This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.

Author(s): Jukka-Pekka Keskinen, Ville Vuorinen, Ossi Kaario and Martti Larmi

Title: Large eddy simulation of a piston-cylinder assembly: the sensitivity ofthe in-cylinder flow field for residual intake and in-cylinder velocitystructures

Year: 2015

Version: Post print

Please cite the original version:Jukka-Pekka Keskinen, Ville Vuorinen, Ossi Kaario and Martti Larmi. Large eddysimulation of a piston-cylinder assembly: the sensitivity of the in-cylinder flow field forresidual intake and in-cylinder velocity structures. Computers and Fluids, 122, 123-135,2015. DOI: 10.1016/j.compfluid.2015.08.028

Rights: © 2015 Elsevier. This is an author accepted version / post print version of the article published by Elsevier"Jukka-Pekka Keskinen, Ville Vuorinen, Ossi Kaario and Martti Larmi. Large eddy simulation of apiston-cylinder assembly: the sensitivity of the in-cylinder flow field for residual intake and in-cylinder velocitystructures. Computers and Fluids, 122, 123-135, 2015". Reprinted with permission.

This publication is included in the electronic version of the article dissertation:Keskinen, Jukka-Pekka. Large Eddy Simulation of In-Cylinder Flows.Aalto University publication series DOCTORAL DISSERTATIONS, 55/2016.

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Large eddy simulation of a piston-cylinderassembly: the sensitivity of the in-cylinder

flow field for residual intake andin-cylinder velocity structures∗

Jukka-Pekka Keskinen†, Ville Vuorinen, Ossi Kaario, andMartti Larmi

Aalto University, School of Engineering, Department ofEnergy Technology, 00076 Aalto, Finland

August 24, 2015

Abstract

Large eddy simulation (LES) in an axisymmetric piston-cylinder ge-ometry was carried out using three LES approaches: 1) Smagorinskysubgrid scale model, 2) implicit LES, and 3) scale selective discretisa-tion (SSD). In addition to the LES subgrid scale model sensitivity study,two additional simulations were carried out in order to understand theroles of the intake and the in-cylinder residual turbulence to the flowstatistics. Altogether twelve cycles were computed for each simulationon a grid with 5 million cells and requiring over a month of wall-clocktime per simulation on a supercomputer. Analysis of velocity statis-tics revealed that the results were not very sensitive to the LES modeltype. However, the residual turbulence was noted to have a clear im-pact on the velocity statistics. In particular, the simulations revealedthat removing the residual turbulence from the intake region at thetop-dead-centre has a clear impact on the overall velocity statistics. Inmany cases the cycle-to-cycle variation (CCV) increased. In a respectivenumerical test, where only the in-cylinder turbulence was removed attop-dead-centre, weaker sensitivity was observed. In addition, the CCVrelative to the mean velocity was in some cases as high as 30 % evenin such a non-reactive case. The present study complements previousstudies on the same set-up by investigating the sensitivity of three LESmodels on flow statistics, quantifying CCV using three different LESapproaches in the standard set-up, and assessing the role of residualturbulence on the flow statistics via modified flow cases.

∗Accepted manuscript. Published in Computers & Fluids 122, 123–135, (2015). DOI:10.1016/j.compfluid.2015.08.028†Corresponding author. Email: jukka-pekka.keskinen@aalto.fi

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1 IntroductionThe flow inside the cylinder of an internal combustion engine has a largeeffect on the performance of the engine and contains several different flowstructures [1]. The intake jets bring fresh air into the cylinder and tur-bulence is created due to the jet break-up. Depending on the cylinder ge-ometry, different large scale flow structures, such as swirl and tumble, areformed. The motion of the piston modifies the flow by changing the dimen-sions of the cylinder and can introduce new flow features such as squish.The interaction of the large scale flow features introduces even more com-plexity to the flow [2]. In fact, the importance of the different in-cylinderflow features on the engine performance has been known and studied formore than a hundred years [3]. In addition to small time scale turbulentfluctuations within one cycle, the engine flows often display long time scaleunsteadiness. The variation in different mean values between differentengine cycles is called cycle-to-cycle variation (CCV) [1]. Generally, an opti-mal internal combustion engine would have minimal variation between itscycles.

Combustion has a very important role in the in-cylinder flow of a realengine. In many cases, the CCV is observed in the cylinder pressure datawhich is tightly connected with combustion processes. According to Hey-wood [1], the main causes behind combustion variation between cycles are:variation in the in-cylinder fluid flow, variation in the amount of fuel andair between the cycles, and variation in mixture composition within thecylinder. In the present study, we limit ourselves to the first of the men-tioned causes. Many consider the variation of in-cylinder flow to be themost important factor related to engine performance [4] and for this reasonmotored (cold) engine flow cases are useful in the study of CCV and theireffect on the performance of a real engine. The motored set-up, where thepiston motion is artificially induced, is also simpler and easier to approachthan the full, fired engine flow case because additional complexities due tochemical reactions can be left out from the simulation. On the other hand,simplifications in the geometry allow CCV to be studied from a more gen-eral viewpoint, giving us an access to the causes behind them.

Large eddy simulation (LES) is based on the spatial filtering of the flowfield so that only the large, energy containing length scales are solved di-rectly. Details of the method can be found, for example, from references[5, 6]. The potential of LES to resolve CCV was realised already during theearly 1990’s, when the first applications of LES on an internal combustionengine flow were carried out [7, 8]. Although these early simulations hada rather modest spatial resolution and only a low number of engine cycleswere computed, CCV was still observed. The contemporary engine LES ischaracterised by computational meshes with up to ten million cells [9], alarge number of computed cycles [10, 11, 12] or the development and test-ing of different modelling approaches [13] and new analysis tools [14, 15].However, as a very large number of cycles is required for properly convergedstatistics [12], the computational requirements are still a limiting factor forthe LES of the internal combustion engine.

A simple piston-cylinder assembly was experimentally studied at theImperial College during the 1970s [16]. The studied geometry has a single,

2

centrally located valve, a circular cylinder and a flat piston. The motionof the piston is harmonic and slow enough so that the flow can be consid-ered incompressible. The measurements [16] show that the flow is turbu-lent and contains many features that are present in realistic engine flows.Measurements of the geometry with an added swirl have also been carriedout [17]. The symmetric piston-cylinder geometry has been simulated mul-tiple times using the Reynolds-averaged Navier-Stokes (RANS), approach[18, 19, 20]. The RANS simulations were able to reproduce the mean ve-locities relatively well while the fluctuating velocities were captured withlower accuracy. In the used unsteady formulation of the RANS approach,the acquired mean velocity represents the ensemble average velocity whileboth the turbulent and the CCV part of the velocity field are lumped to-gether in the fluctuating velocity component [20, 21]. For this reason noCCV can be observed when the RANS approach is used.

