  A new rotational flamelet model with inward swirling flow through a stretched
vortex tube is developed for sub-grid modeling to be coupled with the resolved
flow for turbulent combustion. The model has critical new features compared to
existing models. (i) Non-premixed flames, premixed flames, or multi-branched
flame structures are determined rather than prescribed. (ii) The effects of
vorticity and the related centifugal acceleration are determined. (iii) The
strain rates and vorticity applied at the sub-grid level can be directly
determined from the resolved-scale strain rates and vorticity without a
contrived progress variable. (iv) The flamelet model is three-dimensional. (v)
The effect of variable density is addressed. (vi) The inward swirl is created
by vorticity combined with two compressive normal strain components; this
feature distinguishes the model from counterflow flamelet models. Solutions to
the multicomponent Navier-Stokes equations governing the flamelet model are
obtained. By coordinate transformation, a similar solution is found for the
model, through a system of ordinary differential equations. Vorticity creates a
centrifugal force on the sub-grid counterflow that modifies the molecular
transport rates, burning rates, and flammability limits. Sample computations of
the inward swirling rotational flamelet model without coupling to the resolved
flow are presented to demonstrate the importance of the new features. Premixed,
nonpremixed, and multi-branched flame structures are examined. Parameter
surveys are made with rate of normal strain, vorticity, Damk\"{o}hler number,
and Prandtl number. The centrifugal effect has interesting consequences when
combined with the variable-density field. Flow direction can reverse; burning
rates can be modified; flammability limits can be extended.
