2004-01-1854

Large-Eddy Simulation in IC Engine Geometries

L. Thobois, G. Rymer, T. Soulères PSA Peugeot Citroën

T. Poinsot Cerfacs

Copyright © 2004 SAE International

ABSTRACT

The computation of flows in IC engines is very challenging due to the variety of phenomena taking place. The well-known RANS methods often fail in both qualitative (dynamic of vortex breakdown…) and quantitative (swirl number, discharge coefficient…) predictions of these unsteady flows. The increasing power of computers now allows to investigate these flows using Large Eddy Simulation, which is a very promising technique. In order to explore the capability of LES in engine configurations, two simple IC engine geometries have been treated with a LES code, called AVBP, developed at CERFACS. This code is massively parallel and uses both unstructured and structured grids. First, the academic configuration of Dellenback was tested. It consists of an axisymmetric sudden expansion, which has been computed both with swirl (S=0.6) and without swirl. The LES results are compared to experimental data in terms of both mean and RMS, axial and tangential velocities. Besides, an unstationnary motion called the precessing vortex core is shown in the LES calculation. The influence of the swirl number on the PVC has been studied and compared to experimental data. Then, a more complex configuration with a valve is investigated. This steady state flow bench shows the capability of the code to handle complex geometries, close to a typical IC engine. Again, LES results are compared to experimental LDA measurements. The discharge coefficient is calculated and compared to experimental data. An analysis of the valve jet has been carried out. Finally, the influence of the scheme order (2nd versus 3rd order) and of the mesh type (structured versus unstructured) was investigated on both configurations. The results of this parametric study give more insight into the methodology for the computation of engine configurations with LES.

INTRODUCTION

With the growing of computational power, LES becomes now feasible in IC engines. The interest for LES comes

from the flow pattern in internal combustion engines. The flow is very turbulent with small dissipative structures but it is also composed of main big structures. For instance, in gasoline engines, the top of the cylinder is commonly designed with a roof cylinder head in order to initiate a tumble motion. In diesel engines, a swirl motion is initiated by tangential bended intake ports. LES would be able to resolve these structures and give better results than RANS computations.

Phenomena taking place in internal combustion engines depend on these main structures. They are also more and more important in regards to the new combustion concepts, based on direct injection and stratified charge for example. The typical way to study the aerodynamism of IC geometries is to transform them in a steady state flow bench. Piston and exhaust valves are put out. The airflow passes though the intake port(s), enters the cylinder, which is directly linked to the outlet.

In this study, LES is compared to experiments in two steady state flow benches. On one hand, a configuration with a sudden expansion, called Dellenback’s configuration, is computed to reproduce the first difficulty occurring in IC engines: the strong detachment due to the increase of the diameter between the intake ports and the cylinder. This first step consists of investigating both flows without and with swirl. The results obtained with LES for mean axial and tangential velocity profiles, as well as for axial and tangential velocity fluctuations are quantitatively compared to the experimental measurements. The unsteadiness of the flow is also compared to experimental observations. The motion of the precessing vortex core (PVC) is investigated. Besides, to reproduce a variation of the valve lift, the swirl number initiated at the inlet is decreased. The ability of LES to capture different swirl regimes and the corresponding vortex breakdown regimes is verified. On the other hand, a simple IC engine geometry with one valve is tested. This specific part of IC engines creates strong detachments and a strong pressure gradient. Again, LES velocities profiles are compared to LDA measurements and to RANS computations. Moreover, the static pressure axial profile and the characteristic

discharge coefficient of the engine designers are compared to experimental measurements. A physical analysis of the valve jet is realized. Finally, a parametric study is achieved for the two previous geometries to evaluate the influence of numerical scheme and mesh.

CODE DESCRIPTION

GLOBAL DESCRIPTION

The flow solver used in this study is a compressible LES code, called AVBP [17], developed at Cerfacs (Toulouse, France). This code is massively parallel thanks to a MPI library. This particular architecture leads to a strong flexibility of the code to compute big meshes on as many processors as needed. The code uses both structured and unstructured meshes.

SUBGRID-SCALE MODELS

The sub-grid scale model used in the present study is a specific one, developed at Cerfacs and called, WALE [14]. This sub-grid scale model is a zero-equation closure model. It is based on the Smagorinsky model but doesn’t dissipate small structures near wall.