The symmetric piston-cylinder geometry has been studied using LESseveral times. The cylindrical symmetry of the geometry makes it very at-tractive for LES by reducing the number of simulated cycles required forcollecting statistics. Because of the role of the piston as the force drivingthe flow and the availability of reference measurements, the main focus ofthe first LES studies of the geometry was on the implementation and test-ing of the immersed boundary method. Verzicco et al. [22, 23] simulatedthe flow using both the classic [24] and the dynamic [25, 26] variants of theSmagorinsky subgrid scale model. Although only three cycles were com-puted, the simulations revealed strong CCV and indicated that the dynamicSmagorinsky model outperforms the classical version. The simulations re-ported in [23] were carried out using meshes with approximately 1.6 millionand 640 000 cells and their results showed a better agreement with thereference measurements than what was reached with earlier RANS sim-ulations. The LES of symmetric piston-cylinder geometry was then later[27, 28] used as a successful example of the application of the immersedboundary method.

Around the same time with the development of the immersed boundarymethod, engine LES with a different approach for mesh motion was alsopursued [29, 30]. These simulations were carried out using a rather coarsemesh of 150 000 cells and produced four simulated engine cycles. The firstsimulated cycle was removed from the analysis as it was considered to becontaminated by the unrealistic zero-velocity initial conditions. In additionto the classic and dynamic Smagorinsky model, also the Lagrangian version[31] was used. The results of the simulations were in all cases better thanthose acquired using RANS, confirming the suitability of LES for engineflows. A later study by Liu & Haworth [32] reports quite an extensive sen-sitivity study on the LES of the flow case. Three meshes with 0.17, 1.3, and2.6 million cells were used together with the classic Smagorinsky model anda one-equation model while five different time step sizes were used. Also,two different types of mesh motion were tested: mesh deformation and celllayer addition/removal. Each simulation consisted of seven computed cyclesand two first cycles were excluded from the analysis. The results indicatethat a mesh with 1.3 million cells produces a sufficient spatial resolutionwhile a time step of 0.25 crank angle degrees (CAD) or smaller appears toprovide a sufficient temporal resolution. Neither of the tested subgrid scale

3

models performed constantly better than the other model while no clear dif-ferences were observed between the two different mesh motion types. Thestudy [32] provides a good starting point for any study on the symmetricpiston-cylinder geometry.

The application of proper orthogonal decomposition in engine applica-tions has been another clear theme in the simulation of the symmetricpiston-cylinder geometry. The study of Fogleman et al. [33] introducedproper orthogonal decomposition to engine LES and considered a flow casesimilar to the one studied in the present article. Later studies [34, 35] thenapplied proper orthogonal decomposition to the present flow and used themethod to analyse CCV and other flow features. The simulations of Liu &Haworth [34] were carried out using two meshes with cell counts approx-imately at 170 000 and 1.3 million. The number of simulated cycles was52 and 32 respectively for the meshes. Two first cycles were removed fromthe final analysis and a one-equation model was used as the subgrid scalemodel. The study of Montorfano, Piscaglia, & Onorati [35] was carried outusing a dense mesh with 4.8 million cells and the wall-adapting local eddy-viscosity subgrid scale model [36]. In total ten cycles were simulated and,as appears to be customary, two first simulated cycles were not includedin the analysis of the results. The symmetric piston-cylinder assembly hasalso been studied as a validation case in a more extensive engine relatedLES study [37].

Recently direct numerical simulation (DNS) has been used to study thesymmetric piston-cylinder geometry. The DNS of Schmitt et al. [38] wascarried out using a spectral element method with approximately 60 mil-lion nodes and it required 1.3 million CPU hours. The number of simu-lated cycles was eight and six of the cycles were used in the final analy-sis. The DNS reached a good agreement with the measurements of Morse,Whitelaw, & Yianneskis [16] and provided additional insight into the na-ture of the CCV in the geometry. Instead of making the LES of the sym-metric piston-cylinder geometry redundant, the available DNS data allowsfor a more accurate validation of used numerical methods and paves theway for a deeper LES analysis of CCV and other engine-related phenom-ena.

By studying the direction and the velocity of the flow in the valve chan-nel, Schmitt et al. [38] deduced that the main causes behind the CCV in thepresent geometry are the residual flow structures present in the cylinder attop-dead-centre (i.e. 0 CAD). We intended to study the matter further byusing two modified flow cases where the residual turbulence was removedfrom a part of the geometry. We based our hypothesis to the work of Schmittet al. [38]: if the residual turbulence within the cylinder at top-dead-centreis the cause behind the CCV, their removal should remove the CCV fromthe simulation. Similarly, we expected the removal of residual turbulencefrom the intake region to have no effect on the CCV.

The objectives of the present paper are the following: 1) study the LESmodel sensitivity in engine flows, 2) estimate the level of CCV in the sym-metric piston-cylinder geometry, and 3) study the roles of residual turbu-lence in the intake and the in-cylinder regions of the geometry on the gen-eration of CCV using a numerical experiment. We report the first LES car-ried out using the scale selective discretisation (SSD) approach and the first

4

detailed implicit LES (ILES) on the geometry. An LES using the Smagorin-sky model was also carried out. The resulting velocity statistics of the stan-dard simulations, i.e. those corresponding to the original set-up of Morse,Whitelaw, and Yianneskis [16], were mostly in line with the earlier experi-ments [16] and DNS [38]. However, more interesting results were obtainedfrom the modified flow cases as CCV was present even after the residualturbulence was removed from the cylinder. Especially, in the case of tan-gential velocities, the CCV showed a clear increase when the residual tur-bulence was removed from the intake region.

The present article is structured so that the simulated flow case is firstpresented in section 2. Then, in section 3, details of the used numericalmethods and the simulations are given. The results of the present simula-tions are given in section 4 together with an analysis of the findings.

2 Geometry and flow configurationThe piston-cylinder assembly considered in the present article is introducedby Morse et al. [16]. The geometry is axially symmetric and consists of acylinder, a single centrally-located valve, a flat piston, and an inlet sec-tion. The diameter of the cylinder is 75 mm while the piston, set in har-monic motion at 200 rounds-per-minute (rpm), has a stroke of 60 mm anda clearance of 30 mm. The mean speed of the piston is 0.40 m/s while themaximum speed is 0.63 m/s. The valve gap is a constant 4 mm with a 30opening angle. The inlet region, i.e. the part of the geometry that is lo-cated above the cylinder top, measured 36 cm in the current simulations. Aschematic of the geometry is shown in Figure 1 together with all relevantmeasures. The geometry has been subject to a laser-Doppler anemome-try study in late 1970’s [16] and later to numerous computational studies[18, 19, 20, 22, 29, 23, 27, 30, 32, 34, 37, 35, 38]. Recently a high resolutionDNS study has been published [38]. The velocity measurements and refer-ence DNS data are available for planes perpendicular to the cylinder axisat 36 CAD, 90 CAD, 144 CAD, and 270 CAD.

