Modeling of EGR Mixing in an engine intake manifold using LES

We investigate the mixing process of exhaust gases with fresh air in Internal Combustion Engines (ICE). For this purpose, the flow in an inlet manifold of a six-cylinder heavy-duty Diesel engine is computed using compressible Large Eddy Simulations (LES). The Exhaust Gas Recirculation (EGR) concentration is modeled as a passive scalar. The results are validated by on-engine measurements of the EGR concentration using CO2-probes. The boundary conditions for the highly pulsating flow are taken partly from one-dimensional simulations, partly from pressure measurements on the engine. In order to assess the sensitivity to the boundary conditions, changes are applied to the base-line case. The mixing quality is evaluated in terms of cylinder-to-cylinder distribution and the spatial RMS over the outlet cross-sections. Different averaging techniques are applied. It was found that the temporal and spatial EGR distribution is different among the cylinders. The EGR distribution within the cylinder inlet is non-uniform. These factors imply that one should not use a time-averaged EGR value as indicator for the EGR content. Furthermore, it was found that the flow pulsations at the EGR inlet have a large influence on the EGR distribution. By comparing the LES results with measurements, it was shown that LES gives a better and deeper insight into the mixing in such turbulent, pulsating flow situations. Copyright© 2012 IFPEN Energies nouvelles Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than IFP Energies nouvelles must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee: Request permission from Documentation, IFP Energies nouvelles, fax. +33 1 47 52 70 78, or revueogst@ifpen.fr. 2 Oil & Gas Science and Technology — Rev. IFP Energies nouvelles


INTRODUCTION
Exhaust Gas Recirculation (EGR) is a technique commonly used in modern Internal Combustion Engines (ICE), particularly in Diesel engines.EGR reduces Nitrogen oxide (NOx) emissions by lowering the oxygen concentration of the combustion gases and thereby the peak combustion temperature.This is possible because oxidation of nitrogen occurs only at high temperatures [1].Due to stringent emission legislation EGR rates of up to 50 % are applied in modern engines [2].However, the EGR rate is limited by the increase of particulate emissions at high EGR rates.
In order to achieve EGR, parts of the exhaust gases have to be recycled and to be mixed with the fresh intake air.Due to space restrictions in the engine compartment, the distance from the mixing point to the cylinder intakes is often too short in order to provide homogenous Air/EGR mixtures.A non-uniform mixture (both among and inside the cylinders) can result in an increase of NOx and particulate emission as compared to a fully homogenous mixture.This has been shown by on-engine measurements performed for example by Maiboom et al. [3] and Payri et al. [2].
The issue of EGR/Air mixing has been studied experimentally using Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) by Wiliam & Dupont (2003) [4] in a generic test bench.It was concluded that a Venturi nozzle significantly improves the mixture quality, but also increases the pressure losses and that large cycle-tocycle variations may occur.The latter implies that time or ensemble averages of the concentration are not sufficient for the characterization of the mixing process.
In a study of Siewert et al. [5], an intake manifold for a passenger car was improved in terms of EGR and air mixing, using both experimental and computational methods.It was shown that they can be used to complement each other.
Reynolds Averaged Navier Stokes (RANS) computations have been applied by Karthikeyan et al. (2011) [6] analyzing the impact on the mixing properties of different mixer geometries.A previous study by Sakowitz & Fuchs (2011) [7] has compared unsteady RANS (URANS) calculations to Large Eddy Simulation (LES) data with generic boundary conditions.It was found that the smoothing effect of URANS does not support the analysis of cycle-to-cycle variation.
The current report aims on the investigation of EGR mixing by LES.Implicit LES is applied to the intake manifold of a commercial 6-cylinder heavy-duty Diesel engine (see Figure 1).Common for this type of geometry is the presence of pipe bends upstream of the mixing point resulting in complex flow fields.These flows are among other things characterized by the formation of so called Dean vortices that occur due to flow curvature (see [8]).Furthermore, the presence of engine pulsations gives highly unsteady flow, particularly close to EGR inlet.The mixing quality is quantified in terms of cylinder-to-cylinder variation and the spa-tial variation of the concentration.In order to validate the simulations, experiments were performed in close cooperation.Comparisons are done in terms of cycle-averaged EGR distribution.
A crucial issue of flow simulations in engines is the specification of realistic time-dependent boundary conditions.Most often they are estimated from one-dimensional tools.It is therefore important to assess the sensitivity to uncertainties in the boundary conditions.This is done by altering several parameters of the air and exhaust flow and the outflow to the cylinders.

