The filtered mass density function (FMDF) model (Jaberi et al. 1999 [1]) is employed for large eddy simulations (LES) of “high speed” partially-premixed methane jet flames with the “flamelet” and “finite-rate” kinetics models. The FMDF is the joint probability density function (PDF) of the scalars and is determined via the solution of a set of stochastic differential equations. The LES/FMDF is implemented using a highly scalable, parallel hybrid Eulerian–Lagrangian numerical scheme. The LES/FMDF results are shown to compare well with the experimental data for all flow conditions when “appropriate” reaction and mixing models are employed.

%B International Journal of Heat and Mass Transfer %V 53 %P 2551-2562 %8 05/2010 %G eng %N 11-12 %0 Conference Paper %B 48th AIAA Aerospace Sciences Meeting %D 2010 %T Large-Scale Simulations of Supersonic Turbulent Reacting Flows %A Li, Z. %A Jaberi, F.A. %A Banaeizadeh, A. %XThe scalar filtered mass density function (FMDF) is further developed and employed for large-eddy simulations (LES) of high speed turbulent flows in complex geometries. LES/FMDF is implemented via an efficient, hybrid numerical method. In this method, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved with a generalized, high-order, multi-block, compact differencing scheme. Turbulent mixing and combustion are modeled with the FMDF. The LES/FMDF method is used for simulations of isotropic turbulent flow in a piston-cylinder assembly, the flow in a shock tube and a supersonic co-axial helium-air jet. The critical role of pressure in the FMDF equation when applied to compressible flows is studied. It is shown that LES/FMDF is reliable and is able to simulate compressible turbulent mixing and combustion in supersonic flows.

%B 48th AIAA Aerospace Sciences Meeting %I AIAA %C Orlando, FL %8 01/2010 %G eng %0 Conference Paper %B 48th AIAA Aerospace Sciences Meeting %D 2010 %T Numerical Investigations of Shock-Turbulence Interactions in a Planar Mixing Layer %A Li, Z. %A Jaberi, F.A. %XDirect numerical simulation (DNS) and large-eddy simulation (LES) of spatially developing supersonic mixing layer, interacting with an oblique shock wave are conducted with a new high-order Monotonicity-Preserving scheme. Without the incident shock, the mixing layer grows linearly and exhibits self-similar behavior after the transition. With the shock, significant small-scale turbulence is generated just behind the shock. With an increase in shock angle, the intensity of the shock-generated turbulence is increased and its peak position shifts away from the mixing layer centerline. The effects of turbulence on the shock are also shown to be very significant, such that normal shocklets and large adverse pressure gradients are created in some conditions. Comparison with the DNS data indicates that the LES with the modified kinetic energy viscosity (MKEV) subgrid stress model is able to predict the main features of the flow and shock-turbulence interactions.

%B 48th AIAA Aerospace Sciences Meeting %I AIAA %C Orlando, FL %8 01/2010 %G eng %0 Conference Paper %B International Conference on Liquid Atomization and Spray Systems %D 2009 %T Experimental and Computational Analysis of Fuel Mixing in a Low Pressure Direct Injection Gasoline Engine %A S. Srivastava %A Jaberi, F.A. %A Harold Schock %A David Hung %XAn experimental and computational investigation of the fuel spray mixing in an optically accessible single-cylinder direct-injection engine under realistic operating conditions was performed. High speed flow visualization in the op- tical engine was performed with images taken at a rate of 10,000 frames per second. The numerical simulations were carried out using the KIVA-3V software, which uses the discrete particle method for modeling the spray, with the secondary droplet breakup modeled by the Taylor Analogy Breakup (TAB) model. The nozzle configuration, jet orientation, injection flow rate and other injection parameters were matched with the experimental conditions. The simulated spray patterns in the cylinder were shown to compare well with the fuel distribution images obtained from the high speed flow visualization. The computational and experimental results for the fuel impingement on the cyl- inder walls, piston and valves, and those for the spark plug wetting and evaporated fuel mixing indicate the strong dependency of the fuel-air mixing to the spray pattern.

