  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.
