Janusz Badur

Finite rotations in the description of continuum deformation

Abstract Finite rotations in continuum mechanics are described by means of either a proper orthogonal tensor or finite rotation vectors. Some algebraic relations concerning the finite rotations are reviewed. Formulae expressing them in terms of displacements are given. Along each of the curvilinear coordinate lines the finite rotations are shown to satisfy some systems of the linear first-order differential equations. Each system of the equations is presented in four different but equivalent forms associated with an intermediate stretched basis or with an intermediate rotated basis. Integrability conditions of the system of equations provide various alternative forms of compatibility conditions in continuum mechanics. The displacement field is expressed through the stretch and rotation fields in the form of three successive line integrals. The formula describes the displacements to within a constant finite translation and a constant finite rotation. The procedure proposed here generalizes the formula derived by Cesaro (1906) within the classical linear theory of elasticity.

Exergy Losses in the Szewalski Binary Vapor Cycle

In this publication, we present an energy and exergy analysis of the Szewalski binary vapor cycle based on a model of a supercritical steam power plant. We used energy analysis to conduct a preliminary optimization of the cycle. Exergy loss analysis was employed to perform a comparison of heat-transfer processes, which are essential for hierarchical cycles. The Szewalski binary vapor cycle consists of a steam cycle bottomed with an organic Rankine cycle installation. This coupling has a negative influence on the thermal efficiency of the cycle. However, the primary aim of this modification is to reduce the size of the power unit by decreasing the low-pressure steam turbine cylinder and the steam condenser. The reduction of the “cold end” of the turbine is desirable from economic and technical standpoints. We present the Szewalski binary vapor cycle in addition to a mathematical model of the chosen power plant’s thermodynamic cycle. We elaborate on the procedure of the Szewalski cycle design and its optimization in order to attain an optimal size reduction of the power unit and limit exergy loss.

Influence of strength differential effect on material effort of a turbine guide vane based on thermoelastoplastic analysis

ABSTRACT The strength differential (SD) effect has been observed in many iron-based metals such as 4310, 4330, maraging steel, and HY80 steels as well as titanium, aluminium 2024-T351, magnesium, and nickel-based super alloys such as aged Inconel 718. Moreover, the SD effect increases with temperature. The Huber–Mises–Hencky (HMH) J2 yield condition is insufficient to simulate the response of metals that exhibit the SD effect. Our work demonstrates the importance of taking into account the SD effect during strength analysis of turbine components. Two yield conditions are considered: the HMH condition and the SD-dependent Burzynski condition. The equivalent stresses produced by these conditions in the elastic state are compared. Plastic zone areas and effective strain values predicted by the two conditions are compared. Our investigation was performed based on thermal-fluid-structure interaction (FSI) analysis of a turbine guide vane made of a nickel-based super alloy that exhibits the SD effect. Conjugate heat transfer analysis was performed, and then elastoplastic stress analysis was performed with boundary conditions obtained from the computational fluid dynamics (CFD) analysis. The paraboloid Burzynski yield condition was implemented in an FE code. Implementation was based on the Euler backward method with consistency tangent moduli evaluated in the explicit form.

The effort of the steam turbine caused by a flood wave load

Development of the Thermal-FSI (Fluid Solid Interaction) let to accurate the process of cooling the steam turbine set. It provide to shorter times of maintenance and repairs of the turbine sets. The cooling of the steam turbine which temperature exceeds 500°C can take time of one week. Insulation and housing is taken off when temperature reaches 100°C. In analysis was applied thermal-FSI which takes into account temperature changes between solid material and fluid. In the paper authors propose this way to estimate effort of the turbine structure caused by an intrusion of water into the flow channels.

Quasi-Abelian gauge theory of axisymmetric deformation of shells of revolution

Abstract We call attention to the possibility of constructing the gauge field theory for the classical continuum mechanics. As an example, we show that the Reissners equations of axisymmetric deformation of shells of revolution have the geometric structure of pure (2 + time)-dimensional gauge continuum with Abelian T(2) ▶ SO(2) symmetry group. An essential element of this paper is the identification of several basic objects of gauge theory, such as the pure gauge potential, the strength field tensor and the Yang-Mills equations with basic elements of the Reissners shell equations.

