Abstract: Accurate predictions of turbulent mixing phenomena induced by interfacial instabilities such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) hold significant scientific and engineering importance. In engineering practice, utilizing Reynolds-averaged Navier-Stokes (RANS) model, which is mainly consisted of physical model and model coefficients, to simulate the aforementioned problems is currently and foreseeably the mainstream approach. However, the coupling of multiple complexities in actual engineering problems poses a great challenge for RANS models to uniformly predict different mixing problems. To address that, based on engineering application viewpoint, this study firstly proposes an asymptotic-ideal unified RANS prediction idea and a new method for determining turbulence mixing model coefficients. Then these concepts are applied to the three mainstream RANS mixing models in mixing field. Finally, this study systematically verifies the ability of the model in predicting different mixing problems with the same set of model and coefficients. Here, the investigated problems include both the basic problems, i.e. classical RT, RM, and KH mixing, and complex problems, i.e. re-shocked RM mixing, RT mixing with initial tilted interface and spherical implosion mixing. The temporal evolutions of mixing width agree well with the existing experiments or high-fidelity numerical simulations. This study systematically verifies the applicability and robustness of the asymptotic-ideal unified RANS predictions idea and methodology for determining model coefficients in turbulent mixing field. This work lays a solid foundation for the engineering application of RANS turbulence mixing models, and its core idea is expected to be applied to turbulence models in other fields.