Large Eddy Simulations of Turbulent Spray Combustion in Internal Combustion Engines Farhad Jaberi Department of Mechanical Engineering Michigan State University East Lansing, Michigan

 In-Cylinder Flow: Combination of highly unsteady turbulent flow, separated boundary and shear layers, pressure waves, spray, mixing and combustion in complex geometrical configurations with moving pistons and valves.  CFD & IC Engines: The solver should be able to handle complex geometries with dynamic mesh. LES needs high order numerical method and accurate subgrid turbulence models. For spray, advanced primary and secondary break-up models and fully coupled gas-droplet flow solvers with multi-component droplet evaporation models are needed. Turbulent combustion models with appropriate chemical kinetics mechanisms are also needed.  Previous Works: Mostly based on RANS or low-order LES.  Our Model : LES/FMDF, based on a new Lagrangian-Eulerian- Lagrangian mathematical/numerical methodology. Background

3 LES/FMDF of Single-Phase Turbulent Reacting Flows Scalar FMDF - A Hybrid Eulerian-Lagrangian Methodology  Eulerian: Conventional LES equations for velocity, pressure, density and temperature fields - Deterministic simulations  Lagrangian: Transport equation for FMDF (PDF of SGS temperature and species mass fractions - Monte Carlo simulations  Coupling of Eulerian and Lagrangian fields: A certain degree of “redundancy” (e.g. for filtered temperature) LES/FMDF of a Dump Combustor Monte Carlo Particles Lagrangian Monte Carlo Particles Eulerian Grid

Kinetics: (I) global or reduced kinetics models with direct ODE or ISAT solvers, and (II) flamelet library with detailed mechanisms or complex reduced mechanisms Fuels considered so far: methane, propane, heptane, octane, decane, kerosene, gasoline, JP-10 and ethanol LES of Two-Phase Turbulent Reacting Flows A New Lagrangian-Eulerian-Lagrangian Methodology Eulerian Filtered continuity and momentum equations via a generalized multi-block high-order finite difference Eulerian scheme for high Reynolds number turbulent flows in complex geometries Various closures for subgrid stresses Gasdynamics Field Scalar Field (mass fractions and temperature) Lagrangian Filtered Mass Density Function (FMDF) equation via Lagrangian Monte Carlo method - Ito Eq. for convection, diffusion & reaction Chemistry Droplet Field (spray) Lagrangian Lagrangian model for droplet equations with full mass, momentum and energy couplings between phases and a stochastic sub grid velocity model

Liquid Fuel Droplets LES of Two-Phase Turbulent Reacting Flows A New Lagrangian-Eulerian-Lagrangian Methodology Spray-Controlled Dump Combustor Fuel Injector Wall Monte Carlo Particles - Eulerian Grid Mass,Momentum,Scalar Terms from Droplets LES Solver Eulerian Finite Difference Grid Interpolation / Favre Filter Monte Carlo Particles

Filtered Equations - Eulerian Droplet terms Droplet Equations Lagrangian FMDF Equation Lagrangian Two-phase subgrid scalar FMDF: Reaction term Droplet terms Reaction terms KHRT KH/RT Break-up

Main Features of LES/FMDF  Large scale, unsteady, non-universal, geometry- depended quantities are explicitly computed in LES/FMDF  FMDF accounts for the effects of chemical reactions in an exact manner and may be used for various types of chemical reactions (premixed, nonpremixed, slow, fast, endothermic, exothermic, etc.).  LES/FMDF can be implemented via complex chemical kinetics models and is applicable to 3D simulations of hydrocarbon flames in complex geometries.  FMDF contains high order information on sub-grid or small scale fluctuations.  The Lagrangian Monte Carlo solution of the FMDF is free of artificial (diffusion) numerical errors. This is very important in IC engine simulations as overprediction of temperature could cause numerical ignition!

Application of LES/FMDF to Various Flows Axisymmetric Dump Combustor Spray Controlled Lean Premixed Square Dump Combustor IC Engines with Moving Valves/Piston complex cylinder head/piston, spray and combustion 24 Block grid for a 4-valve Diesel Engine 10 degree After TDC Pressure Iso-Levels Temperature Contours Wall Double Swirl Spray Burner Fuel Injector

20mm 70mm Dyn. Smag-filteredDyn. Smag-AveragedSmag C d =0.01 Exp. Data Axial Velocity Contours LES of Cold Flow Around a Poppet Valve Mean axial velocity RMS of axial velocity x y Graftieux et al Reynolds No = 30,000 Mass rate = kg/s Dimensions in mm y z 5-block LES grid

Piston 5 th cycle instantaneous axial velocity contours m/s Grid compression or expansion 4-block moving structured grid for LES Morse et al. (1978) Comp. ratio 3:1, RPM=200, Re=2000 Crank angle=144 o Crank angle=36 o LES of Flow in a Piston-Cylinder Assembly

Dynamic SmagSmag, C d =0.01 Exp. Data Mean Velocity RMS of Velocity CA=36 o CA=144 o Mean values computed by doing both azimuthal and ensemble averaging over cycles LES of Flow in a Piston-Cylinder Assembly

Rapid Compression Machine – LES/FMDF Predictions In-Cylinder Piston Simple Piston Groove TemperatureContours piston piston Non-Reacting RCM Simulations Temperature Pressure

FD MC MC FD Temperature Contours Fuel Mass Fraction Contours Rapid Compression Machine - LES/FMDF Predictions Reacting Simulations - Consistency between Finite-Difference (FD) and Monte Carlo (MC) values of Temperature and Fuel Mass Fraction