%B International Conference on Liquid Atomization and Spray Systems %C Vail, Colorado %8 07/2009 %G eng %0 Conference Paper %B National Combustion Meeting %D 2009 %T Large-Eddy Simulations of Turbulent Methane Jet Flames with Filtered Mass Density Function %A Yaldizli, M. %A Mehravaran, K. %A Jaberi, F.A. %XThe filtered mass density function (FMDF) model (Jaberi et al. 1999 [1]) is employed for large eddy simulations (LES) of “high speed” partially-premixed methane jet flames with the “flamelet” and “finite-rate” kinetics models. The FMDF is the joint probability density function (PDF) of the scalars and is determined via the solution of a set of stochastic differential equations. The LES/FMDF is implemented using a highly scalable, parallel hybrid Eulerian–Lagrangian numerical scheme. The LES/FMDF results are shown to compare well with the experimental data for all flow conditions when “appropriate” reaction and mixing models are employed.

%B National Combustion Meeting %I The Combustion Institute %C Ann Arbor, Michigan %8 05/2009 %G eng %0 Conference Paper %B 47th AIAA Aerospace Sciences Meeting %D 2009 %T Large-Scale Simulations of High Speed Turbulent Flows %A Li, Z. %A Jaberi, F.A. %XThis paper briefly describes a new class of high-order Monotonicity-Preserving (MP) finite difference methods recently developed for direct numerical simulation (DNS) and large-eddy simulation (LES) of high-speed turbulent flows. The MP method has been implemented together with high-order compact (COMP) and weighted essentially non- oscillatory (WENO) methods in a generalized three-dimensional (3D) code and has been applied to various 1D, 2D and 3D problems. For the LES, compressible versions of the gradient-based subgrid-scale closures are employed. Detailed and extensive analysis of various flows indicates that MP schemes have less numerical dissipation and faster grid convergence than WENO schemes. Simulations conducted with high-order MP schemes preserve sharp changes in flow variables without spurious oscillations and capture the turbulence at the smallest simulated scales. The non-conservative form of the scalar equation solved with MP schemes are shown to generate the same results as COMP schemes for supersonic mixing problems involving shock waves.

%B 47th AIAA Aerospace Sciences Meeting %I American Institute of Aeronautics and Astronautics %C Orlando, FL %8 01/2009 %G eng %0 Conference Paper %B National Combustion Meeting %D 2009 %T LES/FMDF of Spray Combustion in Internal Combustion Engines %A Banaeizadeh, A. %A Harold Schock %A Jaberi, F.A. %XThe two-phase filtered mass density function (FMDF) model is employed for large-eddy simulation (LES) of turbulent spray combustion in internal combustion (IC) engines. The LES/FMDF is implemented with an efficient, hybrid numerical method. In this method, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved with a generalized, high-order, multi-block, compact differencing scheme. The spray and the FMDF are implemented with Lagrangian methods. The LES/FMDF methodology has been used for simulations of turbulent combustion in a rapid compression machine (RCM) and in a direct-injection spark-ignition (DISI) engine. For both RCM and DISI engine, the complex interactions among turbulent velocity, fuel droplets and combustion are shown to be well captured with the LES/FMDF. The results for the DISI engine indicate that the size, velocity, evaporation and combustion of the sprayed fuel droplets are strongly affected by the unsteady, vortical motions generated by the incoming air during the intake stroke. In turn, the droplets are found to change the in-cylinder flow structure.

