Compression of vortex in cavity

Underlying Flow Regime 4-13 © copyright ERCOFTAC 2004

Test Case

Brief description of the study test case

IMFT experiment is composed of a square compression chamber with large windows for optical access. For a detailed presentation, see Marc D. et al., 1997; Marc D., 1998; Maurel S., 2001. A square piston is animated with a sinusoidal motion. Gases flow in and out the chamber through a plane channel that can be closed in phase with piston motion cycles. These devices allow the rig to simulate a cycle with four strokes (cycle with intake, compression, expansion and exhaust). The flow from the inlet channel enters the chamber tangentially to the lower of its face. Such a geometrical configuration creates a large-scale vortex called tumble during the inlet stroke. This experiment is representative of automotive cases in terms of tumble behaviour, volumetric ratio and tumbling number.

Figure 1 The compression chamber

3.1. Compression Chamber

The compression chamber available at IMFT has a square cylinder (100 x 100 mm2) equipped with a flat head. The distance between the piston and cylinder head at the end of the intake stroke is h=100mm. The present data have been obtained with a volumetric ratio of r=4 corresponding to a stroke of the piston of 75 mm. The optical access and PIV laser sheet orientation are sketched in Figure 1. The lateral sides are made of Pyrex and are fully transparent. Two narrow windows have been added in the symmetry plane of the upper and lower walls. The laser sheet is thus carefully aligned with the symmetry plane. Note that PIV data obtained in the transverse plane have been presented and analyzed elsewhere (Borée J. et al., 1999).

The piston is driven at 206 rpm by an alternative machine tool and the maximum piston velocity reaches one meter per second. A magnetic ruler fixed on the machine tool accurately measures the location of the piston within the chamber. It is therefore possible to perform statistical PIV and LDV (Laser Doppler Velocimetry) measurements at a given position of the piston in the "intake-compression" strokes.

The intake system is a portion of a flat channel (length: Le = 300 mm); the ratio width/height is equal to 9.6 (he x le = 10 x 96 mm), which is sufficient to ensure the bi-dimensionality of the flow over a large part — 80% — of the intake channel. A plenum (280x280x280 mm³) is located upstream of the channel in order to prepare seeding for optical measurements. A "guillotine device" the motion of which is directly controlled by the machine tool closes the intake port. During the intake stroke, the Reynolds number based on the hydraulic diameter reaches high values with a maximum Remax ≈ 12000. The channel flow is therefore turbulent. The ratio length/height (Le/he =30) ensures that turbulence in the near wall region only is fully established (Comte-Bellot G., 1965) when the flow reaches the compression chamber.

During the intake stroke, the bi-dimensional intake jet flow, tangential to the cylinder floor, is deflected by the moving piston and generates the tumbling vortex. Two situations are documented in the present database:

For the first one, referred as "compressed", a four-stroke cycle has been defined. The channel is closed by a guillotine device (see part 2) during the compression/expansion strokes. The turbulence generated during the compression stroke therefore decays during the expansion stroke. The guillotine opens during the exhaust and intake strokes.

For the second one, referred as "uncompressed", the channel remains open all the time. This situation is less complex to compute than the compressed situation. It is also a good test case to check the accuracy of the code in computing the inlet stroke and the generation of the large-scale tumble. Moreover, the behaviour of the vortex during exhaust is particularly interesting.

