Unsteady Three-dimensional Rotational Flamelet

A new unsteady flamelet model is developed to be used for sub-grid modeling and coupling with the resolved flow description for turbulent combustion. Difficulties with prior unsteady flamelet models are identified. The model extends the quasi-steady rotational flamelet model which differs from prior models in several critical ways. (i) The effects of shear strain and vorticity are determined, in addition to normal-strain-rate impacts. (ii) The strain rates and vorticity are determined from the conditions of the environment surrounding the flamelet without a contrived progress variable. (iii) The flamelet model is physically three-dimensional but reduced to a one-dimensional, unsteady formulation using similarity. (iv) Variable density is fully addressed in the flamelet model. (v) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. For both quasi-steady and unsteady cases, vorticity creates a centrifugal force on the flamelet counterflow that modifies the transport rates and burning rate. In the unsteady scenario, new unsteady boundary conditions must be formulated to be consistent with the unsteady equations for the rotating counterflow. Eight boundary values on inflowing scalar and velocity properties and vorticity will satisfy four specific relations and therefore cannot all be arbitrarily specified. The temporal variation of vorticity is connected to the variation of applied normal strain rate through the conservation principle for angular momentum. Limitations on the model concerning fluctuation of the inter-facial plane are identified and conditions under which inter-facial plane fluctuation is negligible are explained. An example of a rotating flamelet counterflow with oscillatory behavior is examined with linearization of the fluctuating variables.