The first-moment equations for premixed flames in two turbulent counterflowing streams are established. The turbulent kinetic energy just external to the flame k-infinity and the mean rate of strain a are the two parameters characterizing the fluid mechanical properties of these flows and are used to nondimensionalize all variables. In the present work, molecular transport is neglected and turbulent transport is represented by a gradient model with two descriptions of the turbulent exchange coefficient; the simpler of the two algebraically connects a turbulence Reynolds number to the mean density and the second is based on the k-approximately - epsilon-approximately theory. The chemical behavior is treated in terms of a recently developed model for the mean rate of creation of product, which leads naturally to a Damkohler parameter D(T) involving the mean rate of creation of product at each flamelet crossing, taken here to be constant across the flame, the mean rate of strain parameter, and a characteristic time for flamelet crossings, also taken here to be constant. Applications of the theory with the algebraic exchange coefficient are made to two cases: a single reactant stream flowing counter to a product stream with the same enthalpy and two identical counterflowing reactant streams. The k-approximately - epsilon-approximately theory is applied only to the latter case, the two stream situation of greatest current interest because of the relative simplicity with which it can be studied in the laboratory. In all flows we identify one or two reaction zones within which significant creation of product occurs. When reactant and product streams are opposed, there is a single reaction zone which assumes positions further into the product stream as the mean rate of strain increases. For cases involving two reactant steams and low rates of mean strain there are two distinct reaction zones that assume positions closer to one another as the mean rate of strain increases until they merge at the plane of symmetry. Extinction in the two cases is found to involve significantly different characteristics. In flows with two reactant streams extinction corresponds to the absence of product so that the flow reduces to the case of two isothermal counterflowing turbulent streams. The theory of this case leads to an explicit and simple prediction of the extinction Damkohler number D(Te), a prediction that can be used in connection with experimental data on extinction to assess the validity of the chemical model. When reactant and product streams are opposed, there is no abrupt manifestation of extinction.