The fluid used in the experiments was air. In the present simulations,we characterise the fluid with the kinematic viscosity ν = 1.568× 10−5 m2/s,which corresponds approximately to air at the temperature of 27 C. Themaximum velocity of the intake jet in the present simulations was about10 m/s and was reached together with the maximum piston velocity at 90 CAD.The piston is the only force driving the flow and hence the mass flow in andout of the system is constant between the different cycles. Using the intakejet velocity and the cylinder diameter, the maximum Reynolds number ofthe in-cylinder flow can be estimated to be Remax < 48 000. The flow in thecylinder-valve assembly is turbulent and the majority of the turbulence iscreated by the intake jet.

5

75 mm

34 mm

42 mm30-90 mm

66 mm

34 mm40 mm

17 mm

34 mm

Piston

ValveCylinder top

Valve stem

Figure 1: The symmetric piston-cylinder geometry considered in the cur-rent article. The inlet pipe is not fully shown and the piston moves accord-ing to harmonic motion at 200 rpm.

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3 Numerical aspects3.1 Governing equationsIn LES, the large scales of the flow are solved directly while the smallscales are treated by models. The separation of the length scales is formallyreached by the application of a spatial low-pass filter to the Navier-Stokesequation [5]. In the case of an incompressible fluid, and if we assume thefiltering operation to commute with the differential operators, the filteredNavier-Stokes equation

∂ui∂t

+∂ujui∂xj

= − ∂p

∂xi+ ν

∂2ui∂xj∂xj

−∂τRij∂xj

(1)

is reached. The Einstein summation convention is applied in Equation (1)and in all subsequent equations unless stated otherwise. The filtered vari-ables are denoted with an overbar while the residual stress tensor τRij repre-sents the effects of the unresolved subgrid scales on the solved grid scalesand is modelled. Numerous subgrid scale models exist but none of themcan be considered working perfectly in every flow case. This means that adecision on the used model is required for each simulated flow case. Thesubgrid scale models used in the present study will be presented in section3.2.

In the finite volume framework, we can interpret the cell value of veloc-ity to represent, at least approximately [39, 40], the spatial average of thetrue velocity field in that cell:

ui(~x, t) =1

∆Ω(t)

∫Ω(t)

ui(~x− ~r, t) dr1 dr2 dr3. (2)

The volume of the cell Ω is denoted here with ∆Ω. If the mesh moves ordeforms during the LES, the filter changes and the assumption of the com-mutation of the derivatives and the filter, included in Equation (1), doesnot hold. Carrying out the filtering of the Navier-Stokes equation using thetime dependant filter of Equation (2), the non-static, filtered Navier-Stokesequation for a given cell Ω is reached in the form

1

∆Ω

∂ui∆Ω

∂t+∂(uj − vj)ui

∂xj= − ∂p

∂xi+ ν

∂2ui∂xj∂xj

−∂τRij∂xj

, (3)

where vj is the cell point velocity field of the used mesh. The simulations ofthe present article solve the Navier-Stokes equations in the form given byEquation (3).

3.2 Subgrid scale modelling and numerical schemesThe residual stress tensor needs to be modelled in order to close the filteredNavier-Stokes equation. In the commonly used Smagorinsky model [24],the residual stress tensor is modelled by setting

τRij = −2C2S∆2Sij

√2SklSkl, (4)

7

where Sij is the rate-of-strain tensor

Sij =1

2

(∂ui∂xj

+∂uj∂xi

), (5)

and Cs is the Smagorinsky constant. In the present work, a value of Cs =0.18 was used. This value was chosen because it had been used successfullyin earlier simulations of in-cylinder flows of combustion engines [9, 41, 42].The Smagorinsky model is known to perform incorrectly in the near-wall re-gion [5] and for this reason, the residual stress tensor (4) was scaled in thepresent Smagorinsky simulations using the van Driest damping function[43]. Non-dissipative numerical schemes are preferred when the Smagorin-sky model is used as the model is assumed to provide the simulation witha sufficient amount of dissipation. In the present Smagorinsky simulation,the linear scheme has been used for the convective term.

In the ILES approach [44, 45, 46] the residual stress tensor is not explic-itly included in the numerical solution of the LES equation (3). Instead itis assumed that the used numerical set-up will provide the simulation withdissipation that models the effect of the residual stress tensor. In prac-tice an ILES is carried out by leaving out the explicit subgrid scale modelfrom the simulation set-up and by using a dissipative convection scheme.The resulting implicit modelling depends on the chosen numerical schemes[46, 47]. ILES has been successfully used in a wide range of flow casesand a comprehensive overview of the method can be found in the textbookby Grinstein, Margolin, & Rider [46]. The recent applications of ILES in-clude flows around buildings [48], the Richtmyer-Meshkov instability [49],engine flows [42, 50], jets [51, 52], and sprays [53]. In the present paper, theimplicit subgrid scale modelling is invoked by the use of the OpenFOAM R©scheme termed limitedLinear for the convective term. The scheme utilisesthe flux limiter function

Ψ(r) = max

[0,min

(2r

c, 1

)], (6)

where c ∈ [0, 1] is a control parameter and r is the ratio of the velocitygradients of the neighbouring cells. For example, in the case of a uniformmesh the velocity gradient ratio is calculated as

r =ui,j+1−ui,j

ui,j−ui,j−1(7)

for the velocity component ui in the cell j. More details on flux limiters canbe found in the textbook by Hirsch [54]. The accuracy of the limitedLinearscheme was shown to be of second order by Vuorinen et al. [55].

The third subgrid scale approach used in the current study was the SSDmethod [56]. The method is based on the decomposition of the velocity fieldto a sum of smooth and non-smooth parts within the convective term:

∂ujui∂xj

=∂uj(ui − u′i)

∂xj+∂uju

′i

∂xj, (8)

where the prime is used to denote a high-pass filtered velocity. Different nu-merical schemes are then used for the smooth and non-smooth components

8

so that a non-dissipative method is used for the smooth part and a dissi-pative scheme is used for the non-smooth part. As in the ILES approach,the subgrid scale dissipation comes from the use of a dissipative numericalscheme. In earlier applications of the SSD approach [52, 56, 57], a combina-tion of the central scheme with the upwind scheme or the gamma differenc-ing scheme [58] have been used for the non-smooth term together with thecentral differencing for the smooth part. In the present SSD simulation,the non-smooth part was evaluated using the limitedLinear scheme, i.e.the same scheme as was used in the present ILES, while the smooth partwas calculated using the linear scheme. The high-pass filtering requiredby SSD was carried out here using the Laplace operator in its self-adjointform

u′i = − ∂

∂xj

(∆s2

π2

∂ui∂xj

), (9)

where ∆s is the local distance between cell centres.

