Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.     

Einfluss eines Verbrennungsvorganges auf den Wärme- und Stoffaustausch in einer laminaren Grenzschicht

Summary The influence of combustion on heat and mass transfer is investigated on the following model. A mixture of an inert with a combustible gas (air) flows in steady, laminar flow over a flat plate. A mass flux of gaseous fuel away from the plate surface is produced by some means. Combustion is assumed to occur with very fast reaction rate so that the process is purely controlled by diffusion and the equilibrium is assumed as very close to complete combustion. It is studied under which conditions the combustion occurs at the surface or when the flame is displaced into the boundary layer. The influence of combustion on the heat transfer from a hot gas to the plate surface is calculated, for the condition that combustion occurs at the surface.      

Auto-ignition of diesel spray using the PDF-Eddy Break-Up model

This work presents the development and implementation of auto-ignition modelling for DI diesel engines by using the PDF-Eddy Break-Up (PDF-EBU) model. The key concept of this approach is to combine the chemical reaction rate dealing with low-temperature mode, and the turbulence reaction rate governing the high-temperature part by a reaction progress variable coupling function which represents the level of reaction. The average reaction rate here is evaluated by a probability density function (PDF) averaging approach. In order to assess the potential of this developed model, the well-known Shell ignition model is chosen to compare in auto-ignition analysis. In comparison, the PDF-EBU ignition model yields the ignition delay time in good agreement with the Shell ignition model prediction. However, the ignition kernel location predicted by the Shell model is slightly nearer injector than that by the PDF-EBU model leading to shorter lift-off length. As a result, the PDF-EBU ignition model developed here are fairly satisfactory in predicting the auto-ignition of diesel engines with the Shell ignition model.     

Mathematical modeling on the effect of equivalence ratio in emission characteristics of compression ignition engine with hydrogen substitution

The investigation presented in this paper concerns on the computational simulation of emissions characteristics in compression ignition engine with hydrogen substitution. Combustion process has been modeled based on Equilibrium Constants Method (ECM) with MATLAB program to calculate the mole fractions of 18 combustion products when hydrogen is burnt along with diesel fuel at variable equivalence ratios. It can be observed that hydrogen substitution causes significant increase in NH₃, H₂, atom H emissions during rich combustion and OH, NO₂, HNO₃ emissions during lean combustion. As the equivalence ratio increases during rich combustion, mole fractions of HCN, CH₄, CO and atom C decreases with increment of hydrogen substitution. N₂, atom N and CO₂ emissions decrease whereas no significant changes in O₂, NO, O₃ and atom O emissions throughout all equivalence ratios as hydrogen is added to the combustion.     

Wall effect on determination of laminar burning velocity in a constant volume bomb using a quasi-dimensional model

In experiment, two optical and pressure-based methods are frequently used to evaluate laminar burning velocity of a combustible mixture. In the currently reported work, the pressure-based method was utilized to find the laminar burning velocity using the measurement of pressure variations during the combustion process in a spherical bomb and analyzing them through a multi-zone quasi-dimensional model. To check the results of the method, isooctane–air mixtures were used at equivalence ratios of 0.85 and 1.0 and initial pressures of 95 and 150 kPa with 343 K initial temperature. The time history of the bomb pressure during the combustion event, initial pressure and temperature, fuel type, and equivalence ratio were applied as input to a Fortran program written by the author based on the multi-zone combustion model; and, flame radius-time, flame speed, and laminar burning velocity at different pressures and temperatures were evaluated assuming spherical flame growth. The obtained results were compared with those of some other researchers and a reasonable agreement was observed. The wall effect on the laminar burning velocity at the end of the combustion process was clearly highlighted and a reliable range of burning velocity was distinguished. The results showed that the evaluated laminar burning velocity was not reliable at the late part of the combustion process due to possible local contact of flame front and the bomb wall, the wall effect on the reacting species, flow to small crevices, and the boundary layer effect.     

