Capturing transition and non-transition flows with a new shear stress transport model

A new Shear Stress Transport(SST)k-ω model is devised to integrate salient features of both the non-transitional SST k-ω model and correlation-based γ-Re_(θ) transition model.An exceptionally simplified approach is applied to extend the New SST(NSST)model capabilities toward transition/non-transition predictions.Bradshaw’s stress-intensity factor R_(b)=|-uv|/k can be parameterized with the wall-distance dependent Reynolds number Re_(y)=√ky/v;however,as the Re_(y)is replaced by a“flow-structure-adaptive”parameter R_(μ)=v_(T)/v,the resulting R_(b)is capable of capturing various transition phenomena naturally.The prospective stress-intensity parameter R_(b)=R_(b)(Re_(y),R_(μ))is incorporated in the constitutive relations for eddy-viscosity v_(T) and production term P_(k).The proposed formulation is intrinsically plausible,having a dramatic impact on the prediction of bypass,separation-induced and natural transitions together with non-transitional flows.An extra viscous-production term P_(k)^(lim) is added with the k-equation to ensure proper generation of k at the viscous sublayer when computing separation-induced transition over a Low-Reynolds Number(LRN)airfoil.Results demonstrate that the NSST k-ω model maintains an excellent consistency with both SST k-ω and γ-Re_(θ) models.

Regularities of formation of ternary alloy phases between non-transition metals

Using a four-parameter model based on extended Miedema’ s cellular model of alloy phases and pattern recognition methods, the regularities of formation of ternary intermetallic compounds between non-transition metals have been investigated. The criterion of formation can be expressed as some empirical functions of Φ (electronegativity), nws1/3( valence electron density in Wagn-er-Seitz cell), R (Pauling’s metallic radius) and Z (number of valence electrons in atom).

Regularities of formation of binary intermetallic compounds between transition and non-transition elements

A four-parameter model based on the extended Miedema’s cellular model of alloy phases and pattern recognition methods has been used to study the regularities of the formation of binary intermetallic compounds between tran-sition element and non-transition element. The formation criterion can be expressed as some inequities of electronega-tivity , the valence electron density in Wagner-Seitz cell nws1/3, Pauling’s metallic radius R and the number of valence electrons in atom Z or their functions. According to these empirical criterions, the 'unknown' binary alloy system can be predicted, the predicted result is better than that of Miedema’s two-parameter model.

Playing Rock, Paper, Scissors in Non-Transitive Statistical Thermodynamics

Does non-transitivity in information theory have an analog in thermodynamics? A non-transitive game, “Swap”, is used as a toy thermodynamic model to explore concepts such as temperature, heat flow, equilibrium and entropy. These concepts, found to be inadequate for non-transitive thermodynamic, need to be generalized. Two kinds of temperatures, statistical and kinetic, are distinguished. Statistical temperature is a parameter in statistical distributions. Kinetic temperature is proportional to the expected kinetic energy based on its distribution. Identical for Maxwell-Boltzmann statistics, these temperatures differ in non-Maxwellian statistics when a force is present. Fourier’s law of conduction and entropy should be expressed using statistical temperature, not kinetic temperature. Kinetic temperature is always scalar but statistical temperature and statistical entropy in non-transitive systems have circulation, thereby allowing continuous and circular heat flow. Entropy is relative to underlying statistics, in analogy to the Kullback-Leibler divergence in information theory. The H-theorem, limited by assumptions of homogeneity and indistinguishability, only covers statistically homogeneous systems. The theorem does not cover non-transitive, statistically heterogeneous systems combining different distributions such as Maxwell-Boltzmann, biased half-Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. The second law can be preserved if generalized by expressing it in terms of statistical temperature and statistical entropy.