%B National Combustion Meeting %I The Combustion Institute %C Ann Arbor, Michigan %8 05/2006 %G eng %0 Conference Paper %B National Combustion Meeting %D 2009 %T A New Model for Numerical Simulations of Two-Phase Turbulent Combustion %A Li, Z. %A Jaberi, F.A. %B National Combustion Meeting %I National Combustion Meeting %C Ann Arbor, MI %8 05/2009 %G eng %0 Conference Paper %B SAE World Congress and Exhibit %D 2009 %T Numerical Simulation of a Direct-Injection Spark-Ignition Engine with Different Fuels %A S. Srivastava %A Harold Schock %A Jaberi, F.A. %A David Hung %XThis paper focuses on the numerical investigation of the mixing and combustion of ethanol and gasoline in a single-cylinder 3-valve direct-injection spark-ignition engine. The numerical simulations are conducted with the KIVA code with global reaction models. However, an ignition delay model mitigates some of the deficiencies of the global one-step reaction model and is implemented via a two-dimensional look-up table, which was created using available detailed kinetics models. Simulations demonstrate the problems faced by ethanol operated engines and indicate that some of the strategies used for emission control and downsizing of gasoline engines can be employed for enhancing the combustion efficiency of ethanol operated engines.

%B SAE World Congress and Exhibit %I SAE International %C Detroit, Michigan %8 04/2009 %G eng %0 Journal Article %J Physics of Fluids %D 2009 %T Turbulence-Interface Interactions in a Two-Fluid Homogeneous Flow %A Li, Z. %A Jaberi, F.A. %XThe two-way interactions between the turbulent velocity field and the interface in an incompressible two-fluid homogeneous turbulent flow are studied with a recently developed Lagrangian–Eulerian interfacial particle level-set method. The numerical results confirm that the rate of change of the interface area is directly related to the work done by the surface tension force. While the surface tension damps the surrounding turbulence in the “interface stretching period” to oppose the increase in interface area, it is shown to actually increase the turbulent kinetic energy when the interface experiences compression. Additionally, the surface tension force is found to generate strong vortical motions close to the interface through the baroclinic torque effects. There is also an increase in strain rate and the viscous dissipation rate of turbulent kinetic energy in the interface region. The effect of interface on the surrounding turbulence appears primarily in the direction perpendicular to the interface. Analysis of the vorticity and kinetic energy equations indicates that the turbulence-interface interactions are strongly dependent on the fluids’ density ratio and the Weber number.

%B Physics of Fluids %V 21 %8 09/2009 %G eng %N 9 %0 Conference Paper %B 46th AIAA Aerospace Sciences Meeting and Exhibit %D 2008 %T Filtered Mass Density Function for Numerical Simulations of Spray Combustion %A Li, Z. %A Jaberi, F.A. %A Yaldizli, M. %XThis paper briefly describes our recent efforts on the modeling and numerical simulations of two-phase turbulent reacting flows in realistic combustion systems with a new large-eddy simulation (LES) model. The model is constructed based on the two-phase extension of scalar filtered mass density function (FMDF) and a Lagrangian-Eulerian- Lagrangian mathematical/numerical methodology. In this methodology, the “resolved” fluid velocity field is obtained by solving the filtered form of the compressible Navier-Stokes equations with a high-order finite difference scheme. The liquid (droplet) phase and scalar (temperature and species mass fractions) fields are both obtained by stochastic Lagrangian models. There are two-way interactions between the phases and all the Eulerian and Lagrangian fields. The LES/FMDF is used for systematic analysis of turbulent combustion in the spray-controlled dump combustor and double-swirl spray burner for various flow and spray parameters. The effects of fuel type, spray angle, mass loading ratio, droplet size distribution, fuel/air composition, wall, and inflow/outflow conditions on the combustion are investigated. It has been found that the main features of the turbulence and combustion are modified by changing the inflow/outflow conditions. The LES/FMDF results also confirm the significance of the spray parameters.

%B 46th AIAA Aerospace Sciences Meeting and Exhibit %I AIAA %C Reno, Nevada %8 01/2008 %G eng %0 Journal Article %J International Journal for Numerical Methods in Fluids %D 2008 %T A Hybrid Langrangian-Eulerian Particle-Level Set Method for numerical Simulations of Two-Fluid Turbulent Flows %A Li, Z. %A Jaberi, F.A. %A Shih, T. I-P. %K two-fluid turbulent flows; particle-level set method; interface tracking %XA coupled Lagrangian interface-tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two-fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle-based Lagrangian re-initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface-moving’ problems and two-fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle-level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle-level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable-density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright q 2007 John Wiley & Sons, Ltd.