Rapid Compression Machine - LES/FMDF Predictions Non-Reacting Flows Temperature Contours Flat Piston Non-Reacting Flows Temperature Contours Creviced Piston Reacting Flows without Spray Creviced Piston at 5msec Reacting Flows with Ethanol Spray TemperatureEthanolCO2 Piston Piston Piston

3D Shock Tube Problem – LES/FMDF Predictions 3D Shock Tube p 2 /p 1 =15 p1p1p1p1 p2p2p2p2 Two-Block Grid 5 MC per cell 20 MC per cell 50 MC per cell   Compressibility effect is included in FMDF-MC. Without Compressible term FMDF-MC results are very erroneous.  Number of MC particles per cell is varied but particle number density does not affect the temperature.  By increasing the particle number per cell MC density becomes smoother but temperature is the same for all cases.

Modeling of Engine Configuration Spark PlugExhaust PortInjector Cylinder Piston fuel spray MSU 3-Valve Direct-Injection Spark-Ignition Single-Cylinder Engine Bore 90 mm Stroke 104 mm Compression Ratio 9.8/11 Engine Speed 2500 rpm Intake valves 2 tilted with 5.1 o D = 33 mm Exhaust valve 1 tilted with 5.8 o D = 37 mm

MSU 3-Valve DISI Engine: Bore=90mm Stroke=106mm Direct-Injection Spark-Ignition Engine – LES Predictions 18-block Grid 2D Cross Section of 18-block LES Grid Pressure contours Valve lift= 11mm Piston velocity=13m/s Crank angle=100 o Valve lift= 5mm Piston velocity=1.5m/s Crank angle=175 o Axial Velocity piston

Direct-Injection Spark-Ignition Engine – LES Predictions CA=90 CA=270CA=140 CA=100 o CA=220 o piston CA=340 o Contours of Evaporated Fuel Mass Fraction

LES/FMDF of 3-Valve DISI Engine with Spray and Combustion Consistency between Finite Difference (FD) and Monte Carlo (MC) parts of the hybrid LES/FMDF numerical solver In-Cylinder Temperature Volume Averaged Crank angle of mm from TDC Instantaneous Values

LES/FMDF Predictions of MSU’s 4-Valve Diesel Engine Pressure Contours Temperature Contours 24 Block grid for a 4-valve Diesel Engine Pressure Iso-Levels Beginning of Compression CA=190

LES/FMDF of MSU’s 4-Valve Diesel Engine 14 o Before TDC 6 o Before TDC 6 o After TDC Contours of Evaporated Fuel Mass Fraction and Fuel Droplets Temperature Contours

LES/FMDF of MSU’s 4-Valve Diesel Engine 10 degree After TDC Temperature Contours

Numerical Simulations of 3-Valve DISI Engine Without Spray air mass via cell volume = air mass via ideal gas With Spray – Valves Closed mass of liquid fuel+evaporated fuel = injected liquid fuel Variations of mean Temperature Overall Validation of the model

Simulations of 3-Valve Engine – Spray In-cylinder Spray Modeling:  Initial droplet size, position and velocity distribution  Droplet breakup and collision models  Multi-component non-equilibrium evaporation models  Wall collision and film models Stroke: mm Compression Ratio: 11:1 Eight nozzles with cone angle of 8 degree each. Initial SMD: 30  m Injection Velocity: 50 m/s Secondary Break-up Models: 1) Taylor Analogy Break-up (TAB) - Spring, mass and damper 2) Rayleigh-Taylor Break-up (RTB) - RT instable waves RT instable waves 3) Kelvin-Helmond Break-up (KHB) - KH invisid instable waves KH invisid instable waves 4) KH/RT Break-up model Primary Break-up Model: Parent droplets injected with specific velocities and diameters (bold model)

Simulations of 3-Valve Engine – Chemistry Ethanol Detailed Kinetics: e.g. 372 elementary reactions and 57 species for ethanol Multi-Step Reactions Global Mechanisms Ignition delays calculated from detailed Mechanism using CHEMKIN for homogeneous 0-D reactor based on equivalence ratio and temperature conditions prevalent in the cell By addition of ignition delay, the unphysical phenomenon of autoignition in numerical simulation of SI engines do not occur.

Simulations of 3-Valve DISI Engine – Effects of Fuel Operating conditions are the same for both fuels Mixtures are stoichiometric when all fuel is evaporated and mixed Combustion No combustion for ethanol fuel Vaporization No significant evaporation for ethanol

Summary and Conclusions  A robust and affordable LES model is developed for detailed simulations of various realistic single-cylinder engines: (i) A multi-block compressible LES solver in generalized coordinate system, (ii) Combustion and spray simulations are via a new Lagrangian-Eulerian- Lagrangian LES/FMDF methodology  Several test cases are simulated with the newly developed models: (i) flow around a poppet valve, (ii) flow in a piston-cylinder assembly, (iii) flow in a single-cylinder three-valve direct-injection spark engine, (iv) flow in a single- cylinder four-valve diesel engine  LES with high-order numerical methods, dynamic SGS models and two-phase FMDF can predict the complex in-cylinder turbulent flows with spray and combustion in realistic engines  Detailed experimental data, under controlled and well defined flow conditions are needed for complete validation of LES/FMDF  LES/FMDF is used for studying effects of (i) chemistry model, (ii) spray model and (iii) various parameters on turbulence, mixing and combustion,