Background

Flows in internal combustion engine cylinders are almost always turbulent. Moreover, it is generally believed that, the more turbulent the air motion, the greater the degree of mixing of air and fuel that can be achieved prior to ignition. It is also thought that high turbulence levels at the instant of ignition lead to higher flame speeds and more rapid and complete combustion, which is also highly desirable for engine designers. On the other hand, higher turbulence levels tend to correspond to greater rates of heat transfer to cylinder walls, which reduces thermal efficiency. For these reasons, studies which improve understanding and accuracy of predictions of turbulent velocity fields in IC engine cylinders are very useful.

 FLOW FIELD ANIMATION

There are several experimental techniques which may be used to measure velocity vectors at either single points or over planes or volumes in research engine cylinders, such as laser doppler velocimetry (LDV), particle image velocimetry (PIV) and molecular tagging velocimetry (MTV). Each measures total velocity vectors at known crank-angle positions. A principal difficulty in analyzing turbulent flowfields in engines is deciding how to divide each vector into its turbulent and non-turbulent parts. In statistically stationary flows, the non-turbulent part would be the mean velocity. However, in engine flows, which are not stationary in any sense, and are thought to have appreciable cycle-to-cycle variations, an unambiguous way of decomposing velocity vectors into turbulent and non-turbulent parts does not exist. This problem is particularly vexing because the kinds of computational fluid mechanics codes normally used to predict such flowfields incorporate turbulence models for second moments of turbulent quantities and are developed using stationary-flow measurements as target data. Thus, we would like to find a way to relate predicted second moments, such as <u‘u‘>, <v‘v‘>, <w‘w‘>, <u‘w‘>, and turbulent kinetic energy or dissipation rate, to values of those same quantities inferred from measurements. If we had a reliable way of extracting the turbulent velocity component from experimental measurements of instantaneous vectors of total velocity, comparisons between computational predictions and experiments could be made. Predictive techniques could then be refined, their accuracy in engine flows could be assessed, and they might then be used with confidence to predict how inflow conditions and geometric effects could be used to produce optimal in-cylinder turbulence levels.

Some Decomposition Techniques

The simplest decomposition technique is the phase or ensemble averaging technique. The key assumption of this technique is that the non-turbulent part of the flowfield is identical at each position in the cylinder, at the same crank-angle degree in each engine cycle. Since every combustion event is noticeably different in gasoline fueled SI engines, this assumption is not realistic in firing engines. It effectively counts all cycle-to-cycle variation as if it were turbulence.  Turbulence models in computational fluid dynmaics (CFD) codes do not. Its validity in motored research engines is a matter of continuing debate.

Other techniques involve varying degrees of sophistication but always include some kind of ‘ad hoc’ assumption about what is turbulent and what is not. One approach involves filtering time series of velocity measurements (ref.1). These techniques are usually accompanied by an assumption of a critical frequency, above all motion is turbulent and below all is cyclic variation. Some difficulties with this approach lie in how an unambiguous choice of frequency is to be made, whether it should vary with crank angle, and whether the amount of wrongly apportioned low-frequency turbulence (which always exists) and high-frequency cyclic variation is significant. The same general concerns can be raised about wavelet-based techniques or Karhunen-Loeve decompositions, which require similar assumptions to be applied before they can be used to partition velocity vectors into turbulent and non-turbulent contributions.

Recently, Professor Brereton and Kodal (ref.2) have illustrated some qualities of data-adaptive turbulence filters which recognize the turbulent component of the flow as that portion with the spectral shape similar to that expected in stationary turbulent flows. The remainder of the flow is then the non-turbulent part. This approach uses the expected spectral shape of non-stationary turbulence as its ‘ad hoc’ decomposition assumption and filters accordingly. The mean and any cyclic variation is then the non-turbulent part. Although computationally intensive, it appears to give reasonable decompositions for a range of time and space series measured in nonstationary turbulent flows.

Application of the Stochastic Decomposition to In-Cylinder Velocity Fields

Professor Brereton and Andrew Sasak have recently applied the stochastic decomposition outlined above to velocity fields measured by MTV at 65 degrees BTDC in each of 150 consecutive cycles in a motored AVL Corp. research engine, fitted with a quartz cylinder and the piston crown, cylinder head, intake/exhaust manifolds, and valve gear of a 5.5 liter V-8 engine, with four valves per cylinder and a pent-roof combustion chamber. The engine was motored at 600 rpm. Further details of the measurements and apparatus are given (ref.9). Animations of planes of velocity vectors at 65 degrees BTDC in each sequential cycle are shown in the companion animation. In each figure of the animation a reference vector 2.8 m/sec in the ‘South-East’ direction is included for scaling purposes. The x and y axes describe the relative locations of the measured velocity vectors in the engine cylinder in meters. Below the figures the turbulent cross-correlation coefficients, turbulent intensities, and turbulent intensity-to-cyclic variation intensities are displayed both for the momentary realization and as a running average.

The momentary value of the total velocity measured in each realization is shown in the lower right corner. This velocity field is decomposed into the sum of the turbulent and non-turbulent, or organized, velocity fields, shown in the upper left and upper right corners respectively. The part of the organized velocity field which varies from cycle to cycle is shown in the lower left corner – it is the difference between the momentary organized velocity field and the average of the velocity field over all realizations.

• The total velocity field moves predominantly in the upward direction, driven by the upward piston motion at this crank angle.

• The cycle-to-cycle variation is highly organized, insofar as the entire vector field sweeps in a single direction, which changes from realization to realization.

• The turbulent component varies erratically from one coordinate to another, in any given realization.

• Statistics of the fluid motion reveal a cross-correlation coefficient between u’ and v’ of about –0.05. This value is of the same order as found in motored-engine experiments. The lack of any significant cross correlation can be contrasted with the negative values (about -0.3) found in turbulent wall-bounded flows (against which most turbulence models are calibrated).

• The turbulent intensities are about 3-5% which is similar to turbulent flows away from walls.

• The ratio of intensities of turbulent motion to cycle-to-cycle variation is about 0.5. Consequently for this case, one might expect turbulence levels deduced from ensemble averaged decomposition to be roughly 2 to 3 times larger than those inferred using this technique, or predicted using Reynolds-averaged K-e or Reynolds-stress closures.

Further tests of this decomposition using stationary and weakly non-stationary data series, for which the turbulent component can be identified unambiguously, are planned and should be carried out shortly.

REFERENCES