It is necessary to achieve a precise knowledge of the boundary conditions including geometrical and kinematical description - cycle resolved pressure and piston wall temperature measurements in the compressed case. These data are included under the directory "Boundary conditions" and are provided separately for compressed and uncompressed cases. Concerning temperature, a K-type thermocouple is located within the piston 5mm from the inner surface. The piston material is aluminium, whose conductivity is high and the piston wall is a large exchange surface during the compression. A moderate increase () of the temperature signal is typically measured during the acquisition of a set of 120 velocity fields. This acquisition lasts approximately 90 seconds. The maximum pressure measured during the compression at r=4 is . A very careful adjustment of the guillotine system and of the piston rings was necessary to minimize leakage during the compression (Maurel S., 2001). Three Teflon "rings" enable the piston to be motored without any lubrication between the piston and the walls. Each "ring" is made of four L-shape pieces that overlap along the straight portion. The mass leakage during the compression can be estimated from pressure and temperature measurements associated to thermodynamic analysis. It is approximately 10% of the initial mass. As the flow through small apertures is choked, it is very easy to figure out that the main factor responsible for this low performance is the rotation rate of the machine, which leaves plenty of time for leakage to take place. At a rotation rate of 2000 rpm, the expected mass loss would be approximately 1% but such a rotation rate cannot be achieved with the present set-up.

3.2. KinematicAL description

Piston motion

The machine tool used to create piston motion is originally a filling machine. This kind of tooling needs a relatively slow cutting velocity, the original electrical engine was changed by a faster one to obtain a 206-rpm rotation rate. A higher rotation rate would be destructive for the machine. Nevertheless, chamber geometrical characteristics insure that tumbling motion is similar to common research engine in terms of compression ratio and tumbling ratio.

The piston motion is quasi-sinusoidal.

A precise description of "Boundary conditions" is given in excel data files for each test. It is necessary to select the appropriate boundary conditions when dealing with compressed or uncompressed situations (see database).

Guillotine motion (Compressed case only)

The detailed figure of the guillotine device (Figure 2) shows that inlet channel enters the chamber at 4mm from the lower wall. Furthermore, we notice that this device insures there is no obstacle to the intake or exhaust air stream. This is surely an advantage of this experiment for computation because tumbling motion can be simulated without the perturbing contribution of classical valve stems.

Figure 2 Guillotine motion

Figure 3 Guillotine lift

3.3. Particle Image Velocimetry

This set-up is adapted for Particle Image Velocimetry measurements. Velocity fields discussed in the present paper were acquired in the symmetry plane. The beam of a double-pulsed Yag Laser (Spectra physics PIV 400) is focused through several optical components to produce a double light sheet in this symmetry plane. The thickness of the light sheet at the beam waist is of the order of 500 µm. A Sensicam (12 bits, cooled) CCD sensor 1280*1024 pixels with full double frame is used to collect images of 3 µm oil droplets tracers that seed the tumble flow. The experimental set-up was carefully optimized.

The synchronization of laser shots, camera acquisition and experiment is processed via several PC cards and specially developed software. The phase difference between two images is clearly limited by the repetition rate (f=10Hz) of the laser. Only one velocity field can therefore be obtained per engine cycle. Pictures of tracer fields are analysed using PIV algorithms on 32*32 pixels² cells at intervals of 16 pixels (i.e. with a 50% overlap). If all the CCD is imaged, the size range of a PIV field is therefore "40*32" independent cells, which is still limited. A PIV algorithm using iterative cell shifting and deformation was developed, validated and applied by Maurel S., 2001. has shown that both bias and random errors are significantly reduced when a sub-pixel cell shift is performed in order to obtain a zero displacement from the correlation peak when the process converges. Systematic tests on synthetic images show that the absolute displacement error is pixels (Maurel S., 2001). On real images, a widely accepted estimation of the absolute displacement error using these algorithms is pixels (Foucaut J.M et al., 2001).

On most of the sets, the time interval separating the two laser shots was optimised to reduce out of cell and out of plane errors while keeping the dynamic range for velocity measurements as large as possible. While out of cell error seems the major constraint during intake when the jet velocity is high, the constraint associated with out of plane error is believed to dominate during compression when high turbulence levels are reached. Different thresholds based on predetermined signal to noise ratio, velocity vector amplitude and median filtering are systematically applied during post-processing of each PIV vector field. The number of "bad" vectors is always very low. They are discarded and no interpolation is used to make-up for incomplete data.

