI. Three stages of FFI are identified, i.e., separated flames, merging flames and a merged flame. When the effects of WHL are neglected, the flame front becomes more wrinkling, the flame base moves towards the injectors, and the coal particles are ignited earlier. The pulverized coal flame structure at the lee-side of the flame front is more complicated than that at the leading-edge due to the different flow dynamics, and many burning pockets can be observed at the lee-side.

Evaluation of reaction progress variable - mixture fraction statistics in partially premixed flames

The mixture fraction and reaction progress variables are key for presumed probability density function (PDF) based flamelet models for partially premixed flames. The importance of the joint statistics of these two variables are evaluated using a joint composition-enthalpy transported PDF/Finite Volume method applied to established databases for inhomogeneous jet flames. The accuracy of the approach is first examined for three flames with different mixture fraction inlet profiles and departures from blow-off. The (joint-) statistics of mixture fraction and reaction progress variable are subsequently analysed with the covariance of the two variables used to evaluate the assumption of statistical independence. Results show that the current approach is able to reproduce the near-field features of both homogeneous and inhomogeneous jet flames. The latter leads to a stratified premixed flame that evolves to diffusion-dominated combustion as the influence of the pilot fades. In agreement with measured data, the mixture fraction variance is strongly affected by the near-field combustion mode and the misalignment with the reaction progress variable variance is obvious in the stratified premixed flame. It is shown that the covariance of the mixture fraction and reaction progress variable is influenced by turbulence-chemistry interactions and that, generally, the two parameters remain strongly correlated with the consequence that the assumption of statistical independence is implausible.

Numerical Study of a Cyclonic Combustor under Moderate or Intense Low-Oxygen Dilution Conditions Using Non-adiabatic Tabulated Chemistry

A cyclonic burner operating under moderate or intense low-oxygen dilution (MILD) conditions is simulated using a perfectly stirred reactor (PSR) incorporated within a tabulated chemistry approach. A presumed joint probability density function method is used with appropriate submodels for the turbulence–chemistry interaction. Non-adiabatic effects are included in the PSR calculation to take into account the effects of non-negligible wall heat loss in the burner. Five different operating conditions are investigated, and the computed mean temperatures agree well with measurements. A substantial improvement is observed when the non-adiabatic PSR is used, highlighting the importance of heat transfer effects for burner configurations involving internal exhaust gas recirculation. Furthermore, enhanced reaction homogeneity is observed in this cyclonic configuration for the globally lean case, leading to a more spatially uniform temperature variation with MILD combustion.

Large eddy simulation of turbulent stratified combustion using dynamic thickened flame coupled with tabulated detailed chemistry

• A SGS model of DTF coupled with FGM is developed for investigating stratified flame. • LES transport equation for covariance in the DTF-FGM model is deduced. • An in-depth analysis for the flame structures of Cambridge stratified flames is achieved. A sub-grid scale (SGS) combustion model of the dynamic thickened flame (DTF) coupled with flamelet generated manifolds (FGM) approach (i.e. DTF-FGM) is developed to investigate Cambridge stratified flames. Two issues in developing the DTF-FGM model are addressed. Firstly, the copula method is extended to construct a multivariate joint probability density function (PDF) of the tabulated scalars. A modified laminar flamelet PDF is incorporated to describe the probable asymmetric multimodal distribution for the reaction progress variable. Secondly, large eddy simulation (LES) transport equations for the tabulated scalars, relevant sub-grid variances and covariance in the DTF-FGM model are deduced. LES of Cambridge stratified flames is performed with the DTF-FGM model and the widely used SGS combustion model which combines a presumed PDF with FGM (i.e. PPDF-FGM). Detailed comparisons between simulations and experiments are carried out to evaluate the SGS combustion models and mesh resolution effects. Meanwhile, an in-depth analysis for the flame structures of Cambridge stratified flames is also achieved. The results indicate that the developed SGS combustion model considering the effect of correlations between the mixture fraction and reaction progress variable has the ability to solve the stratified flame structures under LES mesh resolution exactly at a reasonable computational cost.