3.3 Flow and quality parametersCertain flow quantities were computed during the simulation from the solvedvelocity and pressure fields. The kinetic energy of the flow (per unit mass)is defined as

E =1

2uiui (10)

whereas the molecular (resolved) dissipation is given as

εµ = ν∂ui∂xj

∂ui∂xj

. (11)

Multiplying the Navier-Stokes equation by uj and rearranging leads to anequation for the kinetic energy E:

∂E

∂t+∂uiE

∂xi+∂pui∂xi

− ν ∂2E

∂xi∂xi= −εµ. (12)

The total level of dissipation introduced by the numerical schemes and thesubgrid scale model can be estimated by assuming that the total (effective)dissipation ε in the simulation is a sum of molecular εµ and numerical εnumcomponents. If an explicit subgrid scale model is used, the numerical dissi-pation εnum can be thought to include the contribution of both the explicitsubgrid scale model and the numerics. Setting the right-hand side of equa-tion (12) to εµ + εnum and rearranging the terms, we obtain

εnum = −∂E∂t− ∂uiE

∂xi− ∂pui

∂xi+ ν

∂2E

∂xi∂xi− εµ. (13)

In ILES and SSD, the numerical dissipation has the role of a turbulencemodel and hence equation (13) can be used to evaluate the level of implicitmodeling involved in the simulation. This approach is useful also when anexplicit turbulence model is used as in many cases the numerical dissipa-tion can be of the same order as that produced by the turbulence model[59]. An alternative approach to assessing the level numerical dissipation

9

in a simulation [60] is to assume in (12) that the effective viscosity is com-posed of a molecular and a numerical part.

The quality and reliability of an LES can be evaluated in multiple ways.The simplest is a direct comparison with experimental or direct numeri-cal simulation (DNS) data. In the present study, we assessed the qualityof our simulations also by computing the subgrid activity parameter [61].The parameter is defined as the ratio between the modelled kinetic energydissipation and the total dissipation:

SGA =〈εsgs〉Ω

〈εsgs〉Ω + 〈εµ〉Ω, (14)

where the angled brackets denote averaging over the computational do-main Ω and εsgs is the dissipation of the subgrid scale model. Accordingto [61], a value of SGA = 0 correspond to a DNS whereas SGA = 1 indi-cates an LES with the Reynolds number approaching infinity. The originalformulation of the parameter [61] ignores numerical dissipation completelybut the definition (14) can be easily extended to a more general form [62].The influence of both the numerical dissipation εnum and the dissipationof the explicit subgrid scale model εmod can be added to the Definition (14)simply by setting εsgs = εmod+εnum. When an ILES is carried out, εmod = 0and hence εsgs = εnum.

3.4 Quantifying the cycle-to-cycle variationThe level of CCV can be evaluated using the coefficient of variation [1] forthe quantity of interest. The coefficient of variation is defined as the ratioof the standard deviation and the mean and it indicates the relative vari-ation of the quantity of interest. For quantities with a mean value closeto zero, the coefficient can yield unreasonably high values and should beinterpreted with caution.

In the present paper, we calculated the coefficient of variation for a vari-able φ using the formula:

COV =

⟨√⟨(〈φ〉i − 〈φ〉T )

2⟩T

⟩Ω

〈〈φ〉T 〉Ω, (15)

where angled brackets with the subscripts i, T , and Ω indicate averagingin respect to cycle, full simulation, and space, respectively. The cycle aver-ages 〈φ〉i were calculated, for a fixed CAD, by using an averaging windowof 8 CAD and then spatially averaging in the azimuthal direction. The re-sulting average was hence a function of the radius and different for eachcycle. The simulation averages 〈φ〉T were calculated directly by using cyclevalues. The spatial averages 〈φ〉Ω were calculated on the plane or volume ofinterest Ω depending on the quantity. The combination of the described av-eraging processes according to Equation (15) results in a single number foreach region of interest. A similar formulation for the coefficient of variationhas been used by Schmitt et al. [38].

10

Figure 2: Section of the computational mesh used in the simulations show-ing the near-valve region of the mesh at top-dead-centre.

3.5 Mesh and simulation set-upAn unstructured mesh, consisting of approximately 5.1M cells was used inall simulations. The cell sizes varied within the mesh in such a way thata higher resolution was available in areas of interest. The region with rel-atively small cells consisted of the cylinder and the close proximity of thevalve. At top-dead-centre, the cells within the cylinder were at their small-est, at ∆x ≈ 0.7 mm, while at bottom-dead-centre some of the in-cylindercells were stretched up to ∆x ≈ 3 mm. Even smaller cells were used in thenear-wall regions of the cylinder and the valve; the smallest cell measured∆x ≈ 0.08 mm. The mesh resolution was reduced in the inlet region so thatthe cell size was gradually increased towards the inlet. The largest cells inthe mesh were located next to the inlet and were of the size ∆x ≈ 8 mm.Most of the in-cylinder cells were approximately cubical at top-dead-centreand the non-cubical cells were located at the wall layers or in the inlet re-gion. Figure 2 illustrates the cell distribution in the used mesh.

Mesh motion was introduced to the present simulations by moving thepiston boundary according to the harmonic motion of 200 rpm. Then, themesh motion was propagated from the piston boundary to the internalpoints of the mesh through the solution of a Laplace equation [63]. Afterthe moving of the mesh points, the flow equations were solved. There wasno cell layer removal or addition during the simulation and, in order to ac-commodate the piston motion, cells were stretched during the intake strokeand compressed during the exhaust stroke. Mesh point motion was allowedonly in the axial direction and within the cylinder. In order to maintain abetter quality mesh, only minimal cell point motion was allowed close to thepiston and the cylinder top meaning that the bulk of the cell deformation

11

Table 1: The main properties of the simulations carried out in the presentarticle. Two convection schemes are indicated for the SSD simulation asdifferent schemes were applied in the computation of the smooth (u − u′)and the non-smooth (u′) components of the velocity field. The indicated linestyles are used in the plots where the simulations are plotted against eachother.