Large Eddy Simulation
The LES are based on the compressible Navier-Stokes equations, which can be written in the following form where ρ is the density, u i is the velocity component in idirection, e o is the total energy defined as e o = e + 1 2 u 2 , e is the internal specific energy, p is the static pressure, τ i j is the viscous stress tensor and q i is the heat flux.In a Newtonian fluid the viscous stresses are proportional to the strain rate.With the definition of the strain rate tensor τ i j can be written as, Moreover, for the compressible form of the Navier-Stokesequations, an equation of state is necessary in order to close the equation system.It is given by the ideal gas equation: where R is the specific gas constant and T is the temperature.In order to simulate the EGR concentration an equation for a passive scalar is solved additionally.The equation describes passive transport of a mass fraction c by advection and molecular diffusion and has the following form: where D is the molecular diffusivity.However, computing several scalars simultaneously with different diffusivities showed that the molecular diffusivity has only small effects on the mixture distribution in the present case and can be neglected.The mixing process is governed by the advective properties of turbulence and the flow pulsations.
LES resolves the large energy-carrying scales and models the small unresolved scales (see e.g.[9]).This is possible, because the smaller scales can be assumed to be universal and independent of the boundaries of the problem.In engine computations, the correct behavior of the small scales is not of interest, but only their effect on the large scales.The main effect of the small scales are dissipation of turbulent kinetic energy.For large enough Reynolds numbers, the small scales, where dissipation is acting, are separated from the large scales by an inertial sub-range.According to Kolmogorov's theory this inertial sub-range is independent of viscosity.Under such conditions, the exact form of dissipation has no impact on the flow structures and on the large-scale end of the inertial sub-range.Thus, provided that the mesh resolution is fine enough (i.e.resolving a portion of the inertial sub-range whereby the dissipation effects are decoupled from the larger scales), the dissipative behavior, that is unavoidable when using second order schemes, can be used to model the unresolved scales instead of an explicit SGS model.This approach is called Implicit LES (see e.g.[10], [11], [12] and [13]).
The described methods were implemented in the open source code OpenFoam® using a pressure-based formulation and the Pressure Implicit with Splitting of Operators (PISO) algorithm for pressure-correction [14].The maximum CFL number was held constant at 0.7.

Experiments
The experiments were carried out on a 13 liter six-cylinder heavy-duty diesel engine with a power output of 360 hp.
To estimate the distribution of EGR in the intake manifold, the CO 2 concentration was measured in different locations.Two measurement probes at a time were placed inside the manifold, sucking the intake mixture to two gas analyzers.The probes were installed in flexible ducts which allow to suck gas from different positions in the intake manifold.In each of the twelve ports, three positions were measured; bottom, center and top position, as visible in Figure 2. The measurement point lies in the plane that separates the intake manifold from the intake ducts.
For each measurement, the load point was set and run until all gas and coolant temperatures on the engine were stable.The CO 2 -percentage was measured and averaged over 60 seconds.After the measurement, the engine was stopped to be able to move the probe position.All points were measured twice in random order to avoid the influence of drift of the measurement equipment.The trends were reproducible.The data presented in this article are averages over the three measurement positions for each port.

CONFIGURATION, MESH AND BOUNDARY CONDITIONS
The considered geometry for the simulations is the inlet manifold of the engine.EGR is introduced at a junction upstream of the cylinder ducts (see Figure 1).As it is common for engine manifolds, different pipe bends exist upstream of the EGR inlet.The computational mesh is based on a precursor RANSk − computation, from which the integral scales of the flow where estimated according to [15].This lead to an estimation of a cell size of about 2-3 mm inside the domain and Measurement probes for the gas analyses to about 1mm close to walls.A hex-dominant mesh fulfilling these requirements was provided by Scania.The total amount of cells is about one million cells.In order to assure that this resolution gives adequate results, a comparison to a mesh resolution of 1-2 mm resulting in about 4 million cells was performed and showed only minor differences in terms of the EGR distribution.
To obtain the boundary conditions for the 3D-simulation, a combination of experiments and 1D-simulation was used.As inflow boundary conditions for the mesh, measured pressure traces from the air path and the EGR path of the engine were used.The outflow boundary condition, e.g. the mass flow, was computed from a calibrated 1D-simulation with the commercial software GT-Power®.The considered load case is 1200 rpm, the EGR rate is approximately 30% EGR.Furthermore, the temperature was specified at the EGR and Air inlet according to one-dimensional simulations.The temperatures of the fresh air and the exhaust gases are fairly constant in time (within 3%).
Figure 3 shows the inlet and outlet conditions for one engine cycle.The resulting flow is highly pulsating with velocities at the EGR inlet ranging from -100 to 100 m/s.The Reynolds number based on the mean flow velocity and the largest diameter is about 500.000.
The boundary conditions for the EGR concentration is 1 at the EGR inlet, which corresponds to 100% EGR, and 0 at the Air inlet.At the outlets a zero gradient condition is applied.
In order to assess the sensitivity to uncertainties in the boundary conditions, several changes are applied to this base-line case.The mass flow is specified as simplified triangular functions and the amplitude and temperature of the EGR pulses are changed.
The computational time was about 10 hours per engine cycle, when the process was distributed on 64 processors.Boundary conditions; top: pressure from on-engine measurements, bottom: Mass flow to cylinders from one-dimensional simulations

