This dissertation concerns the analysis and modeling of turbulence dynamics in turbulent combustion. In certain regimes of turbulent combustion, dilatation (volumetric expansion) induced by chemical heat release can result in significant modification of turbulence dynamics, leading to the failure of most common turbulence models used in predictive simulations. In this dissertation, the physical mechanisms of interaction between chemical heat release and turbulence are analyzed, scaling theories for the regime dependence of these effects are confirmed, and new turbulence models are introduced to account for these interactions.

Numerical simulation forms the foundation of the analyses in this dissertation. Using a common planar jet configuration, a range of turbulent combustion regimes is accessed via Direct Numerical Simulation (DNS). In order to conduct these simulations accurately and efficiently on large-scale parallel computers, advanced numerical algorithms are introduced. These schemes improve the accuracy of state-of-the-art schemes and reduce the computational cost by approximately a factor of two.

In nonpremixed combustion, heat release effects on turbulence are observed at low turbulent Reynolds number (the ratio of inertial forces to viscous forces), but the impact on turbulence model validity is minimal due to the greatly reduced turbulence intensity. In premixed combustion, scaling theories for the dependence of dilatation effects on Karlovitz number (the ratio of the flame time scale to the Kolmogorov time scale) are confirmed for the first time in turbulent shear flows.

Algebraic combinations of limit-state turbulence models are proposed to account for counter-gradient transport in low Karlovitz number premixed combustion. A variable "efficiency function" controls the regime dependence of counter-gradient effects, and these models are verified a priori using the DNS databases. The algebraic approach successfully captures counter-gradient transport in the flame-normal direction, but the linear nature of these models precludes them from capturing other effects of heat release including effects of instantaneous flame motion. Finally, a new statistical description of turbulence is introduced by conditioning on an independent flame coordinate. Turbulence statistics obtained in this framework explicitly account for effects of flame motion and chemical heat release. Budgets of conditional mean velocity and turbulent kinetic energy are computed, and modeling implications are discussed.