Nonadiabatic Flamelet Formulation for Predicting Wall Heat Transfer in Rocket Engines

A flamelet-based combustion model is proposed for the prediction of wall heat transfer in rocket engines and confined combustion systems. To account for convective heat loss due to the interaction of the flame with the wall, a permeable thermal boundary condition is introduced in the counterflow diffusion flame configuration. The solution of the resulting nonadiabatic flame structure forms a three-dimensional manifold, which is parameterized in terms of mixture fraction, progress variable, and temperature. The performance of the model is first evaluated through a direct numerical simulation analysis of an diffusion flame that is stabilized at an inert isothermal wall. The developed nonadiabatic flamelet model is shown to accurately predict the temperature, chemical composition, and wall heat transfer. Combined with a presumed probability density function closure, the model is then applied to large-eddy simulation of a single-injector rocket combustor to examine effects of heat transfer on the turbulent flame structure in rocket engines.

Model Simulation and Design Optimization of a Can Combustor with Methane/Syngas Fuels for a Micro Gas Turbine

Abstract The design and model simulation of a can combustor has been made for future syngas combustion application in a micro gas turbine. An improved design of the combustor is studied in this work, where a new fuel injection strategy and film cooling are employed. The simulation of the combustor is conducted by a computational model, which consists of three-dimensional, compressible k-ε model for turbulent flows and PPDF (Presumed Probability Density Function) model for combustion process invoking a laminar flamelet assumption generated by detailed chemical kinetics from GRI 3.0. Thermal and prompt NOx mechanisms are adopted to predict the NO formation. The modeling results indicated that the high temperature flames are stabilized in the center of the primary zone by radially injecting the fuel inward. The exit temperatures of the modified can combustor drop and exhibit a more uniform distribution by coupling film cooling, resulting in a low pattern factor. The combustion characteristics were then investigated and the optimization procedures of the fuel compositions and fuel flow rates were developed for future application of methane/syngas fuels in the micro gas turbine.

Thermal and emission characteristics of reverse air flow CAN combustor

Relative assessment of thermal and emission characteristics of conventional and reverse air flow CAN type gas turbine combustor is reported. Large Eddy Simulations (LES) are carried out with Wall Adaptive Local Eddy (WALE) viscosity model for sub grid scale stresses. Turbulence-chemistry interaction is modelled using presumed shape Probability Density Function (PDF) approach. Discrete Ordinates (DO) model is used for radiative heat transfer. Experimental measurement of temperature and NOx emission level at the exit of combustors are reported. Flow pattern and flame shape obtained from numerical analysis for conventional and reverse air flow combustor are correlated to combustor liner wall heating, exit temperature characteristics and NOx emission. The liner wall region of conventional combustor is dominated by hot combustion gases whereas the location of hot flame in reverse air flow combustor is in the vicinity of centreline. The exit temperature measurement shows that the wall side temperature in reverse air flow combustor is relatively low compared to conventional combustor. Reverse air flow arrangement in combustor eliminates the hot spots of high temperature gradient from primary region of combustor which results into significant reduction in NOx emission level in reverse air flow combustor as compared to conventional combustor. Thermal imaging of outer wall of combustors demonstrates that the radiative energy transfer from liner wall to outer wall is small in reverse air flow combustor compared to conventional combustor. This depicts that the wall-cooling requirement decreases in reverse air flow combustor.