PIV is very well adapted to study the evolution of the large-scale structure presented here. However, this technique clearly suffers from a limited resolution of the spatial and velocity scales in a turbulent flow. This resolution can be obtained from the present data (see part 4 at the end of the document). PIV provides an estimation of the most probable instantaneous velocity in the interrogation window. If the local pdf (probability density function) of displacement is approximately symmetrical, this corresponds to the local velocity averaged over a volume that could be compared with filtered fields computed by LES. We therefore implicitly refer to a filtered velocity field.

In all the PIV fields, the origin (x,y)=(0,0) is chosen along the lower wall and the flat cylinder head. The (x,y) position of each arrow (in meter) indicates the real location in the symmetry plane. The piston is located on the right hand side of the figures. and are respectively the horizontal and vertical velocity components. Data acquisition in these alternative machines is time consuming. The sets acquired are composed of 120 double-pictures at a given phase during the intake stroke.

Test Case Experiments

Figure 4 shows the development of the averaged mean velocity field during the intake stroke, with the piston at 30, 60, 90 and 100 mm. At the beginning of the introduction phase, the generation of the vortex core by spiral roll-up of the upper boundary layer is particularly clear, Figure 2a. At the end of the intake phase a clear large-scale vortex is generated. The Reynolds number based on the maximum velocity, U_max~ 5m/s, and vortex radius, R ~ 5cm, is approximately Re=R.U_max/ ν = 16000. The core of the vortex is non-centred and its location is cycle dependent (Marc, 1998). The phase-averaged location of the center of the tumbling motion at BDC differs from the geometric center of the chamber with (x c/l , y c/l) = (0.5, 0.33).

The front views in Figure 4 show that the instantaneous structure is quasi-bidimensional. The phase averaged front mean velocity field not shown here is indeed bidimensional. The secondary flows induced along the fixed lateral end walls by the rotation of the main flow (Ekman flows) have been evaluated (Marc D., 1998) and were expected to be weak.

As the compression progresses, cf Figure 5, the tumbling motion is known to experience a transition from an organized 2D structure to a fully 3D flow when the piston reaches the Top Dead Centre (TDC). The vortex is more and more confined and the mean streamlines near the vortex core become elliptical (Borée, 2002). This process is very hard to analyse from local measurements in which cyclic variations can hide the true mechanisms.




Figure (4) - Development of the phase averaged mean velocity field during the inlet stroke. '(a), ';(b),; (c),; (d),;(e),.




Figure (5) - Evolution of the phase averaged mean velocity fields during the compression and early expansion. (a), ; (b),; (c),; (d),; (e),; (f), (expansion)

CFD Methods

The compressed vortex in cavity gives rise to interesting but challenging CFD application. This is due to the widely varying time and length scale that must be resolved for accurate prediction of the flow in real combustion chamber. Another factor increasing the complexity of the numerical calculations is the presence of moving boundaries.

Most of multidimensional modelling of a compressed vortex in cavity reported in open literature are performed using semi-empirical equation systems (e.g. the k-ε model or one of its variants) to close the Reynolds Averaged Navier-Stokes (RANS) equations (Hill P.G. and Zhang D., 1994). This model has been successfully tested in a wide variety of steady state flows occurring in technical applications, but it suffers from several deficiencies in the modelling of transient vortical flows where the equilibrium turbulence hypothesis is not satisfied any more. In their study McLandress et al. 1996 used two turbulence models: standard k-ε and the RNG modified k-ε to calculate the flow through the port and cylinder of an engine without a piston. The large scale flow features in the simulations agreed moderately with the ensemble averaged PIV results. There were no recirculations zones present in the PIV results.

The IMFT square piston model was the basis of numerical parametric developments, (Horrock G.D et al, 2000). Validation of the numerical model against experimental results shows that the k-ε turbulence model fails to predict the break up of the tumble vortex into smaller vortices during the compression stroke, which is a major fundamental flow feature in the compression stroke.