NUMERICAL METHODS

In AVBP, the discretisation of the governing equations is based on a cell-vertex finite-volume method [2]. A Lax-Wendroff central space differencing is employed. This numerical scheme is commonly used in this study. Nevertheless, a third order scheme is also present in AVBP. TTGC is based on a Taylor-Galerkin Finite-Element approximation [12].

AVBP is fully explicite. For non-reacting flows, the time step is determined by the minimum of the convective time step. The convective time-step is determined by a Courant-Friedrichs-Lewy (CFL) number :

∆tmin < CFL ∆xmin

u + c (1)

Where, ∆xmin, the smallest cell of the domain, u, the local velocity magnitude, and c, the local sound celerity.

The temporal integration of the governing equations is handled by a multi-stage Runge-Kutta method.

BOUNDARY CONDITIONS

The compressible Navier-Stokes equations impose to use non- or few- reflecting formulation for the boundary conditions to let waves exit the computational domain. The NSCBC characteristic method is used to impose flow conditions on the in- and outflow boundaries [16].

INITIAL SOLUTIONS

For flow computation, an initial solution is required. In this study, the flow field is set to zero. The target mass flow rate is progressively increased with a small relaxation coefficient of the characteristic inlet boundary.

ON THE CONTRIBUTION OF LES TO ENGINE DEVELOPMENT

The primary interest of engine designers to LES calculation is to predict accurately characteristic numbers of IC engine geometries.

SWIRL NUMBER

The swirl number characterizes the flow rotation. It is calculated with [5]:

( )( )∫ ∫

∫ ∫×+

×+= R

R

drrduu

drdrwuuw

RS

0

2

0

22

0

2

0

2

'

''1π

π

θρρ

θρρ (2)

Where, R is the radius of the flow section where the swirl is calculated, ρ, the local density, u, the mean axial velocity, u’, the RMS axial velocity, w, the mean tangential velocity and w’, the RMS tangential velocity.

To compare quantitatively the LES velocity profiles with the LDA velocity profile, the formula (2) for the swirl number is adopted all along this study.

DISCHARGE COEFFICIENT:

To optimize the aerodynamism of a given IC engine configuration, engine designers often use the discharge coefficient. This coefficient is given by the formula (3) [10].

2/1)1(

0

/1

0

0

0 11

2−

−

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

γγ

γ

γγ

pp

pp

pTR

AQC T

T

g

R

mD (3)

Where, Qm is the mass flow rate, AR, a reference area, Rg, the perfect gas constant, T0, and P0, the temperature and the pressure in the upstream pipe, PT, the total pressure in the downstream section, and γ, the heat capacity ratio.

The characteristic numbers defined in this section are employed to compare LES results with the experimental results on both the Dellenback’s configuration and on the steady state flow bench.

AXISYMMETRIC SUDDEN EXPANSION

FLOW CONFIGURATION

Description

Fig. 1 shows the experimental configuration of Dellenback [3]. The radius expansion ratio is 2. The experimental measurements obtained by LDA provide the boundary conditions at the inlet.

Three cases are investigated:

1. No swirl initiated at the inlet, Sinlet=0.

2. A medium swirl initiated at the inlet, Sinlet=0.6.

3. A transient regime for which the inlet swirl decreases from 0.6 to 0.05.

Numerical aspects

Computational domain

The computations are performed on a full three-dimensional mesh, because LES in two dimensions cannot reproduce the right behavior of swirling flows as shown by Schlüter et al. [4][11]. The mesh is structured and is composed of 108000 cells.

Figure 1 – Perspective view of the three-dimensional structured mesh.

The computational domain starts two diameters upstream the expansion, where Dellenback made measurements. It ends fourteen diameters downstream the dump.

Numerical parameters

The experiments were performed with liquid water. In this study, the calculation is done with nitrogen. The mass flow rate is chosen to have the same Reynolds number as Dellenback’s experiments.

Diameter [m] D=0.0508 Upstream pipe Length 2D Diameter 4D Downstream pipe Length 14D

Table 1 – Geometrical parameters of the Dellenback’s configuration.

Fluid N2

Numerical scheme Lax-WendroffSubgrid-scale model WALEReynolds number 30000Mass flow rate, Q [kg.s ]m

-1 0.015U [m.s ]bulk

-1 6.3Outlet pressure [Pa] 101300

Table 2 –Parameters used for the LES computation of the Dellenback’s configuration.

WITHOUT SWIRL

First, the case without swirl initiated is studied. Before focusing on results, one can look at the non-reflecting characteristic boundary conditions. Both at the inlet and the outlet, respectively, the mass flow rate and the pressure reach their target value with less than 5 % error.

