Physics-based flame models capable of predicting small-scale fire behaviors reduce computational power needed for predicting fires of large- and giga-scale. However, classical model correlations are often developed for 'free fires' without considering vegetation around. These models may result in inaccurate fire modeling due to wrong 'prior' flame shape estimated from theta similar to wind speed. To overcome this defect, three-dimensional small-scale fires with fireline intensity of 100 KW/m are numerically simulated using large eddy simulation. Fire behaviors such as flame tilt angle and heat transfer mechanisms are extensively studied using a newly proposed configuration space {N-C, CdLAI}. The former one represents the ratio between fire to wind power, and the latter one considering the vegetation effect is for the first time introduced in flame models. Using the configuration space, two model correlations for flame tilt angle and radiative heat power reaching the unburnt fuels are proposed. The flame tilt angle theta is directly related to CdLAI (C-d alpha(s)sigma H-s(F)/2), while inversely related to N-C (2gI/ rho 0C(p,0)T(0)U(0)(3)), in contrast to the model proposed for radiative heat power. Comparisons with several classical models evidenced the capability of new flame models in predicting both free and non-free fires. The limits of the validity of the newly proposed models are also discussed.