%B International Journal for Numerical Methods in Fluids %V 56 %P 2271-2300 %8 4/2008 %G eng %N 12 %0 Conference Paper %D 2008 %T Large Eddy Simulation of High Speed Turbulent Reacting Flows %A Zhaorui, Li %A Banaeizadeh, A. %A Jaberi, F.A. %C Hawaii %8 12/2008 %G eng %0 Conference Paper %B ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2008) %D 2008 %T Large Eddy Simulations of Turbulent Flows in IC Engines %A Banaeizadeh, A. %A Afshari, A. %A Jaberi, F.A. %A H. Schock %XA new computational methodology is developed and tested for large eddy simulation (LES) of turbulent flows in internal combustion (IC) engines. In this methodology, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved via a generalized, high-order, multi-block, compact differencing scheme and various subgrid-scale (SGS) stress closures. Both reacting and nonreacting flows with and without spray are considered. The LES models have been applied to a piston-cylinder assembly with a stationary open valve and harmonically moving flat piston. The flow in a direct-injection spark-ignition (DISI) engine is also considered. It is observed that during the intake stroke of the engine operation, large-scale unsteady turbulent flow motions are developed behind the intake valves. The physical features of these turbulent motions and the ability of LES to capture them are studied and tested by simulating the flow in a simple configuration involving a stationary valve. The flow statistics predicted by LES are shown to compare well with the available experimental data. The DISI configuration includes all the complexities involved in a realistic single-cylinder IC engine, such as the complex geometry, moving valves, moving piston, spray and combustion. The spray combustion is simulated with the recently developed two-phase filtered mass density (FMDF) model.

%B ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2008) %I ASME %C Brooklyn, New York %8 08/2008 %@ 978-0-7918-4327-7 %G eng %0 Conference Paper %B 46TH AIAA Aerospace Sciences Meeting and Exhibit %D 2008 %T Large Eddy Simulations of Two-Phase Turbulent Reacting Flows %A Jaberi, F.A. %A Li, Z. %B 46TH AIAA Aerospace Sciences Meeting and Exhibit %I AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS %C Reno, Nevada %8 01/2008 %G eng %L AIAA 2008-1154 %0 Journal Article %J International Journal of Heat and Mass Transfer %D 2008 %T Large-Eddy Simulation of a Dispersed Particle-Laden Turbulent Round Jet %A Almeida, T. %A Jaberi, F.A. %K Particle-laden jet; dilute %K two-phase flows; turbulent jet; LES %XThe numerical results obtained by large-eddy simulation (LES) of a particle-laden axisymmetric turbulent jet are compared with the available experimental data. The results indicate that with a new stochastic subgrid-scale (SGS) closure, the effects of the particles on the carrier gas and those of the carrier gas on the particles are correctly captured by the LES. Additional numerical experiments are conducted and used to investigate the effects of particle size, mass-loading ratio, and other flow/particle parameters on the statistics of both the carrier gas phase and the particle dispersed phase.