LES approach Convection scheme Velocity manipulation Line styleSmagorinsky linear NoneSSD linear (u− u′) & None

limitedLinear (u′)ILES limitedLinear NoneILES limitedLinear Intake zeroedILES limitedLinear Cylinder zeroed

happened in the central parts of the cylinder. While deforming cells can beexpected to influence the LES commutation error [64, 65, 66, 67, 68, 69], wedo not expect the present set-up to be vulnerable to major effects from themesh motion [57].

The velocity boundary condition for the piston was the predefined pistonvelocity according to the harmonic motion of 200 rpm while all other wallswere set for the usual no-slip condition. The zero gradient boundary condi-tion was used at the inlet. Zero gradient boundary conditions were used forthe pressure on all boundaries except the inlet where a constant pressurecorresponding to 0 Pa was set. The inlet was placed 36 cm above the cylin-der top and was expected to be far enough not to influence the flow insidethe cylinder. All simulations were started from top-dead-centre (0 CAD)and with a zero velocity field. The simulations were continued until twelvefull cycles were completed. The data from the first two cycles was excludedfrom the analysis due to the expected influence of the zero velocity initialcondition.

Five different simulations were carried out. Three of the simulationswere carried out as ILES and utilised a convective scheme with the lim-iter given by Equation (6), one simulation was carried out using the SSDscheme [56], and one simulation was an explicit LES with the Smagorinskymodel [24]. Two of the simulations were carried out in modified flow caseswhere a part of the velocity field was manipulated to zero velocity at top-dead-centre of each cycle. In the first modified case the manipulated regionwas the intake region while in the second it was the cylinder. The modi-fied flows were simulated using with ILES. The overall simulation set-up issummarised in Table 1. Previous research [38] suggests that the turbulenceremaining in the cylinder at top-dead-centre is responsible for the CCV inthe current geometry and we expect the modified flow cases to provide ad-ditional insight into the matter.

All simulations used the second order implicit backward method for thetime discretisation and linear interpolation for the diffusive fluxes. Thetreatment of the convective term varied depending on the chosen subgrid

12

scale modelling approach and the used convection schemes are summarisedin Table 1. In the simulations that utilised the Smagorinsky subgrid scalemodel, linear interpolation was used in order not to introduce any addi-tional numerical dissipation. In the case of the ILES, the convective termwas calculated using the limitedLinear scheme, i.e. using the limiter givenby Equation (6), with c = 0.1. The same limiter was applied to the non-smooth part of the velocity field in the SSD simulation according to the pro-cedure described in Section 3.2 while the smooth part of the velocity fieldwas handled by linear interpolation. In order to increase the numerical sta-bility of the SSD simulation, the SSD approach was blended with the lim-ited scheme based on the level of cell non-orthogonality. The final, modifiedSSD scheme was a fully limited scheme when cell non-orthogonality washigher than 70, fully SSD in orthogonal cells, and linearly blended in cellswith a non-orthogonality between zero and 70. All of the used numericalschemes are expected to be second order accurate [55]. The schemes usedin the present paper have the same order of accuracy as those commonlyused in the simulations of complex, realistic engine geometries [70, 9, 34].

3.6 Software and computationsIn the present work, we used the open source, finite volume, computationalfluid dynamics code OpenFOAM R© version 2.2. As the software is opensource, the building of new solvers and different post-processing tools isstraightforward. The solver applied in this work was an incompressibleengine flow solver that utilised the PISO (pressure-implicit with splittingof operators) pressure correction algorithm [71, 72]. The computationalmesh was unstructured and was created using the blockMesh and snappy-HexMesh mesh generators that are part of OpenFOAM R©.

All of the simulations were carried out using Sisu or Taito supercomput-ers (Intel Sandy Bridge 2.6 GHz) of CSC – IT Center for Science in Finland.The simulations were performed with 128 or 160 cores while the requiredcomputational times ranged between 68 000 and 92 000 CPU hours. Scal-ability tests indicated that an increase in the number of cores would nothave made the computations much faster. This means that the relativelylong simulated time (12 cycles) combined with the small time step requiredby LES is the limiting factor in internal combustion engine LES. The useof a larger time step would be possible from the numerical point of viewbut the LES methodology is based on the idea that all temporal scales areresolved and only spatial filtering is carried out. For this reason, the useof a clearly larger time step can be expected to reduce the reliability of thesimulations by pushing them somewhere in the direction of a RANS sim-ulation. In the case of a realistic engine geometry where axial symmetrycannot be utilised, the number of cycles required for proper velocity statis-tics can be even two magnitudes larger [12]. This means that a reliable,high resolution multi-cycle engine LES is still out of reach of the currentcomputers.

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4 ResultsThe first computed cycle in each of the simulations differed noticeably fromthe other cycles due to the zero velocity initial condition. On the first cy-cle, the start of the break-up process of the intake jet seemed to be some-what delayed and less intense. The results of the second cycle were alreadymostly in line with the rest of the cycles. In order to minimise the effect ofthe initial condition on the results of the simulation, both the first and thesecond cycle were left out from the subsequent analysis.

4.1 Instantaneous flow visualisationThe velocity field during the tenth cycle of the Smagorinsky simulation isshown in Figure 3. The simulations produced qualitatively similar resultsand each of their cycles displayed the same major features. The presentsimulations feature the same major flow structures that have been observedin the measurements [16] and the DNS [38]. During each cycle, the intakeair forms a hollow, circular jet as it enters the cylinder. Two strong toroidalvortices are created by the annular intake jet. The larger of the two, themain vortex (marked with I in Figure 3), is located in the centre of the cylin-der while the smaller one (II) is located in the upper corner of the cylinder.At each cycle, the maximum velocity of the intake jet, approximately 10 m/s,is reached around 90 CAD. After 180 CAD), the flow direction reverses andthe turbulence remaining in the cylinder starts to decay as the piston startsmoving back upwards.

As in the cylinder during the intake stroke, a jet is formed in the intakeregion during the exhaust stroke. The velocity of the exhaust jet is higherthan that of the intake jet due to the contraction of the valve channel andthe strong detachment of the flow from the valve surface. After impingingon the valve stem, the flow in the intake region attaches partly to the stemand moves towards the outlet. Most of the upward flow is located close tothe valve stem and because of this, slow downward flow is observed closeto the outer wall of the intake region, creating a recirculation zone (III).Another recirculation region (IV) is formed between the exhaust jet andthe curved, upper surface of the valve. Qualitatively it seems that morestructures and turbulence remain in the intake region at 0 CAD) of eachcycle than remains in the cylinder at 180 CAD).

4.2 Velocity statisticsIn order to gain smooth statistics, the velocity statistics for each reportedCAD were first temporally averaged over 8 CAD, then temporally over tenseparate cycles, and finally spatially using the cylindrical symmetry of thegeometry. A similar approach has been used in the experiments [16] wherean averaging window of 10 CAD was used for each reported mean value.The standard simulations follow the original set-up of Morse, Whitelaw, andYianneskis [16] closely while the modified simulations introduce numericalmodifications to the standard set-up.