Description of the flow field
The piping upstream of the plenum consists of two 90degree bends and one 45-degree bend.Additionally to that the flow is strongly pulsating, particularly past the EGR inlet, which is situated at the second bend.Figure 4 and Figure 5 show the inplane velocity vectors in cross-sections downstream of the first and the second bend at different phase angles (see Figure 1 for the position of the cross-sections).The background color in Figure 4 shows the magnitude of the streamwise velocity, whereas the background color in Figure 5 shows the phase-averaged EGR concentration.The data is phase-averaged over 20 engine cycles.Dean vortices can be observed downstream of the first bend.However, the occurrence of these vortices depends on the pulsation phase.During the acceleration of the flow, the Dean-vortices are not yet established.They are developing at later times when the flow is at its maximum and are becoming stronger during the deceleration phase.
Past the second bend, the flow is governed by the EGR pulses coming in at the second bend.Due to the position of the EGR inlet pipe, the EGR flow is transported along the pipe walls and a counter-clockwise rotation is induced.This rotation is sustained throughout the plenum and is dominating the flow further downstream.This can be seen in Figure 6, which shows the strong rotation visible in the inplane velocity vectors in cut C-C.

Mixture distribution
The distribution of the exhaust gases among the cylinders and over the cylinder ports is evaluated at port cross-sections close to the outlets.For this purpose, the concentration, the velocity and the density was saved at the port cross-sections shown in Figure 1.The data was saved 100 times per engine cycle.Due to the low frequency response of the experimental apparatus, only time-averaged data over the whole cycle can be obtained experimentally.With LES, however, one is able to evaluate the percentage of EGR that actually passes a cross-section and goes into the cylinders by weighting the concentration with the mass flux through the ports.The conventional cycle average is given by, whereas the weighted average, which gives the EGR percentage of the flow into the cylinders, is defined by, Here, the index i denotes the time sample and the index j denotes the cell count over the cross-section.N is the Number of samples and M the number of cells in the cross-section.u n is the velocity normal to the considered cross-section and A is the cross-section area.
A measure for the mixing quality is the spatial Root Mean Square (RMS) of the concentration over the port crosssections.Also the RMS can be weighted by the mass flux in order to exclude contributions from times where there is no flow through the port.The mean of the spatial RMS over a cross-section is computed as, and the weighted RMS is defined as, where c i,mean is the mean of the concentration over the crosssection at time i.
All averages shown in the following paragraphs are averaged over at least 20 engine cycles, which corresponds to about 20 flow-through-times.10 engine cycles were run before the data acquisition.The data are normalized with the mean EGR rate which changes slightly (±5%) depending on the inflow conditions.
Figure 7 shows the results for the base-line case.At the first cylinder, the spatial non-uniformity over the port crosssection is about 25%.Further downstream, the mixture quality is becoming better as can be seen by the decreasing RMS.The comparison with the experiments shows good agreement.The simulations and the experiments show the same trends and are within 5%.
It is evident from Figure 7 that large differences between the cycle average and the actual percentage of EGR flow to the cylinders can occur.At the second port of cylinder 1 the difference is about 8%.This result implies that the measurement of the time-average might be misleading.Furthermore, it can be concluded, that large non-uniformities over the cross-sections (up to 25%) can occur, even though the cycle average is close to unity.
In order to judge the benefits of LES over RANS, a comparison in terms of the cycle-averaged concentration and the spatial distribution over the cylinder ports Different averages of cylinder-to-cylinder EGR distribution according to eq. 8 and 9).Bars indicate the spatial RMS of the concentration over the outlet cross-sections computed by eq. 10 and 11.The experimental data is the average of the three measurement points (see Figure 2).Figure 8 Comparison of LES cycle-averaged data with URANS results and experimental data between the precursor unsteady RANS-k-computation and the baseline LES is shown in Figure 8. Consistently with previous findings [7], unsteady RANS-k-overpredicts the non-uniformity among the cylinders by up to 10 %.The reason is the non-physical smoothing effect of URANS which is not appropriate for accurate predictions of concentration distributions.
Figure 9 shows the phase-average of the concentration at a crank angle of 580 degrees, when the flow to cylinder 1 has its maximum value.The phase-average was performed on ten engine cycles.The EGR pulses can clearly be identified.At the time of flow into cylinder 1, there is a pulse of exhaust rich air directly in front of the first port.This is why the first port gets more EGR than the second one and implies that the EGR pulses are the major reason for the mal-distribution.Pressure traces with different EGR inlet pressure amplitudes