Figure 2 – Establishment of the target mass flow rate.

Figure 3 – Temporal recording of the instantaneous pressure at the outlet center point.

1D Radial Profiles

The radial profiles of the LES velocity are compared to the LDA velocity profiles at different positions along the configuration.

Figure 4 – Comparison of the radial profiles between the LES time-averaged axial velocity and the LDA mean axial velocity at different positions.

Figure 5 – Comparison of the radial profiles between the LES RMS axial velocity and the LDA axial velocity fluctuations at different positions.

The computation shows a good agreement between LDA and LES profiles for the axial velocity component. The progressive reattachment of the flow to the wall is correctly predicted. The axial velocity fluctuations are also well predicted. The shape of the LES fluctuations profiles is correct in regards to the LDA profiles. However, few differences are observed on their level. This can be explained by the coarse mesh used. On the outermost left axial velocity fluctuation profile (at the inlet), turbulence is not yet developed. But on the third profile, one diameter after the step, turbulence has already reached the right fluctuation level. On the outermost right axial velocity fluctuations, the good level of fluctuations is also predicted.

2D Fields

To illustrate qualitatively the 1D profiles, presented in Figure 4 and Figure 5, contours of the velocity components in the central plane are presented in this section. Although the configuration is geometrically axisymmetric, the instantaneous flow field obtained by LES is not axisymmetric.

Figure 6 –Contours of instantaneous axial velocity.

Figure 7 –Contours of instantaneous tangential velocity.

Mixture Phenomena

The sudden expansion creates a mixing layer between the fluid entering the configuration and the fluid in the test section. Without swirl, the coherent structures developed are well known but their destruction downstream the step is complex as shown by Figure 8.

Figure 8 – Iso-surface of Q-criteria colored by tangential velocity of an instantaneous snapshot of the flow field.

Figure 8 presents an iso-surface of Q-criteria [13], which allows to identify coherent structures.

WITH SWIRL

Swirl flows are widely used in industrial configurations. In diesel engines for instance, swirl controls the homogeneity of the mixture between fuel and air. The second test case corresponds to a swirling flow with Sinlet=0.6.

1D Radial Profiles

Again, the radial profiles of the LES velocity are compared to the LDA velocity profiles at different positions along the configuration.

Figure 9 – Comparison of radial profiles between the LES time-averaged axial velocity and the LDA mean axial velocity at different positions.

Figure 9 shows the radial profiles of the mean axial velocity at different positions along the configuration. The detachment at the step is correctly predicted by LES. The axial recirculation zone is also well predicted. However, the swirl breakdown obtained by LES is a little bit stronger than the one obtained by experimental measurements.

Figure 10 – Comparison of radial profiles between the LES time-averaged tangential velocity and the LDA mean tangential velocity at different positions.

On the radial profile of the mean tangential velocity, one can notice a good agreement for the outermost left and right profiles (Figure 10). But, at the step location, few differences are present between LES and LDA.

Figure 11 – Comparison of the radial profiles between the LES RMS axial velocity and the LDA axial velocity fluctuations at different positions.

Figure 12 – Comparison of the radial profiles between the LES RMS tangential velocity and the LDA tangential velocity fluctuations at different positions.

On the radial profiles of the velocity fluctuations, the two first profiles show again the necessity of turbulence to develop itself (Figure 11 and Figure 12). But, mostly, the level and the shape of the fluctuations are correctly predicted by LES, even near the step.

More quantitatively, the swirl number is calculated with the formula (2). Figure 13 presents the evolution along the configuration of the swirl number. The bar across the experimental data corresponds to a 20 % error margin. The LES captures the axial evolution of swirl correctly except at the end of the duct.

Figure 13 – Comparison of the axial profile between LDA and LES of the swirl number.

2D Fields

Figure 14 shows the axial velocity contours of a time-averaged snapshot. The strong axis recirculation zone is clearly delimited and well structured. However, Figure 15, representing the axial velocity contours of an instantaneous snapshot, shows the opposite. The swirl flow is deeply unsteadiness with a turbulent axial recirculation zone. The physic of the swirl breakdown is complex and asymmetric.

Figure 14 - Contours of a time-averaged axial velocity.

Figure 15 - Contours of an instantaneous axial velocity.