Before progressing further in the analysis, an essential first check is toevaluate the mean and fluctuating velocity statistics. Figures 4 – 9 display

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mean axial velocity (〈uz〉) and the root-mean-square of the axial velocityfluctuation (uz,rms) for each simulation together with the reference data forselected planes with an axial distance z from the cylinder top. At 36 CADall three simulation approaches capture the flow structures well and arein agreement with both the DNS and the measurements. This is under-standable since the mesh is still quite dense near 0 CAD). At 90 CAD, thestandard simulations capture the mean velocities on plane z = 10 mm rela-tively accurately but larger discrepancies can be seen on the other planes.As there are no large differences between the different simulations in thestandard set-up, the failures can be attributed to the used grid. In the DNS[38], the minimum integral length scale (see [5] for the definition) withinthe cylinder at 90 CAD was estimated to be approximately 0.8 mm. Due tothe cell stretching caused by the piston motion, the largest in-cylinder cellsin the present simulations had their axial lengths slightly above the inte-gral length scale. Hence, at 90 CAD the results are likely to be influencedat the stretched mesh. Due to the decrease of flow velocities, the integrallength scale increases above the mesh spacing at later stages of the simu-lation.

The velocity statistics for 144 CAD show already a better match withthe reference data. However, certain discrepancies between the simula-tions can be seen in the mean velocity in the lower parts of the cylinderand in the fluctuating velocity in the central parts of the cylinder. Thepresent simulations agree almost completely with the experimental resultsat 270 CAD and for this reason the velocity statistics are not shown for thatparticular CAD.

The modified simulations are plotted together with the other simula-tions and the reference data in Figures 4 – 9 using dashed and dottedlines. The overall agreement of the modified cases with the measurementsand the DNS is similar to the standard cases. Compared with the corre-sponding standard case, the removal of intake structures at top-dead-centrecauses the mean and fluctuating velocity statistics at all shown crank an-gles to deviate the most from the other cases. However, the effects of theremoval of the velocity structures from the in-cylinder region mostly van-ish at 144 CAD. The zeroing of the intake velocity field appears to delaythe intake jet break-up and to cause the main vortex (I) to extend furtherdown in the cylinder. On the other hand, removing the in-cylinder flowstructures seems to move the main vortex (I) slightly upwards. Althoughthe changes are still relatively moderate, the zeroing the intake velocitystructures seems to lead to more persistent and stronger changes in the ve-locity statistics than the zeroing of the in-cylinder velocity structures. Thisimplies that the residual intake turbulence is important for CCV, contraryto observations in previous research [38], and to the in-cylinder velocitystatistics in general. The finding also makes the widely used practice ofsolving the intake region with very coarse meshes questionable.

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4.3 Cycle-to-cycle variation4.3.1 Axial velocities

The coefficient of variation indicates the relative variation of the quantityof interest and is calculated using Equation (15). Figure 10 shows the coef-ficient of variation for the axial velocity at each of the planes in Figures 4– 9 together with the corresponding values of 270 CAD. The coefficients ofvariation have been normalised with the absolute value of the axial velocityin order to emphasise the magnitude of the CCV.

Due to the low mean velocities, the coefficient of variation on the planesclose to the piston can be expected to provide a less reliable estimate for thelevel of CCV than on the planes closer to the cylinder top. The same appliesto 270 CAD. The main observation from Figure 10 is that the modifiedsimulation where the in-cylinder velocity structures were removed at top-dead-centre displays a lower level for the coefficient of variation than theother simulations at 36 CAD, 90 CAD, and on the upper planes at 144 CAD.On the other hand, the zeroing of the intake velocity field does not changethe coefficient of variation noticeably at 36 CAD and increases its level onthe upper planes at 90 CAD and 144 CAD. This indicates that the residualin-cylinder turbulence has a larger influence on the CCV than the residualintake structures during the early stages of the intake stroke while theopposite holds for the later stages of the intake stroke.

4.3.2 Tangential velocities

As the considered geometry is axially symmetric, the mean flow featuresare essentially two-dimensional and the mean value of the tangential ve-locity component should be zero. For this reason the occurrence of tangen-tial velocities can be seen as a sign of symmetry break-up in the form ofturbulence and CCV. During the exhaust stroke, the exhaust jet producesstrong tangential velocity fluctuations to the intake region. Figures 11 (a)and (b) illustrate how a large, consistent tangential velocity structure ispulled from the intake to the cylinder. Using an isosurface of the Q crite-rion [73], the tangential velocity structure is identified as a vortex whileseveral other, similar structures are also revealed. Figure 11 (c) displaysthe vortices together with the cross sections from Figures 11 (a) and (b).The transport of large vortices from the intake region to the cylinder indi-cates that, contrary to earlier observations [38], there is a mechanism thatallows residual intake turbulence to influence the in-cylinder flow throughthe intake channel.

The square of the tangential velocity, spatially averaged in radial andtangential directions (〈u2

θ〉r,θ) at 36 CAD is plotted as a function of the dis-tance from the cylinder top in Figures 12 and 13. The mean values for eachsimulation, with additional averaging over the cycles, (〈u2

θ〉r,θ,T ) are shownin Figure 12 (a). Within the cylinder, the 〈u2

θ〉r,θ,T of the ILES and SSDsimulation overlap almost perfectly. Also, tangential velocity content of theSmagorinsky LES is very close to those from the ILES and SSD simula-tion. In the intake zone, each standard simulation predicts a different levelof 〈u2

θ〉r,θ,T . The in-cylinder tangential velocities of the modified simulationsare consistently lower than that of the corresponding standard simulation.

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Table 2: The coefficient of variation for the squared tangential velocity ofall simulations at 36 CAD.

Zeroed ZeroedSmag. SSD ILES intake cylinder

Within the intake 0.30 0.26 0.27 0.03 0.23Within the cylinder 0.16 0.15 0.14 0.24 0.13

The zeroing of the velocity field reduces the level of kinetic energy in theflow and can be assumed to explain a part of the lowered level of 〈u2

θ〉r,θ,Tin the cylinder. The break-up of the intake jet can be expected to causethe bulk of the observed tangential velocity content. This means that thebreak-up of the intake jet appears to be delayed or less intense in the mod-ified flow cases and especially when the intake region has been zeroed.