Sensitivity to boundary conditions
The sensitivity of the results to errors in the boundary conditions is assessed by introducing changes to the base-line case.One-dimensional tools, which are used for the estimation of boundary conditions, might be erroneous and the accuracy of these tools is hard to assess.The sensitivity of the mixing process to the amplitude of the EGR pulses is analyzed by applying different EGR amplitudes.Figure 10 shows the different pressure boundary conditions.
The results in terms of the EGR distribution are shown in Figure 11.With increasing pressure amplitude, the cylinderto-cylinder non-uniformity is increased.Also the RMS over the outlet ports is increased due to the introduction of larger pulsations.For the case of smaller pulsation amplitudes, the distribution is quite similar to the base line case.However, at the cylinders 4 to 6, an increase of the spatial RMS over the outlet ports as compared to the base line case can be observed.Pulsations are known to enhance mixing as com- Normalized EGR Concentration c Into Cylinder (eq.9) for different temperature differences.Bars indicate the RMS computed by eq.11 pared to steady flow, which is the reason for the increased RMS with smaller pulsations.On the other hand, higher pulsations introduce larger non-uniformity in the flow, which explains the higher cylinder-to-cylinder variations with the larger pulsation amplitudes.
Figure 12 shows the EGR concentration with different temperature differences between the EGR temperature and the air temperature.Only slight differences can be seen in terms of cycle-to-cycle variation and the RMS over the cross-sections.
Finally, the sensitivity of the results to the outlet conditions is to be assessed.This is done using simplified outlet conditions.The mass flow to the cylinders is estimated as triangular functions (see Figure 13).An opening time of the valves of 200 CAD is assumed and the maximum mass flow is adjusted in order to achieve the same mass flow as with the GT Power data.The results are shown in Figure 14.There are significant deviations at cylinder 2. However, the general trends are unchanged.

CONCLUSIONS
The flow in an inlet manifold of a six-cylinder Diesel engine was analyzed using LES.The focus was the analysis of the mixing process between EGR and Air.On-engine CO 2 -measurements were performed in order to validate the results.The agreement between the experiments and the simulations was within 5%.It was shown that the EGR flow, which is highly pulsating, induces a flow rotation that is sustained throughout the plenum.The EGR pulsations were identified as the largest contributors to the nonuniformity.On the on hand large pulsations are known to enhance mixing, on the other hand large pulsation also introduce higher non-uniformity, which increases the cylinderto-cylinder variation at the more upstream cylinders.
The LES results showed large deviations up to 20% over the port cross-sections.Moreover, different averaging methods indicated that simple time-averaging of the concentration might give misleading results, since it can significantly deviate from the EGR concentration of the actual flow into the cylinders.
A sensitivity study with respect to the boundary condi-tions was performed.The EGR concentration was found to be sensitive on the amplitude of the EGR pulsations.The temperature difference between the exhaust gases and the fresh air seemed to have little impact impact on the results.The same was found for a variation in the outlet conditions.In summary, it was shown that LES is a suitable method to gain more understanding of the mechanisms governing the mixing process and gives important information on the flow not obtainable with the experimental methods.This implies that by LES one should be able to optimize the EGR distribution and thereby improve the engine's emission performance.

Figure 1 Inlet
Figure 1 Inlet manifold from a Scania six cylinder Diesel engine including the definition of cross-sections used in the result section

Figure 4 PhaseFigure 5
Figure 4 Phase averaged inplane velocity vectors past the first bend (cut A-A) at different pulsation phases.Top left: Minimum flow rate, top right: accelerating flow, bottom left: Maximum flow rate, bottom right: decelerating flow, Background colour: Phase-averaged velocity normal to the cross-section

Figure 9 Phase
Figure 9 Phase average of the concentration at CAD = 580, i.e. maximum flow into cylinder one

Oil& 11 Figure 12
Figure 11 Normalized EGR Concentration c Into Cylinder (eq.9) for different EGR pressure pulse amplitudes.Bars indicate the RMS computed by eq.11 Figure 13Simplified outlet boundary condition