Mixture Phenomena

Figure 15 indicates the presence of an unstationnary structure. This turbulent structure is characteristic of a precessing phenomenon, called PVC (precessing vortex core). Figure 16 presents an iso-surface of pressure, allowing to visualize the precessing vortex core. In this particular configuration, the PVC is in a spiral mode [6][7].

Figure 16 – Iso-surface of pressure colored by tangential velocity of an instantaneous snapshot of the flow field.

The PVC characteristic frequency is equal to the one of the swirl, about 80 Hz. Swirl and PVC create strong and complex shear layers downstream of the step. Figure 17 presents an instantaneous iso-surface of Q-criteria [13]. The complex mixture layers network observed here is dramatically different from the one observed on Figure 8 for the case without swirl.

Figure 17 – Iso-surface of Q-criteria colored by tangential velocity of an instantaneous snapshot of the flow field.

TRANSIENT REGIME

The two cases (S=0 and S=0.6) previously described indicate the importance of swirl. They show that LES is able to predict accurately flows without and with swirl in a steady state. At this stage, LES is already an interesting alternative approach to RANS in the development of IC engines. Nevertheless, in real diesel engines, the swirl number of the flow is always varying during a cycle. The main part controlling the swirl number is the valve. An idea would be to use LES to predict the transient regimes of an IC engine, characterized by the valve lift. Although the Dellenback’s configuration is far from an IC engine geometry, a decrease of the swirl initiated at the inlet is realized to evaluate the ability of LES to predict transient regimes and the influence of swirl on the precessing phenomena. The results obtained are then compared qualitatively with the observations done by Dellenback.

Description of the transient regime

The initial converged state of the transient regime corresponds to the case treated with a medium swirl at the inlet of 0.6. Due to numerical costs, only three different levels of swirl are used to decrease the swirl at the inlet from 0.6 to 0.05 (Figure 18).

Figure 18 – Description of the transient regime.

For the first phase, the swirl number at the inlet is reduced of 0.2. At the beginning of all the following phases, the swirl number at the inlet is divided by two. The axial velocity is not modified, that’s why the mass flow rate is kept constant during the transient regime, as shown by Figure 19.

Figure 19 – Temporal recording of the mass flow rate during the transient regime.

Besides, the radial profile of the tangential velocity at the inlet is not changed during the transient regime. Only the maximum tangential velocity at the inlet is decreased, as shown by the formula (4) and (5). The formula (4) is obtained with the definition (2) of the swirl number.

S =umaxwmax

umax[ ]2 R×

fu(r) × fw (r)r2dr∫fu(r)[ ]2 rdr∫

(4)

Where, umax is the maximum axial velocity at inlet, wmax the maximum tangential velocity, R the radius of the upstream pipe, fu, the function, defining the axial velocity profile and fw, the function, defining the tangential velocity profile.

S1

S0

=wmax S1

wmax S0

(5)

Where, wmax S1 is the maximum tangential velocity

corresponding to the inlet swirl of S1 and wmax S0 is the

maximum tangential velocity corresponding to the inlet swirl of S0.

Each phase lasts 0.15 s, except for the final phase. The duration of each level has been determined in considering two criteria:

First, the time of each phase must be superior to the convective time of the configuration, τc, which is calculated by:

bulkc U

L=τ (6)

Where, L is the length of the configuration and Ubulk the ratio of the mass flow rate with the inlet area.

Thus, the whole flow pattern is affected by the modification of the swirl number. The convective time is equal to 0.11 s.

Second, the case with swirl points out the unsteadiness of the flow pattern near the step and especially the dynamic of the recirculation zone. This zone has a different characteristic convective time. The characteristic rotation time of swirl, τS is determined by:

τ S =2πRwmax

(7)

Where, R is the radius of the upstream pipe and wmax, the maximum tangential velocity.

For each phase, the rotation time of swirl τS is obviously different, as shown by Table 3. Table 3 sums up also the number of swirl cycles done during each phase with the phase duration of 0.15 s.

Swirl number at the inlet

τS [ms]

Number of swirl cycles

0.6 15 10 0.4 22.5 6.6 0.2 45 3.3 0.1 90 1.65

0.05 180 < 1 Table 3 – Characteristic rotation time of swirl and number of swirl cycles realized for each phase of the transient regime.

For the low swirl numbers, S=0.1 and S=0.05, the rotation time of swirl does not allow to reach a converged flow field. In order to overcome this difficulty, the last phase is extended to reach ten swirl cycles.