An advanced dynamic process model for industrial horizontal anode baking furnace

The global aluminum industry is facing new challenges due to new technological developments. Carbon anodes, consisting of mainly petroleum coke and coal tar pitch, are used in the electrolytic production of aluminum. High amperage utilization in the electrolytic cells with the objective of increasing production requires high quality carbon anodes. The anode quality depends both on raw material quality, anode recipe as well as forming and baking conditions of anode manufacturing process. The cost of the baking process constitutes 15 to 25% of the total aluminum production cost [1]. The industrial challenge is to produce better quality anodes consuming less energy, and reducing environmental emissions.A transient two dimensional (2D⁺) process model for horizontal anode baking furnace was developed during this study. The main objective was to develop an efficient furnace model with low computation load and time, using the transient Finite Difference Method and simplified furnace geometry. The model represents several phenomena involved during the anode baking process such as heat transfer (convection, radiation and conduction), fuel combustion, volatile matter (tar, methane and hydrogen) generation and combustion, air infiltration and energy loss to the atmosphere from the walls, the top of the furnace and the foundation. The model was developed using two coupled sub-models; the first one describes the thermal conduction through the solid materials (brick refractory wall, packing coke and anode block) as well as the volatile release, and the second one describes the gas flow, heat and mass transfer as well as the combustion of fuel and volatiles in the flue. Compared to the existing process models (where the gas flow in flue is assumed as unidirectional along the horizontal furnace direction), the present model also considers the gas flow in vertical direction and uses four vertical planes per pit section to predict the temperature of the solids. The model predicts 2D temperature distribution within the flue gas (xy plane) and the pit solid materials (yz plane) allowing then the prediction of the pseudo tridimensional distribution of the solid temperature. This model is a useful tool for the continuous monitoring of anode temperature and studying of the horizontal anode baking furnace behaviour. The effect of any change in operational parameters and the energy consumption on the furnace operation can be predicted.     

Evaluation of the approximated diffusion flamelet concept using fuels with different chemical complexity

The ability of flamelet models to reproduce turbulent combustion in devices such as diesel engines or gas turbines has enhanced the usage of these approaches in Computational Fluid Dynamics (CFD) simulations. The models based on turbulent look-up tables generated from counterflow laminar diffusion flames (DF model) permit drastic reduction of the computational cost of the CFD calculation. Nevertheless, for complex molecular fuels, such as n-heptane, the oxidation process involves hundreds of species and the calculation of the transport equations together with the ODE system that models the chemical kinetics for the DF solution becomes unaffordable for industrial devices where hundreds of flamelets are required. In this context, new hypotheses have to be introduced in order to reduce the computational cost maintaining the coherence of the combustion process. Recently, a new model known as Approximated Diffusion Flamelet (ADF) has been proposed with the aim of solving the turbulent combustion for complex fuels in a reduced time. However, the validity of this model is still an open question and has to be verified in order to justify subsequent CFD calculations. This work assesses the ADF model and its ability to reproduce accurately the combustion process and its main parameters for three fuels with different chemical complexity and boundary conditions by its comparison with the DF model. Results show that although some discrepancies arise, the ADF model has the ability to correctly describe the ignition delay and the combustion structure in the auto-ignition zone that is the most relevant one for industrial processes.     

A compressible two-phase flow framework for Large Eddy Simulations of liquid-propellant rocket engines

Atomization of liquid jets is a key feature of many propulsion systems, such as jet engines, internal combustion engines or liquid-propellant rocket engines (LRE). As it controls the characteristics of the spray, atomization has a great influence on the complex interaction between phenomena such as evaporation, turbulence, acoustics and combustion. In this context, Computational Fluid Dynamics is a promising way to bring better understanding of dynamic phenomena involving atomization, such as e.g. high-frequency combustion instabilities in LRE. However the unsteady simulation of primary atomization in reactive compressible two-phase flows is very challenging, due to the variety of the spatial and temporal scales, as well as to the high density, velocity and temperature gradients which require robust and efficient numerical methods. To address this issue, a numerical strategy is proposed in this paper, which is able to describe the dynamics of the whole chain of mechanisms from the liquid injection to its atomization and combustion. Primary atomization is modeled by a coupling between a homogeneous diffuse interface model and a kinetic-based Eulerian model for the spray. This strategy is successfully applied to the unsteady simulation of an operating point of the Onera’s Mascotte test bench, representative of one coaxial injector of LRE operating under subcritical conditions. The dynamics of the liquid core is retrieved and the flame shape as well as Sauter mean diameters are in good agreement with experimental results. These results demonstrate the ability of the strategy to deal with the harsh conditions of cryogenic combustion, and provide a promising framework for future studies of combustion instabilities in LRE.     

