The Conditional Moment Closure is a combustion model that predicts the transport of reactive scalars in conserved scalar space. In the formulation of CMC, an assumption had to be made. This was that a process in scalar space is obeys the rules of a Markov process. This assumption was termed the Markov hypothesis.
While there have been numerous tests of CMC to date (Klimenko and Bilger 1999, Kim et al 2000), there has yet to be a direct test of the Markov hypothesis. This thesis was written in conjuction with a PhD study by Andrew Wandel in an attempt to validate the Markov hypothesis using Direct Numerical Simulation. The code simulated a cube of homogenous turbulence of side length 2p . This cube was divided into a grid of N sides (where N is an power of 2). A number of simulations were run using f orced turbulence on a grid of 643 to support Wandel’s simulations of decaying turbulence on a 643 field. Then forced simulations were run on a 1283 grid. This provides better resolution and allows for simulations of turbulence of a higher Reynolds number, but at the cost of processing power and time.
Analysis of the particle field for the forced 643 simulation has shown that th e scalar velocity, while not identical to a Markov process, approaches it very closely. The physical velocities on the other hand, show a great deal less resemblance. The data generated for the 1283 simulations was found to be not properly resolved. However, the trend of the data still supports the hypothesis in that the scalar velocity decorrelates faster then the physical.
The fact that the data obtained validates the only assumption made in the formulation of CMC means that CMC is also valid and may be confidently used as a turbulent combustion model.