A theoretical, numerical and experimental verification of the Reynolds thermal transpiration law

Purpose The purpose of this paper is the theoretical presentation of tensorial formulation with surface mobility forces and numerical verification of Reynolds thermal transpiration law in a contemporary experiment with nanoflow. Design/methodology/approach The velocity profiles in a single microchannel are calculated by solving the momentum equations and using thermal transpiration force as the boundary conditions. The mass flow rate and pressure of unstationary thermal transpiration modeling of the benchmark experiment has been achieved by the implementation of the thermal transpiration mobility force closure for the thermal momentum accommodation coefficient. Findings An original and easy-to-implement method has been developed to numerically prove that at the final equilibrium, i.e. zero-flow state, there is a connection between the Poiseuille flow in the center of channel and counter thermal transpiration flow on the surface. The numerical implementation of the Reynolds model of thermal transpiration has been performed, and its usefulness for the description of the benchmark experiment has been verified. Research limitations/implications The simplified procedure requires the measurement or assumption of the helium-glass slip length. Practical implications The procedure can be very useful in the design of micro-electro-mechanical systems and nano-electro-mechanical systems, especially for accommodation pumping. Originality/value The paper discussed possible constitutive equations in the transpiration shell-like layer. The new approach can be helpful for modeling phenomena occurring at a fluid–solid phase interface at the micro- and nanoscales.

Pure gauge theory of the cosserat surface

Abstract Within the framework of classical gauge field theory we present the Cosserat model of a surface described by two-dimensional gauge continuum with T(3) > SO(3) symmetry group. The essential result of this paper is the identification of several basic objects of gauge theory, such as the pure gauge potential, the strength field tensor and the Yang-Mills equations with the basic objects of the Cosserat surface theory. This allows to derive several new results both within the Cosserat surface theory and the gauge field theory itself.

Generalized Helmholtz theorem for multi-forms

Abstract The classical theory of Helmholtz is extended to the case of one- and two-forms in the space of two, three and four dimensions. We show that the Helmholtz decomposition into the scalar, vector and tensor potential is invariant with respect to a transformation which is a generalization of the classical Abelian gauge transformation. Applications of the theorem to the ideal compressible fluids, classical electrodynamics and continuum dislocation theory indicate that there exists a possibility of participation of the constitutive equations in the decomposition of multi-forms.

Numerical analysis of the oscillation frequency of the shock wave and the evaporation level on the Mach disc in the IMP PAN nozzle

In the present paper, we have focused on the phenomena occurring in the supersonic part of the de Laval nozzle, characterised by oscillation of the shock wave in steam flow. The effect of shock oscillation was observed by using the Topler optical system in the IMP PAN experiment carried out on a symmetrical planar de Laval nozzle. Having observed the shock fluctuation in wet steam flow, according to Puzyrewskis observations, we analysed the oscillation frequency in the IMP PAN nozzle depending on the pressure conditions. Additionally, we analysed the evaporation level of condensate droplets during passage through the Mach disc depending on the inlet conditions. The model of a single continuum wet steam model with a special microstructure growing up during phase transitions was validated on an experiment carried out by Dykas et al. in 2013 on the half arc nozzle. The present work includes simulations results of oscillation frequency of the shock wave and the evaporation level of the liquid phase on the Mach disc.

Analiza termodynamiczna i techniczna zeroemisyjnejelektrowni dla pomorza

Abstract This paper presents the results of a thermodynamic analysis and a method of selecting individual devices and their components to design a zero-emission power plant project in Pomerania. Another aim of the paper is to present the technological abilities of the application of gas-steam turbines with a particular emphasis on enhanced energy conversion in the construction of a wet combustion chamber using cooling water transpiration and a gas-steam expander.