A study on torsional vibration attenuation in automotive drivetrains using absorbers with smooth and non-smooth nonlinearities

The automotive industry is predominantly driven by legislations on stringent emissions. This has led to the introduction of downsized engines, incorporating turbocharging to maintain output power. As downsized engines have higher combustion pressures, the resulting torsional oscillations (engine order vibrations) are of broadband nature with an increasing severity, which affect noise and vibration response of the drive train system. Palliative devices, such as clutch pre-dampers and dual mass flywheel have been used to mitigate the effect of transmitted engine torsional oscillations. Nevertheless, the effectiveness of these palliative measures is confined to a narrow band of response frequencies. The nonlinear targeted energy transfer is a promising approach to study vibration mitigation within a broader range of frequencies, using nonlinear vibration absorbers (or nonlinear energy sinks – NESs). These devices would either redistribute vibration energy within the modal space of the primary structure, thus dissipating the vibrational energy more efficiently through structural damping, or passively absorb and locally dissipate a part of this energy (in a nearly irreversible manner) from the primary structure. The absence of a linear resonance frequency of an NES, enables its broadband operation (in contrast to the narrowband operation of current linear tuned mass dampers). Parametric studies are reported to determine the effectiveness of various smooth or non-smooth nonlinear stiffness characteristics of such absorbers. A reduced drivetrain model, incorporating single and multiple absorber attachments is used and comparison of the predictions to numerical integrations proves its efficacy.     

Simulation of quasi-dimensional combustion model for predicting diesel engine performance

In order to improve the precision of quasi-dimensional combustion model for predicting diesel engine performance and promote the real time operating performance of the simulation model, a new phase-divided spray mixing model is proposed and the quasi-dimensional combustion model of diesel engine working process is developed. The software MATLAB/Simulink is utilized to build the quasi-dimensional combustion model of diesel engine working process, and the performance for diesel engine is simulated. The simulation results agree with experimental data quite well. The comparisons between them show that the relative error of power and brake specific fuel consumption is less than 2.8% and the relative error of nitric oxide and soot emissions is less than 9.1%. By utilization of this simulation model with personal computer, the average computational time for one diesel engine working process is 36 s, which presents good real time operating performance of the model. At the same time, the influence of parameters in calculation of air entrainment on prediction precision of diesel engine’s simulation model is analyzed.     

Large eddy simulation of non-premixed pulverized coal combustion in corner-fired furnace for various excess air ratios

Large-eddy simulations (LES) were carried out to study the effects of burning atmosphere on the coal combustion process in a corner-fired furnace. The LES for the turbulent gas was coupled with the discrete phase model (DPM) for coal particles trajectories and the non-premixed mixture fraction probability density function (MF-PDF) combustion model for pulverized coal combustion. The coal combustion processes, including the flame characteristics, burning coal behaviors and NO_x pollutant emissions, for different burning atmospheres are analyzed qualitatively and quantitatively. The heat and momentum transfer between burning coal and turbulent gas are greatly enhanced by the corner-fired flow. With a given particle size, the char particles present a similar distribution in the whole chamber. For a fuel-rich atmosphere, the concentration is obviously much higher and exhibits much higher spatial variability than the other two conditions. The coal combustion efficiency decreases in oxygen-rich and fuel-rich burning atmospheres, but the flame stability is more affected at the fuel-rich atmosphere by the lack of oxygen. NO pollutant is obviously reduced at the fuel-rich atmospheres, and the NO pollutant emissions are more affected by the reducing atmosphere than the low temperature. These findings may provide insight into strategies to design and monitor tangentially-fired pulverized coal boilers.     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of conjugated and radiant heat exchange on the process of non-stationary combustion of the products of intense gasification of a solid in a stream of gas