Numerical Investigation of Turbulent Diffusion Flame in the Aluminum Anode Baking Furnace Employing Presumed PDF

A modern aluminum smelter has a capacity of 1-2 million tons of aluminum per annum which requires more than 0.5-1.0 million tons of heat treated (baked) carbon anodes per year. Anode baking homogeneity strongly depends on flow distribution in the flue wall cavity which consists of several baffles with certain geometrical design. Moreover, fuel consumption and pollutants emissions are major concerns in the aluminum anode baking furnace (ABF). In the numerical modeling of the turbulent reactive flows, the accuracy of the model highly depends on the description of turbulence-chemistry interaction (TCI). Hence, the present study tested different TCI frameworks for confined diffusion flames and results are compared the results with the reported numerical and experimental data in the literature. It was observed thatk - ε realizable turbulence model combined with presumed probability density function (PDF) method shows an excellent agreement with the experimental data. The developed numerical framework was employed to investigate the effects of flue wall design modification on combustion and emissions characteristics of ABF. It is observed that by closing the openings at the top of the baffles, the same average flue gas temperature can be obtained by reducing the global equivalence ratio (φglob) from 1.0 to 0.125. Lower φglob value results in a lower fuel consumption which consequently translates into less CO, NOx and soot concentration.

Influence of fuel injection method on performance of upward swirl can-type combustor

A new concept of reverse fuel injection is introduced to enhance the fuel-burning rate in upward swirl can-type gas turbine combustor. The existing combustor has conical shaped injector where fuel jets are arranged on 90° cone. In reverse fuel injection, the injectant exits the fuelling device in reverse axial direction towards the wall of hemispherical dome. The dome wall deaccelerates the fuel jet first and then fuel flows in all directions. The injector length is chosen as design variable for analysis of reverse fuel injection flow field. Combustion experiments are carried out for existing conical injector and different reverse fuel injectors. Large Eddy Simulations (LES) are carried out to simulate non-premixed turbulent combustion flow field and it is combined with Discrete Ordinates (DO) method for the radiation modelling. The turbulence-chemistry interaction is modelled using presumed shape Probability Density Function (PDF) approach. Results obtained show that reverse fuel injection provides rapid near field mixing and better fuel penetration. Improved mixing results into release of large amount of heat energy during combustion, which increases combustion efficiency and reduces CO emission level without adversely affecting the NOx emission level. The obtained results show that injector length influences mixing efficiency, residence time and emission level. There exists an optimal penetration height for efficient mixing and total pressure recovery efficiency and it is achieved when injector length is kept at 5 mm in the present study. Thermal imaging of outer wall of combustor demonstrates that reverse fuel injection does not adversely affect the wall temperature.

Large eddy simulation of turbulent lifted flame in a hot vitiated coflow using tabulated detailed chemistry

Large eddy simulation (LES) of Cabra flame is carried out by a sub-grid scale (SGS) model of tabulated detailed chemistry combined with presumed probability density function (PDF). The chemistry table is constructed by utilizing the coupling of auto-ignition model and premixed flame propagation model. The copula method is applied to build multivariate joint PDF of mixture fraction and reaction progress variable. LES transport equations for characteristic scalars, relevant sub-grid variances and covariance are deduced. The LES results show that the developed SGS model can give an accurate prediction for lift-off height and flame structures. The stabilization mechanism and combustion regime of Cabra flame are discussed.

The Effect of Partial Premixing and Heat Loss on the Reacting Flow Field Prediction of a Swirl Stabilized Gas Turbine Model Combustor

This work addresses the prediction of the reacting flow field in a swirl stabilized gas turbine model combustor using large-eddy simulation. The modeling of the combustion chemistry is based on laminar premixed flamelets and the effect of turbulence-chemistry interaction is considered by a presumed shape probability density function. The prediction capabilities of the presented combustion model for perfectly premixed and partially premixed conditions are demonstrated. The effect of partial premixing for the prediction of the reacting flow field is assessed by comparison of a perfectly premixed and partially premixed simulation. Even though significant mixture fraction fluctuations are observed, only small impact of the non-perfect premixing is found on the flow field and flame dynamics. Subsequently, the effect of heat loss to the walls is assessed assuming perfectly premixing. The adiabatic baseline case is compared to heat loss simulations with adiabatic and non-adiabatic chemistry tabulation. The results highlight the importance of considering the effect of heat loss on the chemical kinetics for an accurate prediction of the flow features. Both heat loss simulations significantly improve the temperature prediction, but the non-adiabatic chemistry tabulation is required to accurately capture the chemical composition in the reacting layers.

