Analysis of Mean Orientation Vector and Mean Curvature in Statistically Steady Turbulent Premixed Combustion

Formal governing equations are derived for the mean orientation vector, 〈n〉_f, and the mean curvature, 〈∇ · n〉_f, in turbulent premixed combustion. Balance is checked to evaluate all component terms and to understand their physical implications in DNS of two test flames. The terms involving ∇_T(v_n + S_d) and n″(v_n + S_d)″ are dominant to determine 〈n〉_f through a flame brush and at the leading edge. All listed terms are relevant to determine 〈∇·n〉_f, while those involving $∇T2νn+SdΣ′f$ and (∇·n)″ (v_n + S_d)″ become important at the edges. Different trends are observed on the dominant terms for thicker flamelets with the Karlovitz number greater than unity. Further investigation may be required to clarify relative importance of the component terms in different regimes of realistic flame conditions.