Temporal evolution at point B

To observe the influence of the decrease of the swirl number at the inlet, a temporal recording is realized at the step location on the axis. This probe is called point B. The temporal recording of the axial velocity at point B on Figure 20 shows that the axial recirculation zone disappears for a swirl number of 0.2 at time t=2.8 s. This indicates that different regimes of swirl breakdown exist. Moreover, the Figure 21 representing the tangential velocity at point B indicates that an unsteady structure is present on the center of the configuration. This unsteady structure is the PVC. One can notice that for medium swirl numbers (S=0.6 and S=0.4), the unsteadiness of the PVC is strong. Indeed, the peek of the tangential velocity reaches a magnitude of 8 m.s-1, which corresponds to the maximum axial velocity. Once the

swirl number is decreased to 0.2, the PVC seems to vanish. But, for low swirl numbers, it comes back.

Figure 20 – Temporal recording of the axial velocity during the transient regime at the point B.

Figure 21 – Temporal recording of the tangential velocity during the transient regime at the point B.

1D Axial Profile

The axial profiles of the mean axial velocity for each phase on Figure 22 confirm that different swirl regimes are present.

Figure 22 – Axial profile of mean axial velocity for each phase of the transient regime.

Rotation of PVC

Table 4 sums up the observations realized with the LES results and the ones obtained experimentally by Dellenback.

Transition threshold Experimentally Numerically

Precessing phenomena

S > 0.37 S > 0.4 Precession in same sense to swirl

0.18<S<0.37 0.2 < S < 0.4 No more precessing phenomena

0<S<0.18 0 < S < 0.2 Precession opposite to swirl

Table 4 – Comparison of the swirl influence on precessing phenomena between the observations realized on the results obtained experimentally and numerically.

Strouhal number of PVC

In doing a fast Fourier transform on the pressure at point B, the characteristic frequency of PVC is obtained. The corresponding Strouhal number is calculated by:

mQfRSt

38ρ= (8)

Where, ρ is the mean inlet density, f the frequency of the instantaneous velocity recoding, R the radius of the upstream pipe and, Q the mass flow rate. m

Figure 23 presents the influence of the swirl number at the inlet on the Strouhal number of the PVC at point B.

Figure 23 – Influence of the swirl number on the Strouhal number, characterizing the PVC at point B.

The numerical and experimental results are in good agreement. The impact of the swirl number on the Strouhal number is well predicted. When the swirl number at the inlet is decreased, the Strouhal number of the PVC decreases also. For the low swirl numbers, PVC turns in the opposite sense of the swirl.

STEADY STATE FLOW BENCH

FLOW CONFIGURATION

Description

The second configuration is a sudden expansion with a expansion ratio of 3.5 and a valve. The objective of this configuration is to evaluate the potentialities of LES to compute a geometry closer to an IC engine geometry than the Dellenback’s configuration. The additional difficulty in this kind of configuration is to correctly predict the strong pressure gradient due to the valve. The results obtained are compared to the experimental measurements. Besides, some velocity profiles are compared with RANS profiles [9].

Numerical aspects

Computational domain

The computations are performed on a full three-dimensional structured mesh. This mesh is composed of 400000 cells.

Figure 24 – Perspective view of the three-dimensional structured mesh of the steady state flow bench.

Figure 25 - Two-dimensional view of the three-dimensional structured mesh of the steady state flow bench.

The mesh of the cylinder contains an H-mesh on its center. The cell size is progressively increased toward the outermost left, inlet and the outermost right outlet. Near the valve seat, the mesh is refined.

Ld [mm] 300 Lu [mm] 104 Di [mm] 17 De [mm] 34 D [mm] 60 Valve lift [mm] 10 Inner seat diameter [mm] 40 Valve seat [mm] 4

Table 5 – Geometrical parameters of the steady state flow bench.

Numerical parameters

The experimental data begins 90 mm in the upstream pipe before the valve. As the computational domain

begins before, an inlet profile must be adopted. No swirl is initiated at the inlet. Thus a plate profile is imposed at the inlet. Again, as done for the Dellenback’s configuration, the mass flow rate is chosen to have the same Reynolds number as the experiments.

Parameters ValueFluid N2

Numerical scheme Lax-WendroffSubgrid-scale model WALEReynolds number 30000Mass flow rate, Q [kg s ]m

-1 0.055

U [m.s ]bulk-1 65

Outlet pressure [Pa] 101300Table 6 – Sum up of the parameters used for the LES computation of the steady state flow bench.

