Above: Spatial distribution of sub-grid segregation of chemical species for the test reaction. This information is critical for the accurate prediction of the test reaction yield.

Below: DQMoM-IEM yields versus test case data. Tsai and Fox (1994) - doi:10.1016/0009-2509(94)00270-3, Li and Toor (1986) - doi:10.1002/aic.690320809.

CFD methods typically solve for average quantities, for example species concentration and temperature. Turbulent reacting flow models must approximate the rates of species formation and energy release based on these average quantities. This is often a poor approximation.

Existing models used for CFD calculations of turbulent reacting flow are normally make strong assumptions about the chemistry or the flow. For example, that the chemistry is very fast and the reaction is controlled by the rate of turbulent mixing. and the flow. This type of assumption is not suitable for many important slower reactions, such as those responsible for describing the formation of NOx and soot in a diesel engine.


The most general approach to turbulent reaction models are probability density function methods. These make no assumptions about either the chemistry or the flow and are widely used by the combustion research community. However, existing solution methods are computationally expensive and are not amenable to conventional CFD. The challenge was to combine the benefits of the probability density function approach with standard CFD methods. The objective was to develop a fast and generally applicable method that could be used as an add-on to off-the-shelf CFD codes to enable complex turbulent reaction chemistry to be combined with the 3D modelling capability of the CFD.


Efficient and robust algorithms were developed for two recent probability density function methods. The implementation enables the model to be used as an add-on with conventional CFD codes.

The capabilities of the model were assessed against a known test case.



The SF method uses an efficient Monte Carlo solver. It is suitable for chemistry of arbitrary complexity. Users may refine the level of Monte Carlo approximation to move between quick 'back of the envelope' calculations and more expensive highly detailed calculations.


The DQMoM-IEM method replaces the SF Monte Carlo solver with a deterministic method. Users may refine the level of approximation as required without incurring any statistical error. This provides the option of very fast calculations with results that are far batter than just 'back of the envelope'. See the figures to the left.