When 〈u2θ〉r,θ of each cycle is plotted together with the simulation mean

value, a view of the cyclic variability is achieved. The standard cases, in Fig-ures 12 (b)-(d), display approximately the same level of variation around thesimulation mean. The overall variation is larger in the intake region thanin the cylinder for all standard simulations. The coefficients of variationhave been calculated for the squared tangential velocities and are shownin Table 2 for each simulation, both for the intake and in-cylinder regions.They confirm the observation by indicating that there is almost twice asmuch variation in the intake region compared with the cylinder. The highCCV is another clear indicator for the importance of properly accountingfor the region above the valve in engine LES.

In a similar manner, the 〈u2θ〉r,θ of the modified flow cases are plotted in

Figure 13 together with the corresponding simulation mean values. Com-paring the modified simulations with the standard ILES, the CCV withinthe cylinder appears to be more pronounced when the intake region hasbeen zeroed. Especially, the cycles 4 and 11 are seen to deviate clearlyfrom the simulation mean value. On the other hand, the variation is ap-proximately the same in the cylinder-zeroed simulation and the standardILES. The calculated coefficients of variation in Table 2 confirm the earlierobservations by indicating only a small decrease (0.01) in the in-cylinderCCV when the in-cylinder velocities have been zeroed while a clear increase(0.10) is seen when the intake velocities have been removed. The observa-tion implies that the variations are not only due to the residual in-cylinderturbulence in the present geometry, as concluded in [38]. When the residualintake turbulence is removed, the increase in the variation is seen togetherwith a delay in the jet break-up. The velocity structures in the intake regionwould thus appear to influence the stability of the intake jet by triggeringan earlier break-up.

Although the cycle values of 〈u2θ〉r,θ have been calculated using averaging

in both the radial and the tangential directions, this might not be enoughto provide a statistically converged average. In order to confirm that theobserved variation around the simulation mean value is indeed CCV, uθ isaveraged, while keeping the sign, in the same manner as u2

θ. Due to the

17

symmetry of the geometry, the value of 〈uθ〉2r,θ should be zero and hence itsmagnitude gives an estimate on the degree of statistical convergence. Thesimulation average 〈〈uθ〉2r,θ〉T is plotted in Figures 12 (b)-(d) and 13 usingthe dot-dashed line. Although 〈〈uθ〉2r,θ〉T is not exactly zero, it is everywheresignificantly smaller than 〈u2

θ〉r,θ. This indicates that the earlier analysison CCV can be considered valid.

4.4 Evaluation of numerical dissipationThe cycle-averaged, in-cylinder mean values of the subgrid activity parame-ter and the dissipation are shown in Figure 14. Based on the velocity statis-tics in Section 4.2, the subgrid activity parameter seems to be able to placethe different simulations into a relative order in respect of the simulationperformance. However, all simulations show a good fit with the referencedata at 270 CAD even though the subgrid activity parameter indicates thatthe simulations quality is at its worst.

The Smagorinsky simulation resolves more dissipation at around 90 CADthan the other simulations and adds less numerical/modelled dissipation atall times. The first peak of the subgrid activity parameter at 90 CAD cor-responds to a high total and resolved dissipation while the second peak at270 CAD corresponds to a combination of intermediate numerical/modelleddissipation and low resolved dissipation. The first peak can be explained bythe turbulence and velocity structures associated with the intake jet. How-ever, no significant velocity structures are present in the cylinder duringthe second peak of dissipation. The piston velocity has its second maxi-mum at 270 CAD meaning that also the mesh deformation rate is the high-est. Thus the increase in numerical dissipation around 270 CAD appears tobe caused by the mesh deformation.

5 ConclusionsHere we reported the simulation results of the flow in an axially symmetricpiston-cylinder assembly that has been studied experimentally by Morse etal. [16] and with DNS by Schmitt et al. [38]. Three different numerical ap-proaches, Smagorinsky LES, SSD, and ILES, were used in the simulations.Two additional, modified flow cases were simulated in order to study therole of the intake region and the in-cylinder region on the flow dynamicsand the CCV. In total five simulations were carried out and in each simula-tion, twelve cycles were computed.

Comparison of the velocity statistics of the present simulations withthose from the measurements and the DNS revealed a good agreement onthree out of four of the considered CADs. At 90 CAD the mean and the fluc-tuating velocities did not fully agree with the reference data although themain flow features were successfully captured. This was most likely due tosomewhat insufficient cell sizes in the stretched mesh combined with highvelocities present in the intake jet. At earlier and later stages of the cycle,the mesh resolution was considered adequate. Out of the different numer-ical approaches, the Smagorinsky model performed the best although thedifferences with regard to the other simulations were minor. The better

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performance of the Smagorinsky model in comparison with the SSD andthe ILES approaches is most likely due to the moderate grid resolution atcertain CADs.

The removal of the velocity structures from the intake region appearedto have a larger overall effect on the in-cylinder velocity statistics andenergy content than the removal of the in-cylinder flow structures. Thesquared tangential velocity content was observed to decrease clearly in thein-cylinder region when the velocity field was zeroed in the intake region.At the same time, a clear increase was seen in the CCV of the squaredtangential velocity. The zeroing of the in-cylinder velocity field resulted atlowered variation in the in-cylinder axial velocity during the first half ofthe intake stroke while the tangential velocity component was mostly unaf-fected. The CCV of the mean velocity, quantified in terms of the coefficientof variation, was up to 30 %. Such a value can be considered relativelylarge considering the fact that the present flow is non-reacting. Hence, ina much more complicated, reacting flow case even larger CCVs could beanticipated.

Most of the earlier simulations of the present geometry have concen-trated on the flow within the cylinder and have mostly disregarded the flowfield in the intake section. However, the main conclusion from the modifiedflow cases of the present article is that residual turbulence in the intakeregion has a clear influence on the flow field and the level of CCV also inthe cylinder. Consequently, our results suggest that more attention shouldbe paid to the region above the valve in future simulations even if one isinterested only in the in-cylinder flow statistics and the in-cylinder CCV.Lastly, we note that the present results were still limited to cold flow casesand the full understanding of CCV using LES would require in-depth stud-ies on the highly complex, compressible, reacting combustion processes inthe cylinder.

6 AcknowledgementsThe research has been funded by the Finnish Graduate School for Com-putational Fluid Dynamics, by the FCEP research program of Cleen Ltd.,and by the Aalto University School of Engineering. The revision stage ofthe article has been partly funded by Merenkulun säätiö. The authors aregrateful for CSC – IT Center for Science Ltd. for the computational re-sources. The authors would like to acknowledge also Dr. Schmitt (ETHZürich) for allowing us to access the reference data in digital form and theresearchers of the engine group of Politecnico di Milano for providing thegeometry in digital form.