RESULTS

1D Radial Profiles

As for the Dellenback’s configuration, the LES radial profiles of the different velocities and fluctuations at different location along the steady state flow bench are compared to the LDA profiles.

Figure 26 - Radial profiles of the LES time-averaged axial velocity and the LDA mean axial velocity at different positions.

Figure 26 indicates a good agreement for the mean axial velocity profiles between LES and LDA. The last profile shows that the time used to average the LES flow field is not sufficient. The jet valve breakdown is correctly predicted by LES. Besides, the recirculation zone seems also to be correctly taken into account.

Figure 27 – Radial profiles of the LES time-averaged tangential velocity and LDA mean tangential velocity at different positions.

On the mean tangential velocity profiles, presented in Figure 27, the results are not as good as the one obtained for the mean axial velocity profiles. Indeed, although the experimental apparatus wasn’t built to impose a swirl, a small swirl appears in the experimental data. That can be observed on the two first radial profiles on Figure 27. This residual swirl affects the following profiles. Nevertheless, the shape of the profiles is mostly correct for the fourth and fifth radial profiles.

Figure 28 – Comparison of the radial profiles between the LES RMS axial velocity and the LDA axial velocity fluctuations at different positions.

Figure 29 – Comparison of the radial profiles between the LES RMS tangential velocity and the LDA tangential velocity fluctuations at different positions.

Figure 28 and Figure 29 show that there is a good agreement for the axial and tangential velocity fluctuations between LES and LDA. On the three last profiles, the right level and shape of the fluctuations is predicted by LES. One can notice that turbulence needs time to develop. This is why the two first profiles don’t have the right levels of turbulence.

Figure 30 – Comparison of the radial profiles between the LES mean axial velocity and the LDA mean axial velocity at Z=20 mm.

Figure 31 – Comparison of the radial profiles between the LES mean axial velocity and the LDA mean axial velocity at Z=70 mm.

Near the valve, in the region of strong velocity gradients, Figure 30 shows the capability of LES to compute unsteady flow. Indeed, there is a good agreement between LES and LDA. One can observe that the RANS approach equipped with a classic k-epsilon[9] is not able to reproduce such a flow. However, on Figure 31, RANS and LES agree with LDA on the mean axial velocity at Z=70 mm. The limited result obtained by LES can be explained by the insufficient time used to average the LES fields.

Figure 32 – Comparison of the radial profiles between the LES axial velocity fluctuations and the LDA axial velocity fluctuations at Z=20 mm.

Figure 33 – Comparison of the radial profiles between the LES axial velocity fluctuations and the LDA axial velocity fluctuations at Z=70 mm.

Again, at Z=20 mm, the LES approach gives better results than the RANS approach on the axial velocity fluctuations. But at Z=70 mm, RANS is better than LES. On the tangential velocity fluctuations, presented on figures 40 and 41, both LES and RANS give results close to the experimental measurements.

Figure 34 – Comparison of the radial profiles between the LES tangential velocity fluctuations and the LDA tangential velocity fluctuations at Z=20 mm.

Figure 35 – Comparison of the radial profiles between the LES tangential velocity fluctuations and the LDA tangential velocity fluctuations at Z=70 mm.

Figure 36 – Comparison of the axial profile of mean axial velocity between LDA, LES and RANS.

Figure 36 shows the difficulty to predict correctly the axial profile of the mean axial velocity. LES is closer to the experimental profile than RANS. For instance, the recirculation length is with LES, underestimated of 20 mm, whereas it is overestimated of 40 mm with RANS. Besides, the minimum of axial velocity is accurately predicted with LES, whereas RANS predicts it with 200 % of error.

Figure 37 – Comparison of the axial profile of pressure between LDA and LES.

The axial profile of static pressure obtained experimentally indicates the complexity of such a configuration. Nevertheless, LES predicts correctly the static pressure profile. The pressure loss is estimated within 10 %. The impact of the valve jet to the wall is correctly predicted. The reattachment of the flow to the wall is also well predicted. Two differences remain. Firstly, as at the inlet condition the mass flow rate is imposed, there is a difference between the experimental and numerical pressure. This difference is mainly due to the wall-treatment. Secondly, the minimum of pressure due to the valve is underestimated. In addition, the discharge coefficients, CD, obtained experimentally and numerically are calculated with the formula (3). The experimental discharge coefficient is equal to 0.279, whereas the numerical one is 0.260. In this case, LES is able to predict a discharge coefficient with an error of 6.6 %.

