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A physical-mathematical model of a plane supersonic boundary layer of a vibrationally excited dissociating gas in the Prandtl approximation is presented. The simplest case of a diatomic gas parameterized according to the data for nitrogen is considered. A number of simplified formulas for calculating the transport coefficients and the dissociation and recombination rates for a molecular-atomic mixture, which are admissible for typical conditions of supersonic and hypersonic boundary layers, are substantiated. Comparative calculations of numerical and locally self-similar solutions of the boundary layer equations on a flat plate for typical conditions of a high-enthalpy wind tunnel and hypersonic flight in the upper atmosphere are performed. It is shown that the atomic concentration profiles calculated on the basis of these approaches differ significantly. In this regard, in order to adequately take into account the effect of chemical reactions in the boundary layer stability calculations, it is necessary to use the profiles of hydrodynamic parameters calculated numerically on the basis of full boundary layer equations. Locally self-similar solutions can serve as initial conditions for numerical calculations. [ABSTRACT FROM AUTHOR]

Fatigue crack growth is simulated for an elastic solid with a cyclic cohesive zone model (CZM). Material degradation and thus separation follows from the current damage state, which represents the amount of maximum transferable traction across the cohesive zone. The traction-separation relation proposed in the cyclic CZM includes non-linear paths for both un- and reloading. This allows a smooth transition from reversible to damaged state. The exponential traction-separation envelope is controlled by two shape parameters. Moreover, a lower bound for damage evolution is introduced by a local damage dependent endurance limit, which enters the damage evolution equation. The cyclic CZM is applied to mode I fatigue crack growth under $$K_{\mathrm{I}}$$ -controlled external loading conditions. The influences of the model parameters with respect to static failure load $$K_{\mathrm{0}}$$ , threshold load $$\varDelta K_{\mathrm{th}}$$ and Paris parameters $$m, C$$ are investigated. The study reveals that the proposed endurance limit formulation is well suited to control the ratio $$\varDelta K_{\mathrm{th}}/K_{\mathrm{0}}$$ independent of $$m$$ and $$C$$ . An identification procedure is suggested to identify the cohesive parameters with the help of Wöhler diagrams and fatigue crack growth rate curves. [ABSTRACT FROM AUTHOR]

In this paper, a model of heat exchange and resistance in the channels with cylindrical grooves on the walls is presented. We compare the calculated data with the experimental results and give some recommendations for designers of power plants. [ABSTRACT FROM AUTHOR]

A quasi three–dimensional, intermediate planetary boundary layer (PBL) model is developed by including inertial acceleration with the Ekman momentum approximation, but a nonlinear eddy viscosity based on Blackadar’s scheme was included to improve the theoretical model proposed by Tan and Wu (1993). The model could keep the same complexity as the classical Ekman model in numerical, but extends the conventional Ekman model to include the horizontal accelerated flow with the Ekman momentum approximation. A comparison between this modified Ekman model and other simplified accelerating PBL models is made. Results show that the Ekman model overestimates (underestimates) the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow due to the neglect of the acceleration flow, however, the semi–geostrophic Ekman model overestimates the acceleration effects resulting from the underestimating (overestimating) of the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow. The Ekman momentum approximation boundary layer model could be applied to the baroclinic atmosphere. The baroclinic Ekman momentum approximation boundary layer solution has both features of classical baroclinic Ekman layer and the Ekman momentum approximate boundary lager. [ABSTRACT FROM AUTHOR]

Similar solutions for the boundary layer equations of a second-order fluid flow over a stretching sheet are presented to obtain the coefficients of skin-friction and heat transfer. [ABSTRACT FROM AUTHOR]