%B International Journal of Heat and Mass Transfer %V 51 %P 683-695 %8 2/2008 %G eng %N 3-4 %0 Journal Article %J AIAA Journal %D 2008 %T Large-Eddy Simulation of Turbulent Flow in an Axisymmetric Dump Combustor %A Afshari, A. %A Jaberi, F.A. %K combustion %K Gas turbine; modeling; combustion chamber; Monte Carlo method; Lagragian Method; turbulent flow; large eddy simulation %XA hybrid Eulerian–Lagrangian, mathematical/computational methodology is developed and evaluated for large- eddy simulations of turbulent combustion in complex geometries. The formulation for turbulence is based on the standard subgrid-scale stress models. The formulation for subgrid-scale combustion is based on the filtered mass density function and its equivalent stochastic Lagrangian equations. An algorithm based on high-order compact differencing on generalized multiblock grids is developed for numerical solution of the coupled Eulerian–Lagrangian equations. The results obtained by large-eddy simulations/filtered mass density function show the computational method to be more efficient than existing methods for similar hybrid systems. The consistency, convergence, and accuracy of the filtered mass density function and its Lagrangian–Monte Carlo solver is established for both reacting and nonreacting flows in a dump combustor. The results show that the finite difference and the Monte Carlo numerical methods employed are both accurate and consistent. The results for a reacting premixed dump combustor also agree well with available experimental data. Additionally, the results obtained for other nonreacting turbulent flows are found to be in good agreement with the experimental and high-order numerical data. Filtered mass density function simulations are performed to examine the effects of boundary conditions, subgrid-scale models, as well as physical and geometrical parameters on dump-combustor flows. The results generated for combustors with and without an inlet nozzle are found to be similar as long as appropriate boundary conditions are employed.

%B AIAA Journal %V 46 %P 1576-1592 %8 07/2008 %G eng %N 7 %0 Journal Article %J Combustion and Flame %D 2008 %T The Structure of Partially-Premixed Methane Flames in High Intensity Turbulent Flows %A Yaldizli, M. %A Mohammad, H. %A Mehravaran, K. %A Jaberi, F.A. %K DNS; Methane combustion %K turbulent reacting flows; partially premixed flames; reduced chemistry models %XDirect numerical simulations (DNS) are conducted to study the structure of partially premixed and non-premixed methane flames in high-intensity two-dimensional isotropic turbulent flows. The results obtained via “flame normal analysis” show local extinction and reignition for both non-premixed and partially premixed flames. Dynamical analysis of the flame with a Lagrangian method indicates that the time integrated strain rate characterizes the finite-rate chemistry effects and the flame extinction better than the strain rate. It is observed that the flame behavior is affected by the “pressure-dilatation” and “viscous-dissipation” in addition to strain rate. Consistent with previous studies, high vorticity values are detected close to the reaction zone, where the vorticity generation by the “baroclinic torque” was found to be significant. The influences of (initial) Reynolds and Damköhler numbers, and various air–fuel premixing levels on flame and turbulence variables are also studied. It is observed that the flame extinction occurs similarly in flames with different fuel–air premixing. Our simulations also indicate that the CO emission increases as the partial premixing of the fuel with air increases. Higher values of the temperature, the OH mass fraction and the CO mass fraction are observed within the flame zone at higher Reynolds numbers.

%B Combustion and Flame %V 154 %P 692-714 %8 09/2008 %G eng %N 4 %0 Conference Paper %B 46th AIAA Aerospace Sciences Meeting and Exhibit %D 2007 %T Filtered Mass Density Function for Numerical Simulations of Spray Combustion %A Yaldizli, M. %A Li, Z. %A Jaberi, F.A. %XThis paper briefly describes our recent efforts on the modeling and numerical simulations of two-phase turbulent reacting flows in realistic combustion systems with a new large-eddy simulation (LES) model. The model is constructed based on the two-phase extension of scalar filtered mass density function (FMDF) and a Lagrangian-Eulerian- Lagrangian mathematical/numerical methodology. In this methodology, the “resolved” fluid velocity field is obtained by solving the filtered form of the compressible Navier-Stokes equations with a high-order finite difference scheme. The liquid (droplet) phase and scalar (temperature and species mass fractions) fields are both obtained by stochastic Lagrangian models. There are two-way interactions between the phases and all the Eulerian and Lagrangian fields. The LES/FMDF is used for systematic analysis of turbulent combustion in the spray-controlled dump combustor and double-swirl spray burner for various flow and spray parameters. The effects of fuel type, spray angle, mass loading ratio, droplet size distribution, fuel/air composition, wall, and inflow/outflow conditions on the combustion are investigated. It has been found that the main features of the turbulence and combustion are modified by changing the inflow/outflow conditions. The LES/FMDF results also confirm the significance of the spray parameters.