Analysis of the Valve Jet

The valve increases the velocity gradients. Figure 38 presents an iso-surface of Q-criteria. On this figure, a strong toroidal vortex is present in the head of the valve jet. One can also notice smaller vortices, which indicate the unsteadiness of the valve jet. Upstream of the valve, big coherent structures can be observed. They are probably created by the valve stream. These structures might have an influence on the valve jet dynamic.

Figure 38 – Snapshots Iso-surface of Q-criteria colored by tangential velocity of an instantaneous snapshot of the flow field.

LES METHODOLOGY

In this part, a parametric study is realized so as to obtain the optimized set of parameters to create a base for the future LES methodology to adopt when simulating IC engines.

DEFINITION OF THE CRITERIA

Reduced efficiency

To evaluate the numerical costs of the different numerical schemes and types of mesh tested, the reduced efficiency for the computation of each parameter is calculated with the formula (9):

RE =T × n

Niter × Nnode

(9)

Where T is the CPU time taken by the simulation, n the number of processors used, Niter the number of iteration computed, and Nnode the number of nodes of the mesh.

Averaged Swirl number

A global swirl number <S>, based on the swirl number S, obtained with the formula (2) is calculated:

S =1L

S(x)0

L∫ dx (10)

Where , L is the length of the computational domain and, S(x) the swirl number calculated by eq. (2) at a given abscise.

NUMERICAL SCHEME

The choice of the numerical scheme is one of the most important parameters to fix. Although the results obtained with Lax-Wendroff are close to the experimental results, the LES computation of a third order scheme, like TTGC, allows to take into account smaller turbulent structures. The flow field is more turbulent and unsteady. But such a numerical scheme costs two times more than Lax-Wendroff. Table 7 sums up the criteria used to compare the Lax-Wendroff scheme and the TTGC scheme.

Dellenback Cases CFD LDA Scheme LW TTGC X RE [µs] 26.2 58.2 X RETTGC / RELW 1 2.22 X

<S> 1.03 0.91 0.81

%∆(<S>LES-LDA) 27.1 12.3 0

Table 7 – Influence of numerical scheme.

Dellenback

With TTGC, the swirl number axial profile is closer to the experimental profile than with Lax-Wendroff, as shown by Figure 39. Figure 40 represents an iso-surface of Q-criteria. The coherent structures observed look continuous and more real than the coherent structures obtained with Lax-Wendroff on Figure 17.

Figure 39 – Comparison of the axial profiles of the swirl number obtained with LW or TTGC on a structured mesh.

Figure 40 - Iso-surface of Q-criteria of an instantaneous snapshot of the flow field. LES computation of the Dellenback’s configuration with TTGC.

MESH

The LES computation of complex IC geometries requires robust numerical methods and meshes with small stretching ratios. In complex geometries, one can prefer to create an unstructured mesh in order to better control the stretching ratio and the nodes distribution. Moreover, the unstructured meshes are faster to realize than structured meshes. But unstructured meshes are often more dissipative and less efficient than the structured meshes. The objectives of this part are to evaluate the advantages and the disadvantages of the structured and the unstructured meshes on the Dellenback’s configuration and on the steady state flow bench. Table 8 sums up the global parameters.

Cases Dellenback Steady state flow bench

Meshes Struct. Unstruct Struct. Unstruct. Nodes 108000 41000 413000 221000 RE [µs] 26.2 62.3 34.4 79.2 REUNSTRUCT / RESTRUCT

1 2.4 1 2.3

<S> 1.03 0.78 0.1 0.06

%∆(<S>LES-LDA) 27.1 3.7 71.4 82.9

Cd X X 0.26 0.262

%∆(CdLES-LDA) X X 6.6 6.1

Table 8 – Influence of the kind of mesh.

Dellenback

The results, presented on Figure 41, on the Dellenback’s configuration show that unstructured meshes can be as accurate as the structured meshes. On the visualization of the Q-criteria iso-surface on Figure 42, the coherent

structures revealed are more continuous than the ones obtained on a structured mesh (Figure 17).

Figure 41 - Comparison of the axial profiles of the swirl number obtained with structured or unstructured meshes with LW scheme.

Figure 42 - Iso-surface of Q-criteria of an instantaneous snapshot of the flow field. LES of the Dellenback’s configuration on an unstructured mesh with LW scheme.

