Theoretical and Numerical Investigations of Scalar Fields in Isotropic Turbulence.
Abstract
The behavior of turbulent scalar fields is investigated both theoretically and numerically. The first class of problem concerns the joint probability density function(pdf) of a scalar and its gradient in isotropic turbulence. A relation is derived between this pdf and the pdf of a scalar and its xderivative. Qualitative analysis suggests that the xderivative is distributed normally if the scalar is nonreacting. Thus, the pdf of the xderivative of the scalar conditioned on the scalar value is expanded according to a GramCharlier expansion in the hope that this pdf can be approximated well by the first few terms of the expansion. The direct numerical simulation(DNS) technique is employed to calculate the expansion coefficients of scalar fields advected by isotropic stationary turbulence. The results suggest that the higher order coefficients are indeed very small and the interdependence between a scalar and its gradient is weak for nonreacting scalars. The pseudospectral method is discussed and the DNS code is modified to accommodate reacting scalars. It is shown that the introduction of chemical source terms under moderate reaction rates does not impose further restriction on numerical stability. Other aspects of the numerical method, such as the generation of the initial scalar fields, are also discussed. Results for single scalar and two scalar simple reactions are presented. Finally, a parallel/consecutive reaction scheme is simulated and the numerical data is used to test a closure model.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT........25G
 Keywords:

 Engineering: Mechanical; Physics: Fluid and Plasma;
 Computerized Simulation;
 Field Theory (Physics);
 Isotropic Turbulence;
 Scalars;
 Numerical Analysis;
 Probability Density Functions;
 Series Expansion;
 Fluid Mechanics and Heat Transfer