Experimental and Theoretical Study of Combustion under Elevated Pressure within Porous Inert Media

AbstractGas combustion occurring within porous inert media (PIM) results in intensified heat and mass transfer in comparison to free laminar combustion. This leads to considerably lower emissions of pollutant species, that is, NOx and CO, larger flame stability range, lower thermo‐acoustic instabilities, gradual response to operative changes, and geometric flexibility of design. In this work, experiments were carried out to describe the influence of flow rate, pressure, temperature, and air‐to‐fuel ratio on the flame stability within PIM at nearly adiabatic conditions. The macroscopic thermal flame thickness and the burning velocity were calculated from measured temperature profiles and flow rates. As the main result, it was observed that the pressure effect on the burning velocity can differ considerably from that of laminar free flames, that is, the increase of pressure can positively affect the burning velocity. The obtained results were supported by theoretical modeling. A new model to average the species production rates in a volume‐averaged numerical model was proposed. The model considered spatial deviations of temperature and mass fractions along the cross‐sectional area using presumed probability density functions. Using this new model, results of burning velocities and profiles of average temperature were satisfactorily predicted when compared to experimental results shown here. Furthermore, easy‐to‐use tools for porous burner design were formulated and validated.

A parametric study of microjet assisted methane/air turbulent flames

A parametric study of microjet assisted methane/air turbulent flames characteristics is numerically investigated. The Presumed Probability Density Function model and the Discrete Ordinates model are respectively considered for combustion and radiation modeling. The k-epsilon Standard model with Pope Correction is adopted as a turbulence closure model. The two step Tesner model is used to quantify the soot particle production in the flame configuration. Comparison with our previous work using the k-epsilon Realizable model shows that the k-epsilon Standard model with Pope Correction ensures better predictions. The microjet velocity and diameter effects on thermal field, mixing process and soot emission are then discussed. Numerical findings show that the microjet can be used as an efficient tool controlling methane/air turbulent flames. On the one hand, it is shown that the microjet creates an inner flame in the vicinity of the central nozzle exit but does not globally alter the methane/air flame shape. On the other hand, mixing process can be enhanced for high microjet Reynolds number either by increasing the microjet velocity or by decreasing its nozzle diameter for a constant microjet mass flow rate. Soot production can be consequently reduced for low microjet diameter and high velocity values.

Flame volume prediction and validation for lean blow-out of gas turbine combustor

ABSTRACTLean Blow-Out (LBO) limits are critically important in the operation of aero engines. Previously, Lefebvre's LBO empirical correlation has been extended to the flame volume concept by the authors. Flame volume takes into account the effects of geometric configuration, spatial interaction of mixing jets, turbulence, heat transfer and combustion processes inside the gas turbine combustion chamber. For these reasons, LBO predictions based on flame volume are more accurate. Although LBO prediction accuracy has improved, it poses a challenge associated with Vfestimation in real gas turbine combustors. This work extends the approach of flame volume prediction based on fuel iterative approximation with cold flow simulations to reactive flow simulations. Flame volume for 11 combustor configurations were simulated and validated against experimental data. To make prediction methodology robust, as required in preliminary design stage, reactive flow simulations were carried out with the combination of presumed Probability Density Function (PDF) and discrete phase model (DPM) in Fluent 15.0 The criterion for flame identification was defined. Two important parameters—critical injection diameter (Dp,crit) and critical temperature (Tcrit)—were identified and their influence on reactive flow simulation was studied for Vfestimation. Results exhibit ±15% error in Vf estimation with experimental data.