This paper develops further the results obtained in /1–4/ and uses the approximate mathematical model /2/ of the combustion of the products of intense gasification of the neighbourhood of the leading stagnation point of the body to analyse the effect of the conjugation parameters on the heat exchange, radiation and other factors on the conditions of uniqueness and stability of the stationary combustion modes. When the gasification is carried out at a constant mass flow rate, an analogy is established, depending on the relations between the parameters of the problem, between the model in question and the models of a homogeneous chemical continuous action reactor with a fluidized catalyst layer, and a reactor with a temperature regulator /5/. Simple necessary conditions for the instability of the stationary modes and the appearance of selfexcited oscillations are obtained. A strong stabilizing influence of the conjugated heat exchange and intense injection on the combustion process is established, and a destablishing influence of radiant heat exchange is found.     

Advective–diffusive mass transfer in binary regular structures in the steady-state regime

Having analyzed the stationary processes of admixture transfer in two-phase regular structures with taking into account periodical character of advective phenomena, we propose a method of constructing exact analytic solutions for such class of boundary value problems. This technique is based on the application of integral transformations individually for each contacting domain. The relation between these corresponding integral transformations is obtained from the nonideal boundary conditions. We have obtained the analytic solution of a diffusion problem for a two-phase layer of a regular structure with advective mass transfer mechanism in one of its phases. The expressions describing admixture flow through a certain body surface are derived, mass flows through the interface is investigated. Having analyzed the concentration of migrating particles in the structural elements of the body and the admixture flow through the given body surface, we present results graphically. The conditions of the existence of a limit passage from the contact boundary value problem of advective diffusion in regular structures to the continual model of advective two-way heterodiffusion are determined. A natural dimensionless form is introduced.     

Numerical simulation of two-stage combustion in SI engine with prechamber

Burning lean mixture in spark ignition (SI) engine leads to decrease in temperature of combustion process and is one of the methods of limiting nitric oxide emission and increasing the engine efficiency. The two-stage combustion system of stratified mixture (engine with prechamber) can be an effective method of lean mixture combustion. The paper presents the results of three-dimensional modeling of fuel mixture preparation and combustion in SI engine with sectional combustion chamber powered by liquefied fuel. Three dimensional modeling was performed in KIVA-3V code. The modeling results were compared with results obtained from the analysis of experimental measurements of two-stage combustion test engine operating at the Institute of Internal Combustion Engines and Control Engineering (Czestochowa University of Technology). The performed simulations of the combustion process provided data concerning the spatial and temporal distributions of turbulent kinetic energy, pressure, temperature and nitric oxides concentration in the combustion chambers of the engine. The engine model with two-stage combustion system properly represents the real processes which occur in the combustion chambers of the test engine. Pressure and temperature courses in function of CA obtained from the experiment and modeling were in good qualitative and quantitative consistence. Comparison of modeled and measured nitric oxide emissions revealed relatively significant discrepancies. In case of λ = 1.4, the measured values of NO_x concentration were 1.75 times higher than the modeled values. In case of λ = 2.0, the modeled and measured values were close to each other and were within the range of measurement error.     

Model order reduction by projection applied to the universal Reynolds equation

The approach presented in this paper yields a reduced order solution to the universal Reynolds equation for incompressible fluids, which is valid in lubrication as well as in cavitation regions, applied to oil-film lubricated journal bearings in internal combustion engines. The extent of cavitation region poses a free boundary condition to the problem and is determined by an iterative spatial evaluation of a superposed modal solution. Using a Condensed Galerkin and Petrov–Galerkin method, the number of degrees of freedom of the original grid is reduced to obtain a fast but still accurate short-term prediction of the solution. Based on the assumption that a detailed solution of a previous combustion cycle is available, a basis and an optimal test space for the Galerkin method is generated. The resulting reduced order model is efficiently exploited in a time-saving evaluation of the Jacobian matrix describing the elastohydrodynamic coupling in a multi-body dynamics simulation using flexible components. Finally, numerical results are presented for a single crankshaft main bearing of typical dimensions.     

