Probability density function approach for multidimensional turbulentflow calculations with application to in-cylinder flows in reciprocating engines

The probability density function (pdf) method is extended to two- and three-dimensional transient turbulent flows. The numerical approach couples a Lagrangian Monte Carlo method to solve for the joint pdf of velocity and scalar compositions with an Eulerian finite-volume algorithm to calculate mean pressure and a turbulence time scale. A general approach applicable to variable-density chemically reacting flows has been taken; the present results are for nearly uniform density inert flows. Three engine-like configurations have been investigated: 1) a noncompressing axisymmetric cylinder-piston assembly with a central port; 2) a noncompressing axisymmetric cylinder-piston assembly with an annular port; and 3) a compressing three-dimensional configuration with an off-center valve. Pdf results are compared with measurements and with conventional k-ϵ calculations for the two axisymmetric geometries. For these noncompressing flows the pdf approach is found to have little advantage over a k-ϵ model. Mean velocity profiles from both models are in good agreement with experiment for the central port case, whereas agreement for the annular port is less satisfying. Root-mean-square axial velocities from both models are low at early times in the intake process, but improve later in the cycle. Influence of numerical parameters on solution accuracy is assessed. The present work confirms the feasibility of the pdf approach for complex turbulent flows and represents an intermediate step in the application of pdf methods to multidimensional turbulent reacting flows, where they are expected to offer their greatest advantage.