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25

36 CAD 90 CAD 144 CAD 270 CAD

I

II

I

II

IIIIII

IV

|~u| (m/s)

Figure 3: Velocity magnitude fields for the Smagorinsky simulations fromthe 10th cycle. The colours indicate velocity magnitude according to thecolour bar. The main vortices are marked using Roman numerals on thesubfigures 90 CAD and 270 CAD.

26

0 10 20 30

−4

−2

0

2

4z = 10 mm

−4

−2

0

2

4z = 20 mm

〈uz〉(

m/s

)

0 10 20 30−4

−2

0

2

4z = 30 mm

r (mm)

Figure 4: Mean axial velocity component at 36 CAD for the SmagorinskyLES ( ), the SSD simulation ( ), the standard ILES ( ), the zeroedintake ILES ( ), and the zeroed cylinder ILES ( ) together with theDNS of Schmitt et al. [38] ( ) and the Measurements of Morse et al. [16] ( ).

27

0 10 20 30

0

1

2z = 10 mm

0

1

2z = 20 mm

uz,rms

(m/s

)

0 10 20 300

1

2z = 30 mm

r (mm)

Figure 5: Root-mean-square of the axial fluctuating velocity component at36 CAD. See Table 1 or the caption of Figure 4 for the used line styles.

28

0 10 20 30

−4

−2

0

2

4z = 10 mm

−4

−2

0

2

4z = 20 mm

−4

−2

0

2

4z = 30 mm

〈uz〉(

m/s

)

−4

−2

0

2

4z = 40 mm

0 10 20 30−4

−2

0

2

4z = 50 mm

r (mm)

Figure 6: Mean axial velocity component at 90 CAD. See Table 1 or thecaption of Figure 4 for the used line styles.

29

0 10 20 30

0

1

2z = 10 mm

0

1

2z = 20 mm

0

1

2z = 30 mm

uz,rms

(m/s

)

0

1

2z = 40 mm

0 10 20 300

1

2z = 50 mm

r (mm)

Figure 7: Root-mean-square of the axial fluctuating velocity component at90 CAD. See Table 1 or the caption of Figure 4 for the used line styles.

30

0 10 20 30

−4

−2

0

2

4z = 10 mm

−4

−2

0

2

4z = 20 mm

−4

−2

0

2

4z = 30 mm

〈uz〉(

m/s

)

−4

−2

0

2

4z = 40 mm

0 10 20 30−4

−2

0

2

4z = 50 mm

r (mm)

Figure 8: Mean axial velocity component at 144 CAD. See Table 1 or thecaption of Figure 4 for the used line styles.

31

−4

−2

0

2

4z = 60 mm

−4

−2

0

2

4z = 70 mm

〈uz〉(

m/s

)

0 10 20 30−4

−2

0

2

4z = 77.5 mm

r (mm)

Figure 8: Continued.

32

0 10 20 30

0

1

2z = 10 mm

0

1

2z = 20 mm

0

1

2z = 30 mm

uz,rms

(m/s

)

0

1

2z = 40 mm

0 10 20 300

1

2z = 50 mm

r (mm)

Figure 9: Root-mean-square of the axial fluctuating velocity component at144 CAD. See Table 1 or the caption of Figure 4 for the used line styles.

33

0

1

2z = 60 mm

0

1

2z = 70 mm

uz,rms

(m/s

)

0 10 20 300

1

2z = 77.5 mm

r (mm)

Figure 9: Continued.

34

COV0 0.2 0.4

0

10

20

30

36 CAD

z(m

m)

0 0.2 0.40

10

20

30

40

50

90 CAD

z(m

m)

COV0 0.2 0.4

0

10

20

30

40

50

60

70

80

144 CAD

z(m

m)

0 0.2 0.40

10

20

30

40

50

270 CADz

(mm

)

Figure 10: Coefficient of variation for the axial cycle-averaged velocitieson the planes shown in Figures 4 – 9 and the corresponding ones from270 CAD. See Table 1 or the caption of Figure 4 for the used line styles.

35

(a)

|uθ| (m/s)

(b)

(c)

Figure 11: The Smagorinsky simulation at 90 CAD of the 8th cycle. (a):Vertical cross section of the cylinder and the near-valve region showing thetangential velocity field. (b): Horizontal cross-section of the valve channelshowing the tangential velocity field. The colours on the cross sections in-dicate the absolute value of the tangential velocity according to the showncolour bar. (c): Q isosurface visualisation of selected vortices on top of thecross sections. The vortices are shown with green colour.

36

0 0.2 0.4 0.6

−20

0

20

u2θ (m2/s2)

z(m

m)

(a) Simulation mean values

0 0.2 0.4 0.6

−20

0

20

u2θ (m2/s2)

z(m

m)

(b) Smagorinsky

0 0.2 0.4 0.6

−20

0

20

u2θ (m2/s2)

z(m

m)

(c) SSD

0 0.2 0.4 0.6

−20

0

20

u2θ (m2/s2)

z(m

m)

(d) ILES

Figure 12: Tangential velocity content at 36 CAD. The vertical axis indi-cates distance from the cylinder top so that negative values refer to theintake region. (a): Simulation mean value, 〈u2

θ〉r,θ,T , see Table 1 or the cap-tion of Figure 4 for the used line styles. (b)-(d): The black, dashed linerepresents the simulations mean 〈u2

θ〉r,θ,T while cycle values, 〈u2θ〉r,θ, are

drawn with a different colour for each cycle. The dot-dashed line represents〈〈uθ〉2r,θ〉T and it gives an estimate for the extent of statistical convergence.

37

0 0.2 0.4 0.6

−20

0

20

Cycle 4

Cycle 11

u2θ (m2/s2)

z(m

m)

(a) Intake velocities zeroed

0 0.2 0.4 0.6

−20

0

20

u2θ (m2/s2)

z(m

m)

(b) In-cylinder velocities zeroed

Figure 13: Tangential velocity content at 36 CAD for modified flow cases.The vertical axis indicates distance from the cylinder top so that negativevalues refer to the intake region. The black, dashed line represents thesimulations mean 〈u2

θ〉r,θ,T while cycle values, 〈u2θ〉r,θ, are drawn with a dif-

ferent colour for each cycle. The dot-dashed line represents 〈〈uθ〉2r,θ〉T andit gives an estimate for the extent of statistical convergence.

38

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

Time (CAD)

SGA

(a) Subgrid activity parameter.

0 50 100 150 200 250 300 3500

50

100

150

200

Time (CAD)

ε(J

/kgs

)

(b) Total dissipation (upper set of lines) and resolved molecular dissipation (lower set oflines).

Figure 14: Subgrid activity and dissipation statistics for the in-cylindervelocity field. See Table 1 or the caption of Figure 4 for the used line styles.

39