Numerical study on the effect of the injection pressure on spray penetration length

This paper investigates the fuel spray behavior and variation of the spray characteristics under different injection pressures in internal combustion engines. In diesel engines the fuel spray is affected by the cavitation phenomenon which occurs in the injector orifice. The cavitation is one of the important phenomena which has a significant effect on the fuel spray characteristics. In this paper, for a specified geometry of the nozzle and the combustion chamber, the effect of the cavitation phenomenon on the spray characteristics, i.e. spray penetration length, the Sauter main diameter and evaporation are studied numerically for different values of the injection pressures. High injection pressure causes high velocity of the fuel in the injector orifice which leads to an effective atomization process with small and dispersed fuel droplets. The fluid flow equations are calculated in the combustion chamber to obtain the spray model. Since it is known that, high injection pressure together with low discharge pressure leads to creation of cavitation phenomenon inside the injector orifice, then for having cavitation phenomenon inside the injector orifice and consequently for investigating the cavitation phenomenon effects on the spray characteristics, the injection pressure values of 10–150 MPa are considered while the discharge pressure remains constant. The injector and combustion chamber are simulated in separated regions and the results of the outlet of the nozzle are used as the boundary conditions for solving the fuel flow inside the combustion chamber to achieve the spray simulation. The results of this study show that by increasing the injection pressure, the value of the spray penetration length increases and the Sauter main diameter decreases for constant discharge pressure. The Hydraulic Flip phenomenon occurs after the injection pressure of 120 MPa on the base of the results of this work.     

Effects of mean piston speed,equivalence ratio and cylinder wall temperature on performance of an Atkinson engine

The performance of an air standard Atkinson cycle is analyzed using finite-time thermodynamics. In the model, the linear relation between the specific heat ratio of the working fluid and its temperature, the friction loss computed according to the mean velocity of the piston, the internal irreversibility described by using the compression and expansion efficiencies and the heat transfer loss are considered. The relations between the power output and the compression ratio and between the power output and the thermal efficiency are derived by detailed numerical examples. The results show that if the compression ratio is less than a certain value, the power output decreases with increasing mean piston speed, while if the compression ratio exceeds a certain value, the power output first increases and then starts to decrease with increasing mean piston speed. With further increase in the compression ratio, the increase of mean piston speed results in decreasing the power output. Throughout the compression ratio range, the power output increases with increasing cylinder wall temperature while it first increases and then starts to decrease with the increase of equivalence ratio. The conclusions of this investigation are of importance when considering the designs of actual Atkinson engines.     

Large eddy simulation of an ethylene-air turbulent premixed V-flame

Large eddy simulation (LES) using a dynamic eddy viscosity subgrid scale stress model and a fast-chemistry combustion model without accounting for the finite-rate chemical kinetics is applied to study the ignition and propagation of a turbulent premixed V-flame. A progress variable c-equation is applied to describe the flame front propagation. The equations are solved two dimensionally by a projection-based fractional step method for low Mach number flows. The flow field with a stabilizing rod without reaction is first obtained as the initial field and ignition happens just upstream of the stabilizing rod. The shape of the flame is affected by the velocity field, and following the flame propagation, the vortices fade and move to locations along the flame front. The LES computed time-averaged velocity agrees well with data obtained from experiments.     

Numerical Investigation of Dense Turbulent Sprays with an Eulerian Approach and DQMOM

The spray characteristics of the injected liquid fuel predominantly influence the combustion and emissions in IC-engines and gas turbines. This is predetermined by a dense spray region in which droplet-droplet interaction processes play a significant role. In order to accurately describe and control the dense spray behavior in modern engines, an appropriate numerical modeling tool is needed. This contribution aims at including droplet-droplet interactions into an Eulerian approach coupled to the Direct Quadrature Method of Moments (DQMOM) in order to describe evaporating droplet polydispersity and analyze dense turbulent sprays phenomena. Among the advantages of the Eulerian approach are a lower computational cost through optimal parallel computing and a straightforward liquid-gas phase coupling. To assess the designed tool, numerical results are compared to Phase Doppler Anemometry (PDA) measurements of a hollow-cone water spray. The experiment provides comprehensive validation data that include gas velocities, droplet size distribution, droplet mass fluxes and droplet velocities. Turbulence is captured by two different k-ε based models. Preliminary results show that the designed tool is able to capture the process under study in a satisfactory way. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)