%B 46th AIAA Aerospace Sciences Meeting and Exhibit %I AIAA %C Reno, Nevada %8 01/2008 %G eng %0 Conference Paper %B 45th AIAA Aerospace Sciences Meeting and Exhibit %D 2007 %T LES/FMDF of Turbulent Combustion in Complex Flow Systems %A Afshari, A. %A Jaberi, F.A. %A Shih, T. I-P. %XA high-order Lagrangian/Eulerian method based on the the filtered mass density func- tion (FMDF) for subgrid-scale (SGS) combustion closure was developed to perform large eddy simulation (LES) of turbulent reacting flows in complex geometrical configurations in multi-block structured grids. In particular, an efficient algorithm has been developed to search and locate particles in multi-block, hexahedral-structured grid system. Also, the consistency, convergence, and accuracy of the FMDF and the Monte Carlo solution of its equivalent stochastic differential equations were assessed. The consistency between Eulerian and Lagrangian fields were established for a reacting flow in a dump combustor. The results obtained for a reacting flow in an axisymmetric, premixed dump-combustor, were found to compare favorably with measured experimental data.

%B 45th AIAA Aerospace Sciences Meeting and Exhibit %I AIAA %C Reno, Nevada %8 01/2007 %G eng %0 Conference Proceedings %B ASME Conference Proceedings, Computers and Information in Engineering Conference %D 2007 %T Numerical Simulations of Two-Phase Turbulent Combustion in Spray Burners %A Li, Z. %A Yaldizli, M. %A Jaberi, F.A. %XThe complex interactions among turbulence, combustion and spray in liquid-fuel burners are modeled and simulated via a new two-phase Lagrangian-Eulerian-Lagrangian large eddy simulation (LES) methodology. In this methodology, the spray is modeled with a Lagrangian mathematical/computational method which allows two-way mass, momentum and energy coupling between phases. The subgrid gas-liquid combustion is based on the two-phase filtered mass density function (FMDF) that has several advantages over “conventional” two-phase combustion models. The LES/FMDF is employed in conjunction with non-equilibrium reaction and droplet models. Simulations of turbulent combustion in a spray-controlled double-swirl burner are conducted via LES/FMDF. The generated results are used for better understanding of spray combustion in realistic turbulent flow configurations. The effects of spray angle, mass loading ratio, fuel type, droplet size distribution, wall and inflow/outflow conditions on the flow and combustion are investigated. The LES/FMDF predictions are shown to be consistent with the experimental results.

%B ASME Conference Proceedings, Computers and Information in Engineering Conference %I ASME %C Las Vegas, Nevada %8 09/2007 %@ 0-7918-4803-5 %G eng %0 Journal Article %J International Journal of Heat and Mass Transfer %D 2006 %T Direct Numerical Simulations of a Planar Jet Laden with Evaporating Droplets %A Almeida, T. %A Jaberi, F.A. %K droplet-laden turbulent jet; two-phase planar jet; droplet evaporation; DNS %XA direct numerical simulation (DNS) study is conducted on the various aspects of phase interactions in a planar turbulent gas-jet laden with non-evaporative and evaporative liquid droplets. A compressible computational model utilizing a finite difference scheme for the carrier gas and a Lagrangian solver for the droplet phase is used to conduct the numerical experiments. The effects of droplet time constant, mass-loading and mass/momentum/energy coupling between phases on droplet and gas-jet fields are investigated. Significant changes in velocity, temperature, density and turbulence production on account of the coupling between the liquid and gas phases are observed in non-isothermal jets with evaporating droplets. Most of these changes are attributed to the density stratification in the carrier gas that is caused by droplet momentum and heat transfer.

%B International Journal of Heat and Mass Transfer %V 49 %P 2113-2123 %8 07/2006 %G eng %N 13-14