Steady state flow bench

In a configuration like the steady state flow bench, the choice between a structured and an unstructured mesh is not obvious. For the prediction of the axial velocity profile, the structured mesh gives better results than the unstructured mesh on Figure 43 in comparison with the experimental measurements. The comparison of the swirl number profiles obtained with a structured or an

unstructured mesh is difficult due to the uncertainty on the experimental results, where a swirl is initiated at the inlet. Figure 44, presenting the pressure axial profile does not allow to conclude in favor of a structured mesh or an unstructured mesh. The pressure profile obtained on the unstructured mesh has the right shape downstream the valve. But upstream of the valve, the pressure at the inlet predicted by the LES on the unstructured mesh is too high of about 700 Pa. Besides, the unstructured mesh gives a little bit better prediction of the discharge coefficient of the steady state flow bench. Finally, the qualitative comparison provided by Figure 45 does not allow to conclude definitely which kind of mesh is more adapted to IC engine geometries. Nevertheless, in regards to the time gained to create an unstructured mesh instead of a structured one, the use of unstructured meshes seems to be easier than structured meshes for complex IC engines.

Figure 43 – Comparison of the axial profile of the averaged axial velocity obtained with structured or an unstructured mesh and with LW scheme.

Figure 44 - Comparison of the axial profile of the averaged static pressure obtained with a structured or an unstructured mesh with LW scheme.

Figure 45 - Iso-surface of Q-criteria of an instantaneous snapshot of the flow field with an unstructured mesh and with LW scheme.

CONCLUSION

In this paper, LES of two simple IC engine geometries have been realized. The problem of the numerical calculation of IC engines has been divided into smaller problems. Firstly, an axisymmetric sudden expansion has been simulated both without and with swirl. Quantitative comparisons have been made between the experimental and numerical velocity profiles. Good agreements are observed. The 2D fields obtained with

LES computation show the difficulty to reproduce such asymmetric, anisotropic and turbulent flows. The presence of an unsteady coherent structure has been observed on the centerline of the configuration. This unsteady and periodic structure is characteristic of the precessing phenomena. To simulate the impact of the valve lift on the swirl number of the flow entering the cylinder of an IC engine, a transient regime has been initiated at the inlet in decreasing the swirl number. Several swirl regimes have been observed and for each regime a specific precessing motion has been found out. The numerical observations have been compared to the results of Dellenback. Again, there are good agreements between numerical and experimental observations. In a second step, a steady state flow bench has been simulated. It consists of a sudden expansion with a valve. The LES velocity profiles obtained have been compared to the LDA velocity profiles showing a good adequation. The static pressure profile and the discharge coefficient have been also correctly predicted by the LES.

Finally, the influence of the numerical scheme and the influence of the kind of mesh have been achieved on the Dellenback’s configuration and on the steady state flow bench. TTGC, the third order scheme gives better results on the swirl number profiles than Lax-Wendroff. A comparison between the results obtained on a structured or an unstructured mesh has been achieved. It does not allow to conclude clearly on which kind of mesh is more appropriate to handle LES computation of IC engine geometries. However, the shorter time of meshing and the better mesh refinement control of unstructured meshes make them more adapted.

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DEFINITIONS, ACRONYMS, ABBREVIATIONS

Abbr. Unit Definition AR m2 Inner seat diameter <S> 0 Averaged swirl number CD 0 Discharge coefficient D mm Diameter of the upstream pipe ∆P Pa Pressure loss hmin mm Minimum cell to cell distance L m Configuration length p0 Pa Upstream stagnation pressure pT Pa Total pressure Q-crit. 0 Identification of coherent

structures Qm kg.s-1 Mass flow rate R m Radius of the configuration Rg Pa.kg-1

.m-3.K-1Perfect gas constant

Re 0 Reynolds number RE s.node-1.

iteration-1. processor

Reduced efficiency

S 0 Swirl number S* 0 Swirl number St 0 Strouhal number T0 K Upstream stagnation

temperature u m.s-1 Mean axial velocity umax m.s-1 Max. axial velocity at the inlet Ubulk m.s-1 Rating velocity Uc m.s-1 Centerline axial velocity w m.s-1 Mean tangential velocity wmax m.s-1 Max. tangential velocity at the

inlet y+ 0 Adimensional wall coordinate γ 0 Heat capacity ratio ρ kg.m-3 Density ξ 0 Pressure loss coefficient τc s Convective time τS s Rotation time of swirl