Both the k-ε and the Reynolds Stress Model (RSM) predicted the bulk flow field accurately during the intake stroke. However, both models inaccurately predicted some velocity and turbulence histories at various points in the flow, also reported in Lebrère L. et al, 1996. When velocity and turbulence at a number of points of the domain were compared to the experimental results there were some discrepancies with the Reynolds Stress Model, but overall the Reynolds Stress Model formulation proved superior to the k-ε model.

RSM schemes do not employ the eddy viscosity concept but solve the transport equations for the individual Reynolds stresses. Therefore, they are supposed to be better adapted to simulate complex strain fields as well as transport and history effects and anisotropy of turbulence. They automatically account for the effects of streamline curvature and rotation. It is well accepted that Reynolds stress models have a greater potential to represent turbulent flow phenomena more correctly than the two-equation models, their success so far has been moderate.

In-cylinder turbulence includes motion at length scale as small as 10^-5 m. This is a factor of 10000 smaller than the largest flow scales, which are the size of the cylinder bore. It is impossible to fully resolve over such a wide range. For this reason, the effect of the small-scale on the large flow average is modelled through modifications to the governing equations.

Employing the Large Eddy Simulation (LES) technique is a way to eliminate many of the shortcomings and assumptions made in RANS simulations. The LES technique can capture the most important large-scale fluctuations in the flow quantities, leaving only the relatively small scales to be modelled empirically. As the grid is made finer, LES leads to a better resolution of turbulence scales and the modelling assumptions at the sub-grid scale level become less important. The small-scale structures of turbulence are believed to be more isotropic hence the usual eddy-viscosity type models may work well as sub-grid scale (SGS) models.

Although significant advances were made with LES in other fields, its application in internal combustion engine cylinder flows is still at its primary stage because of complications introduced by compressibility, complex and moving boundaries.

According to Celik I.et al, 2000, the first potential application of LES to internal combustion engine flow was performed by Naitoh K. et al.1992, with a relatively coarse grid, and first order Euler time marching scheme. Another study using a finite volume CFD code (Verzicco R., 2000) reported very encouraging results in predicting the ensemble-averaged trends for an experimental axisymmetric one-valve engine cylinder under motored conditions at 200 rpm.

Developments by Smirnov et al 1999 demonstrate LES capabilities to model realistic IC engine geometries and flow types. The early numerical developments concerned the unsteady chaotic turbulence processes that occur during the intake stroke of a typical IC engine using the KIVA-3V code. The simulations were performed using 440,000 grid nodes including portions of the intake and exhaust ducts where relatively large grid size was used. In the cylinder region the average grid size was about one millimetre. The time scheme was first order for the convective terms.

An order of magnitude analysis of the normalized truncation error showed that with a time step of 1.0e-07 seconds the dominant error will be due to spatial discretisation.

As for the numerical scheme applied to convective terms, it was possible to capture sufficient details of turbulent fluctuations (i.e. larger eddies) either by using the quasi second order upwind scheme with no sub-grid scale turbulence model, or using CD (central differencing) with a standard Smagorinsky model.

It was reported that the vortical flow during the compression phase gave more difficulties, which could be explained by the version of sub-grid scale (SGS) model, which was empirical. The ability of the model to predict the generation and decay of turbulence during compression, is not known yet.

Further numerical developments concerned both intake and compression strokes. The predicted decay of turbulent fluctuations in the end of intake and the beginning of compression stroke was in agreement with the experimental observation. The computed turbulence spectrum captures the main characteristics of the experimental spectra, which gives promise for LES of in-cylinder flows. With 1 mm mesh size and time step of 10e-8 -10e-5 s it is possible to capture about 70% of the turbulent kinetic energy spectrum. This figure should improve with a higher grid resolution.

Contributors: Afif Ahmed - RENAULT